# Results from PAMELA, ATIC and FERMI : Pulsars or Dark Matter ?

Debtosh Chowdhury<EMAIL_ADDRESS>Centre for High Energy Physics,
Indian Institute of Science, Bangalore, India  Chanda J. Jog
<EMAIL_ADDRESS>Department of Physics, Indian Institute of
Science, Bangalore, India  Sudhir K. Vempati<EMAIL_ADDRESS>Centre
for High Energy Physics, Indian Institute of Science, Bangalore, India

###### Abstract

It is well known that the dark matter dominates the dynamics of galaxies and
clusters of galaxies. Its constituents remain a mystery despite an assiduous
search for them over the past three decades. Recent results from the
satellite-based PAMELA experiment detect an excess in the positron fraction at
energies between $10-100$ GeV in the secondary cosmic ray spectrum. Other
experiments namely ATIC, HESS and FERMI show an excess in the total electron
($e^{+}$\+ $e^{-}$) spectrum for energies greater 100 GeV. These excesses in
the positron fraction as well as the electron spectrum could arise in local
astrophysical processes like pulsars, or can be attributed to the annihilation
of the dark matter particles. The second possibility gives clues to the
possible candidates for the dark matter in galaxies and other astrophysical
systems. In this article, we give a report of these exciting developments.

##  I Introduction

The evidence for the existence of dark matter in various astrophysical systems
has been gathering over the past three decades. It is now well-recognized that
the presence of dark matter is required in order to explain the observations
of galaxies and other astrophysical systems on larger scales. The clearest
support for the existence of dark matter comes from the now well-known
observation of nearly flat rotation curves or constant rotation velocity in
the outer parts of galaxies rubin ; Sofue:2000jx . Surprisingly the rotation
velocity is observed to remain nearly constant till the last point at which it
can be measured111In the absence of dark matter, one would expect that the
curves to fall off as we move towards the outer parts of the galaxy.. The
simple principle of rotational equilibrium then tells one that the amount of
dark to visible mass must increase at larger radii. Thus the existence of the
dark matter is deduced from its dynamical effect on the visible matter, namely
the stars and the interstellar gas in galaxies.

The presence of dark matter in the elliptical galaxies is more problematic to
ascertain since these do not contain much interstellar hydrogen gas which
could be used as a tracer of their dynamics, and also because these galaxies
are not rotationally supported. These galaxies are instead supported by
pressure or random motion of stars (see Binney Binney:1987  for details of
physical properties of the spiral and elliptical galaxies). As a result, the
total mass cannot be deduced using the rotation curve for elliptical galaxies.
Instead, here the motions of planetary nebulae which arise from old, evolved
stars, as well as lensing, have been used to trace the dark matter dekel05 .
The fraction of dark matter at four effective radii is still uncertain with
values ranging from 20% to 60% given in the literature, for the extensively
studied elliptical galaxy NGC 3379 mamon .

Historically the first evidence for the unseen or dark matter was found in
clusters of galaxies. Assuming the cluster to be in a virial equilibrium, the
total or the virial mass can be deduced from the observed kinematics. Zwicky
zwicky  noted that there is a discrepancy of a factor of $\sim$ 10 between the
observed mass in clusters of galaxies and the virial mass deduced from the
kinematics. In other words, the random motions are too large for the cluster
to be bound and a substantial amount of dark matter ($\sim$ 10 times the
visible matter in galaxies) is needed for the clusters of galaxies to remain
bound. This discrepancy remained a puzzle for over four decades, and was only
realized to be a part of the general trend after the galactic-scale dark
matter was discovered in the late 1970’s.

On the much larger cosmological scale, there has been some evidence for non-
baryonic dark matter from theoretical estimates of primordial elements during
Big Bang Nucleosynthesis and measurements of them, particularly, primordial
deuterium. Accurate measurements of the Cosmic Microwave Background Radiation
(CMBR) could as well give information about the total dark matter relic
density of the Universe. The satellite based COBE experiment was one of the
first experiments to provide accurate “ mapping” of the CMBRcobe . The recent
high precision determination of the cosmological parameters using Type I
supernova data sndata  as well as precise measurements of the cosmic
background radiation by the WMAP collaboration wmap ; kom08  has pinpointed
the total relic dark matter density in the early universe with an accuracy of
a few percent. Accordingly, dark matter forms almost 26% of all the matter
density of the universe, with visible matter about 4% and the dark energy
roughly about 70% of the total energy density. This goes under the name of
$\Lambda$CDM model with $\Lambda$ standing for dark energy and denoted by the
Einstein’s constant, and CDM standing for Cold Dark Matter cosmoreviews .

Numerical simulations for the currently popular scenario of galaxy formation,
based on the ${\Lambda}$CDM model, predicts a universal profile for the dark
matter in halos of spherical galaxies NFW97 . While this model was initially
successful, over the years many discrepancies between the predictions from it
and the observations have been pointed out. The strongest one has been the
‘cusp-core’ issue of the central mass distribution. While Navarro et al. NFW97
predict a cuspy222Sharp increase in the density at the centre. central mass
distribution, the observations of rotation curves of central regions of
galaxies, especially the low surface brightness galaxies, when modeled show a
flat or cored density distribution BMBR01 .

A significantly different alternative to the dark matter, which can be used to
explain the rotation curves of the galaxies and clusters was proposed early on
by Milgrom. He claimed that Milgrom:1983ca  for low accelerations, Newtonian
law has to be modified by addition of a small repulsive term. This idea is
known as ‘MOND’ or the MOdified Newtonian Dynamics. While initially this idea
was not taken seriously by the majority of astrophysics community, it has
gained more acceptance in the recent years. For example some of the standard
features seen in galaxies such as the frequency of bars can be better
explained under the MOND paradigm, see Tiret et al. Tiret:2007dd . For a
summary of the predictions and comparisons of these two alternatives (dark
matter and MOND), see Combes et al. Combes:2009ab .

So far the most direct empirical proof for the existence of dark matter, and
hence the evidence against MOND, comes from the study of the so-called Bullet
clusterClowe:2006eq . This is a pair of galaxies undergoing a supersonic
collision at a redshift of $\sim 0.3$. The main visible baryonic component in
clusters is hot, X-ray emitting gas. In a supersonic collision, this hot gas
would collide and be left at the center of mass of the colliding system while
the stars will just pass through since they occupy a small volume333This is
exactly analogous to the reason why the atomic hydrogen gas from two colliding
galaxies is left at the center of mass while the stars and the molecular gas
pass through each other unaffected, as proposed and studied by Valluri et
al.jog:1990  to explain the observed HI deficiency but normal molecular gas
content of galaxies in clusters..

In the Bullet cluster, the gravitational potential as traced by the weak-
lensing shows peaks that are separated from the central region traced by the
hot gas. In MOND, these two would be expected to coincide444The relativistic
MOND theory Bek1  proposed by Bekenstein could be used to explain the Bullet
Cluster Bek2 ., since the gravitational potential would trace the dominant
visible component namely the hot gas, while if there is dark matter it would
be expected to peak at the location of the stellar component in the galaxies.
The latter case is what has been observed as can been seen in Fig.1 of
Clowe:2006eq . For the rest of the article, we will not consider the MOND
explanation, but instead take the view point that the flat rotation curves of
galaxies and clusters at large radii as an evidence for the existence of dark
matter. Furthermore, we believe that the dark matter explanation is much
simpler and more natural compared to the MOND explanation.

Despite the fact that the existence of dark matter has been postulated for
over three decades, there is still no consensus of what its constituents are.
This has been summarized well in many review articles. Refs trimble87 ; AKS09
are couple of examples that span from the early to recent times on this topic.
Over the years, both astrophysicists as well as particle physicists have
speculated on the nature of dark matter.

The baryonic dark matter in the form of low-mass stars, binary stars, or
Jupiter-like massive planets were ruled out early on (see trimble87  for a
summary). From the amount of dark matter required to explain the flat rotation
curves, it can be shown that the number densities required of these possible
constituents would be large, and hence it would be hard to hide these massive
objects. Because, if present in these forms, they should have been detected
either from their absorption or from their emission signals. It has also been
proposed that the galactic dark matter could be in the form of dense, cold
molecular clumps PCM94 , though this has not yet been detected. This
alternative cannot be expected to explain the dark matter necessary to “fit”
the observations of clusters, or indeed the elliptical galaxies since the
latter have very little interstellar gas.

There is also a more interesting possibility of the dark matter being
essentially of baryonic nature, but due to the dynamics of the QCD phase
transition in the early universe which left behind a form of cold quark-gluon-
plasma, the baryon number content of the dark matter is hidden from us. This
idea was first proposed by Witten in 1984 witten , who called these quantities
as quark nuggets. An upper limit on the total number of baryons in a quark
nugget is determined by the baryon to photon ratio in the early universe (See
for example raha1 ). Taking in to consideration these constraints, it is
possible to fit the observed relic density with a mass (density) distribution
of the quark nuggets raha2 . For the observational possibilities of such quark
nuggets, see for example, Ref.nuggetstudy .

From a more fundamental point of view, it is not clear what kind of elementary
particle could form dark matter. The standard model of particle physics
describes all matter to be made up of quarks and leptons of which neutrinos
are the only ones which can play the role of dark matter as they are
electrically neutral. However with the present indications from various
neutrino oscillation experiments putting the standard model neutrino masses in
the range $\lesssim 1$ eV valleneutrinoreview  they will not form significant
amount of dark matter. There could however, be non-standard sterile neutrinos
with masses of the order of keV-MeV which could form warm555Depending on the
mass of the particle which sets its thermal and relativistic properties, dark
matter can be classified as  hot, warm and cold Peacock:1999ye .dark matter
(for reviews, see Refs. strumiavissani ; julien1 ). Cold Dark Matter (CDM), on
the other hand, is favored over the warm dark matter by the hierarchical
clustering observed in numerical simulations for large scale structure
formation, see for example Ref.Peacock:1999ye . Recent analysis including
X-ray flux observations from Coma Cluster and Andromeda galaxy have shown that
the room for sterile neutrino warm dark matter is highly constrained julien2 .
However, if one does not insist that the total relic dark matter density is
due to sterile neutrinos then, it is still possible that they form a sub-
dominant warm component of the total dark matter silk2  relic density666On the
other hand, if the neutrinos are not thermally produced and their production
is suppressed like in models with low reheating temperature gelmini1 , it is
possible to weaken the cosmological bounds, especially from extra galactic
radiation and distortion of CMBR spectra gelmini2 . See also julupdate ..

The Standard Model thus, needs to be extended to incorporate a dark matter
candidate. The simplest extensions would be to just include a new particle
which is a singlet under the SM gauge group (i.e., does not carry the Standard
Model interactions). Further, we might have to impose an additional symmetry
under which the Dark Matter particle transforms non-trivially to keep it
stable or at least sufficiently long lived with a life time typically larger
than the age of the universe. Some of the simplest models would just involve
adding additional light ($\sim$ GeV) scalar particles to the SM and with an
additional $U(1)$ symmetry (see for example, Boehm et al. fayet1 ). Similar
extensions of SM can be constructed with fermions too fayet2 ; wells . An
interesting aspect of these set of models is that they can be tested at
existing $e^{+}e^{-}$ colliders like for the example, the one at present at
Frascati, Italy dreeschoudhury . A heavier set of dark matter candidates can
be achived by extending the Higgs sector by adding additional Higgs scalar
doublets. These go by the name of inert Higgs models Barbieri:2005kf ;
marajaji . In this extension, there is a additional neutral higgs boson which
does not have SM gauge interactions (hence inert), which can be a dark matter
candidate. With the inclusion of this extra inert higgs doublet, the SM
particle spectrum has some added features, like it can evade the “naturalness
problem” up to 1.5 TeV while preserving the perturbativity of Higgs couplings
up to high scales and further it is consistent with the electroweak precision
tests Barbieri:2006dq .

On the other hand, there exist extensions of the Standard Model (generally
labeled Beyond Standard Model (BSM) physics) which have been constructed to
address a completely different problem called the hierarchy problem. The
hierarchy problem addresses the lack the symmetry for the mass of the Higgs
boson in the Standard Model and the consequences of this in the light of the
large difference of energy scales between the weak interaction scale ($\sim
10^{2}$ GeV) and the quantum gravity or grand unification scale ($\sim
10^{16}$ GeV). Such a huge difference in the energy scales could destabilize
the Higgs mass due to quantum corrections. To protect the Higgs mass from
these dangerous radiative corrections, new theories such as supersymmetry,
large extra dimensions and little Higgs have been proposed. It turns out that
most of these BSM physics models contain a particle which can be the dark
matter. A few examples of these theories and the corresponding candidates for
dark matter are as follows. (i) Axions are pseudo-scalar particles which
appear in theories with Peccei-Quinn symmetry Peccei:1977hh ; Peccei:2006as
proposed as solution to the strong CP problem of the standard model. They also
appear in Superstring theories which are theories of quantum gravity. The
present limits on axions are Bertone:2004pz  extremely strong from
astrophysical data. In spite of this, there is still room for axions to form a
significant part of the dark matter relic density.

(ii) Supersymmetric theories Martin:1997ns ; Drees:2004jm  which incorporate
fermion-boson interchange symmetry are proposed as extensions of Standard
Model to protect the Higgs mass from large radiative corrections. The dark
matter candidate is the lightest supersymmetric particle (LSP) which is stable
or sufficiently long lived as mentioned before777The corresponding symmetry
here is called $R$-parity. If this symmetry is exact, the particle is stable.
If is broken very mildly, the LSP could be sufficiently long lived, close to
the age of the universe.. Depending on how supersymmetry is broken jun96 ,
there are several possible dark matter candidates in these models. In some
models, the lightest supersymmetric particle and hence the dark matter
candidate is a neutralino. The neutralino is a linear combination of super-
partners of $Z,\gamma$ as well as the neutral Higgs bosons888The neutralino
could be either gaugino dominated or higgsino dominated depending on the
composition. It turns out that neutralino composition should be sufficiently
well-temperedArkaniHamed:2006mb  to explain the observed relic density. While
one might debate the some what philosophical requirement of ‘fine-tuning’, it
is now known that in simplest models of supersymmetry breaking, like mSUGRA,
only special regions in the parameter space, corresponding to the special
conditions in the neutralino-neutralino annihilation channels satisfy the
relic density constraint dreesdjouadi . . The other possible candidates are
the super-partner of the graviton, called the gravitino and the super-partners
of the axinos, the scalar saxion and the fermionic axino. These particles also
can explain the observed relic density covireview .

(iii) Other classic extensions of the Standard Model either based on
additional space dimensions or larger symmetries also have dark matter
candidates. In both versions of the extra dimensional models, i.e., the
Arkani-Hamed, Dimopoulos, Dvali (ADD) ArkaniHamed:1998rs ; ArkaniHamed:1998nn
and Randall-Sundrum (RS) Randall:1999ee ; Randall:1999vf , models, the
lightest Kaluza-Klein particle999The extra space dimensions are compactified.
The compact extra dimension manifests it selves in ordinary four dimensional
space-time as an infinite tower of massive particles called Kaluza-Klein (KK)
particles. can be considered as the dark matter candidate Servant:2002aq ;
Hooper:2007qk ; che02 ; Bertone:2002ms . Similarly, in the little-Higgs models
where the Higgs boson is a pseudo-Goldstone boson of a much larger symmetry, a
symmetry called T-parity Hubisz:2004ft  assures us a stable and neutral
particle which can form the dark matter. Very heavy neutrinos with masses of
$\mathcal{O}(100~{}\text{GeV}-1~{}\text{TeV})$ can also naturally appear
within some classes of Randall-Sundrum and Little Higgs models. Under suitable
conditions, these neutrinos can act like cold dark matter. (For a recent
study, please see geraldine  ). In addition to these particles, more exotic
candidates like simpzillas simpzillas  and wimpzillas kolb2  with masses close
to the GUT scale ($\sim 10^{15}$ GeV) have also been proposed in the
literature. Indirect searches like ICECUBE icecube  (discussed below) already
have strong constraints on simpzillas.

##  II Dark Matter Experiments

If the dark matter candidate is indeed a new particle and it has interactions
other than gravitational interactions101010It cannot have electromagnetic
interactions as this would mean it is charged, and it cannot have strong
interactions as this would most likely mean it would be baryonic in form -
both these prospects are already ruled out by experiments., then the most
probable interactions it could have are the weak interactions111111In spite of
being electrically neutral, dark-matter particle can have a nonzero electric
and/or magnetic dipole moment, if it has a nonzero spin. In such a case the
strongest constraint comes from Big Bang Nucleosynthesis. Interested readers
are referred to the paper by Kamoinkowski et al. Sigurdson:2004zp  and
particularly Fig. 1 therein.. This weakly interacting particle, dubbed as WIMP
(Weakly Interacting Massive Particle) could interact with ordinary matter and
leave traces of its nature. There are two ways in which the WIMP could be
detected (a) Direct Detection: here one looks for the interaction of the WIMP
on a target, the target being typically nuclei in a scintillator. It is
expected that the WIMPs present all over the galaxy scatter off the target
nuclei once in a while. Measuring the recoil of the nuclei in these rarely
occurring events would give us information about the properties of the WIMP.
The scattering cross section would depend on whether it was elastic or
inelastic and is a function of the spin of the WIMP 121212More generally, the
WIMP-Nucleon cross section can be divided as (i) elastic spin-dependent (eSD),
(ii) elastic spin-independent (eSI) , (iii) in-elastic spin-dependent ( iSD)
and (iv) in-elastic spin-independent (iSI).. There are more than 20
experiments located all over the world, which are currently looking for WIMP
through this technique. Some of them are DAMA, CDMS, CRESST, CUORICINO, DRIFT
etc. (b) Indirect detection : when WIMPs cluster together in the galatic halo,
they can annihilate with themselves giving rise to electron-positron pairs,
gamma rays, proton-anti-proton pairs, neutrinos etc. The flux of such
radiation is directly proportional to the annihilation rate and the the WIMP
matter density. Observation of this radiation could lead to information about
the mass and the cross section strength of the WIMPs. Currently, there are
several experiments which are looking for this radiation131313These are
typically the same experiments which measure the cosmic ray spectrum. For a
comprehensive list of all these experiments and other useful information like
propagation packages, please have a look at:
http://www.mpi-hd.mpg.de/hfm/CosmicRay/CosmicRaySites.html. (i) MAGIC, HESS,
CANGAROO, FERMI/GLAST, EGRET etc. look for the gamma ray photons. (ii) HEAT,
CAPRICE, BESS, PAMELA, AMS can observe anti-protons and positron flux.
(iii)Very highly energetic neutrinos/cosmic rays $\sim$ a few TeV to multi-TeV
can be observed by large detectors like AMANDA, ANTARES, ICECUBE etc. (for a
more detailed discussion see Bertone:2004pz ; pijush1 ).

Over the years, there have been indications of presence of the dark matter
through both direct and indirect experiments. The most popular of these
signals are INTEGRAL and DAMA results (for a nice discussion on these topics
please see, Hooper:2009zm ). INTEGRAL (International Gamma -Ray Astrophysics
Laboratory) is a satellite based experiment looking for gamma rays in outer
space. In 2003, it has observed a very bright emission of the 511 keV photons
from the Galactic Bulge integral1  at the centre. The 511 KeV line is special
as it is dominated by $e^{+}e^{-}$ annihilations via the positronium. The
observed rate of (3-15) $\times 10^{42}$ positrons/sec in the inner galaxy was
much larger than the expected rate from pair creation via cosmic ray
interactions with the interstellar medium in the galactic bulge by orders of
magnitude141414It should be noted that the Integral spectrometer has a very
good resolution of about 2 KeV over a range of energies 20 keV to 8 MeV..
Further, the signal is approximately spherically symmetric with very little
positrons from galactic bulge contributing to the signal integral2 . Several
explanations have been put forward to explain this excess. Astrophysical
entities like hypernovae, gamma ray burts and X-ray binaries have been
proposed as the likely objects contributing to this excess. On the other hand,
this signal can also be attributed to the presence of dark matter which could
annihilate itself giving rise to electron-positron pairs. To explain the
INTEGRAL signal in terms of dark matter, extensions of Standard Model
involving light $\sim(\text{MeV}-\text{GeV})$ particles and light gauge bosons
($\sim\text{GeV}$) are ideally suited. These models which have been already
reviewed in the previous section, can be probed directly at the existing and
future $e^{+}e^{-}$ colliders and hence could be tested. Until further
confirmation from either future astrophysical experiments or through ground
based colliders comes about, the INTEGRAL remains an ‘anomaly’ as of now.

While the INTEGRAL is an indirect detection experiment, the DAMA (DArk MAtter
) is a direct detection experiment located in the Gran Sasso mountains of
Italy. The target material consists of highly radio pure NaI crystal
scintillators; the scintillating light from WIMP-Nucleon scattering and recoil
is measured. The experiment looks for an annual modulation of the signal as
the earth revolves around the sun dama1 . Such modulation of the signal is due
to the gravitational effects of the Sun as well as rotatory motion of the
earth151515Looking for such modulations further limit any systematics present
in the experiment.. DAMA and its upgraded version DAMA/LIBRA have collected
data for seven annual cycles and four annual cycles respectively161616These
results have been recently updated with six annual cycles for DAMA/LIBRA; the
CL has now moved up to $8.9\sigma$ dama2 .. Together they have reported an
annual modulation at 8.2$\sigma$ confidence level. If confirmed, the DAMA
results would be the first direct experimental evidence for the existence of
WIMP dark matter particle. However, the DAMA results became controversial as
this positive signal has not been confirmed by other experiments like XENON
and CDMS, which have all reported null results in the spin independent WIMP-
Nucleon scattering signal region.

The Xenon 10 detector also at Gran Sasso laboratories uses a Xenon target
while measuring simultaneously the scintillation and ionization produced by
the scattering of the dark matter particle. The simultaneous measurement
reduces the background significantly down to $4.5~{}\text{KeV}$. With a
fiducial mass of 5.4 Kg, they set an upper limit of WIMP-Nucleon spin
independent cross section to be 8.8 $\times~{}10^{-44}\text{cm}^{2}$ for a
WIMP mass of 100 GeVxenon1 . An upgraded version Xenon 100 has roughly double
the fiducial mass has started taking data from Oct 2009. In the first results,
they present null results, with upper limits of about $3.4\times
10^{-44}\text{cm}^{2}$ for 55 GeV WIMPs xenon2 . These results severely
constraint interpretation of the DAMA results in terms of an elastic spin
independent WIMP-nucleon scattering.

The CDMS (Cryogenic Dark Matter Search ) experiment has 19 Germanium detectors
located in the underground Soudan Mine, USA. It is maintained at temperatures
$\sim 40\text{mK}$ (milli-Kelvin). Nuclear recoils can be “seen” by measuring
the ionisation energy in the detector. Efficient separation between electron
recoils and nuclear recoils is possible by employing various techniques like
signal timing and measuring the ratios of the ionization energies. Similar to
Xenon, this experiment cdms1  too reported null results in the signal
region171717The final results have a non-zero probability of two events in the
signal region, we comment on it in the next section. and puts an upper limit
$\sim 4.6\times 10^{-44}\text{cm}^{2}$ on the WIMP-Nucleon cross-section for a
WIMP mass of around 60 GeV.

The CoGeNT (Cryogenic Germanium Neutrino Technology) collaboration runs
another recent experiment which uses ultra low noise Germanium detectors. It
is also located in the Soudan Man, USA. The experiment has one of the lowest
backgrounds below 3 KeVee ( KeV electron equivalent (ee) ionisation energy).
It could further go down to 0.4 KeVee, the electron noise threshold. The first
initial runs have again reported null results cogent1  consistent with the
observed background. At this point, the experiment did not have the
sensitivity to confirm/rule out the DAMA results. However, later runs have
shown some excess events over the expected background in the low energy
regions cogent2 . While, the collaboration could not find a suitable
explanation for this excess ( as of now) there is a possibility of these
excess events having their origins in a very light WIMP dark matter particle.
However, care should be taken before proceeding with this interpretation as
the CoGeNT collaboration does not distinguish between electron recoils and
nucleon recoilsweinercogent .

In the light of these experimental results, the DAMA results are hard to
explain. One of the ways out to make the DAMA results consistent with other
experiments is to include an effect called “channelling” which could be
present only in the NaI crystals which DAMA uses. However, even the inclusion
of this effect does not improve the situation significantly. To summarize, the
situation is as follows for various interpretations of the WIMP-Nucleon cross
section. For eSI (elastic Spin Independent) interpretation, the DAMA regions
are excluded by both CDMS as well as Xenon 10. This is irrespective of whether
one considers the channeling effect or not. It is also hard to reconcile DAMA
results with CoGeNT in this case. For elastic Spin Dependent (eSD)
interpretation, the DAMA and CoGeNT results though consistent with each other
are in conflict with other experiments. For an interpretation in terms of
WIMP-proton scattering, the results are in conflict with several experiments
like SIMPLE , PICASSO etc. On the other hand, an interpretation in terms of
WIMP-neutron scattering is ruled out by XENON and CDMS data. For the inelastic
dark matter interpretations, spin -independent cross section with a medium
mass ($\sim 50~{}\text{GeV}$) WIMP is disfavored by CRESST as well as CDMS
data. For a low mass (close to 10 GeV) WIMP, with the help of channeling in
the NaI crystals, it is possible to explain the DAMA results, in terms of
spin- independent inelastic dark matter - nucleon scattering. However, the
relevant parameters (dark matter mass and mass splittings) should be fine
tuned and further, the WIMP velocity distribution in the galaxy should be
close to the escape velocity. Inelastic Spin dependent interpretation of the
DAMA results is a possibility (because it can change relative signals at
different experiments koppzupan  ) which does not have significant constraints
from other experiments. However, it has been shownweinercogent  that inelastic
dark matter either with spin dependent or spin independent interpretation of
the DAMA results is difficult to reconcile with the CoGeNT results, unless one
introduces substantial exponential background in the CoGeNT data.

##  III The Data

The focus of the present topical review is a set of new experimental results
which have appeared over the past year. In terms of the discussion in the
previous section, these experiments follow “indirect” methods to detect dark
matter. The data from these experiments seems to be pointing to either
“discovery” of the dark matter or some yet non-understood new astrophysics
being operative within the vicinity of our Galaxy. The four main experiments
which have led to this excitement are (i) PAMELAAdriani:2008zr  (ii)
ATIC:2008zzr  (iii) HESSCollaboration:2008aaa  and (iv) FERMIAbdo:2009zk . All
of these experiments involve international collaborations spanning several
nations. While PAMELA and FERMI are satellite based experiments, ATIC is a
balloon borne experiment and HESS is a ground based telescope. All these
experiments contain significant improvements in technology over previous
generation experiments of similar type. The H.E.S.S experiment has a factor
$\sim 10$ improvement in $\gamma$-ray flux sensitivity over previous
experiments largely due to its superior rejection of the hadronic background.
Similarly, ATIC is the next generation balloon based experiment equipped to
have higher resolution as well as larger statistics. Similar statements also
hold for the satellite based experiments, PAMELA and FERMI. It should be noted
that the satellite based experiments have some inherent advantages over the
balloon based ones. Firstly, they have enhanced data taking period, unlike the
balloon based ones which can take data only for small periods. And
furthermore, these experiments also do not have problems with the residual
atmosphere on the top of the instrument which plagues the balloon based
experiments.

Figure 1: Results from PAMELA and ATIC with theoretical models. The left panel
shows PAMELAAdriani:2008zr  positron fraction along with theoretical model.
The solid black line shows a calculation by Moskalenko & Strongmos98  for pure
secondary production of positrons during the propagation of cosmic-rays in the
Galaxy. The right panel shows the differential electron energy spectrum
measured by ATIC:2008zzr  (red filled circles) compared with other experiments
and also with theoretical prediction using the GALPROPStrong:2001fu  code
(solid line). The other data points are from AMSAguilar:2002ad (green stars),
HEATBarwick:1997kh  (open black triangles), BETSTorii:2001aw  (open blue
circles), PPB-BETSTorii:2008xu  (blue crosses) and emulsion chambers (black
open diamonds) and the dashed curve at the beginning is the spectrum of solar
modulated electron. All the data points have uncertainties of one standard
deviation. The ATIC spectrum is scaled by $E_{e}^{3.0}$. The figures of PAMELA
and ATIC are reproduced from their original papers cited above.

The satellite-based Payload for Antimatter Matter Exploration and Light-nuclei
Astrophysics or PAMELA collects cosmic ray protons, anti-protons, electrons,
positrons and also light nuclei like Helium and anti-Helium. One of the main
strengths of PAMELA is that it could distinguish between electrons and anti-
electrons, protons and anti-protons and measure their energies accurately. The
sensitivity of the experiment in the positron channel is up to approximately
300 GeV and in the anti-proton channel up to approximately 200 GeV. Since it
was launched in June 2006, it was placed in an elliptical orbit at an altitude
ranging between $350-610$ km with an inclination of 70.0°. About 500 days of
data was analyzed and recently presented. The present data is from 1.5 GeV to
100 GeV has been published in the journal Nature Adriani:2008zr . In this
paper, PAMELA reported an excess of positron flux compared to earlier
experiments. In the left panel of the Fig. 1, we see PAMELA results along with
the other existing results. The y-axis is given by
$\phi(e^{+})/(\phi(e^{-})+\phi(e^{+}))$, which $\phi$ represents the flux of
the corresponding particle. According to the analysis presented by PAMELA, the
results of PAMELA are consistent with the earlier experiments up to 20 GeV,
taking into consideration the solar modulations between the times of PAMELA
and previous experiments. Particles with energies up to 20 GeV are strongly
effected by solar wind activity which varies with the solar cycle. On the
other hand, PAMELA has data from 10 GeV to 100 GeV, which sees an increase in
the positron flux (Fig. 1). The only other experimental data in this energy
regime (up to 40 GeV) are the AMS and HEAT, which while having large errors
are consistent with the excess seen by PAMELA. In the low energy regime most
other experiments are in accordance with each other but have large error bars.

Figure 2: The Fermi LAT CR electron spectrum. The red filled circles shows the
data from Fermi along with the gray bands showing systematic errors. The
dashed line correspond to a theoretical model by Moskalenko et al.
Strong:2004de . The figure of FERMI is reproduced from their original paper
cited above.

Cosmic ray positrons at these energies are expected to be from secondary
sources i.e. as result of interactions of primary cosmic rays (mainly protons
and electrons) with interstellar medium. The flux of this secondary sources
can be estimated by numerical simulations. There are several numerical codes
available to compute the secondary flux, the most popular publicly available
codes being GALPROP galprop ; galprop2  and CRPropa crpropa . These codes
compute the effects of interactions and energy loses during cosmic ray
propagation within galactic medium taking also in to account the galactic
magnetic fields. GALPROP solves the differential equations of motion either
using a 2D grid or a 3D grid while CRPropa does the same using a 1D or 3D
grids. While GALPROP contains a detailed exponential model of the galactic
magnetic fields, CRPropa implements only extragalactic turbulent magnetic
fields. In particular CRPropa is not optimised for convoluted galactic
magnetic fields. For this reason, GALPROP is best suited for solving diffusion
equations involving low energy (GeV-TeV) cosmic rays in galactic magnetic
fields.

The main input parameters of the GALPROP code are the primary cosmic ray
injection spectra, the spatial distribution of cosmic ray sources, the size of
the propagation region, the spatial and momentum diffusion coefficients and
their dependencies on particle rigidity. These inputs are mostly fixed by
observations, like the interstellar gas distribution is based on observations
of neutral atomic and molecular gas, ionized gas ; cross sections and energy
fitting functions are build from Nuclear Data sheets (based on Las Almos
Nuclear compilation of nuclear crosssections and modern nuclear codes) and
other phenomenological estimates. Interstellar radiation fields and galactic
magnetic fields are based on various models present in literature. The
uncertainties in these inputs would constitute the main uncertainties in the
flux computation from GALPROP181818Some codes are constructed to fix the
various parameters of their own cosmic ray propagation model. See for example,
DRAGON dragon . Here one can fix the diffusion coefficients from PAMELA and
other experimental data.. Recently, a new code called CRT which emphasizes
more on the minimization of the computation time was introduced. Here most of
the input parameters are user defined crt . Finally, using the popular Monte
Carlo routine GEANT geant  one can construct cosmic ray propagation code as
has been done by desorgher1 ; strumia . On the other hand, dark matter relic
density calculators like DARKSUSY Gondolo:2004sc  also compute cosmic ray
propagation in the galaxies required for indirect searches of dark matter. It
is further interfaced with GALPROP.

In summary, GALPROP is most suited for the present purposes i.e, understanding
of PAMELA and ATIC data which is mostly in the GeV-TeV range. It has been
shown the results from these experiments do not vary much if one instead
chooses to use a GEANT simulation. In fact, most of the experimental
collaborations use GALPROP for their predictions of secondary cosmic ray
spectrum. In the left panel of Fig. 1, the expectations based on GALPROP are
given as a solid line running across the figure. From the figure it is obvious
that PAMELA results show that the positron fraction increases with energy
compared to what GALPROP expects. The excess in the positron fraction as
measured by PAMELA with respect to GALPROP indicates that this could be a
result due to new primary sources rather than secondary sources 191919For an
independent analysis which confirms the PAMELA excess, please see, delahaye2 .
This new primary source could be either dark matter decay/annihilation or a
nearby astrophysical object like a pulsar. Before going to the details of the
interpretations, let us summarize the results from ATIC and FERMI also.

Advanced Thin Ionization Calorimeter or in short ATIC is a balloon-borne
experiment to measure energy spectrum of individual cosmic ray elements within
the region of GeV up to almost a TeV (thousand GeV) with high precision. As
mentioned, this experiment was designed to be a high-resolution and high
statistics experiment in this energy regime compared to the earlier ones. ATIC
measures all the components of the cosmic rays such as electrons, protons (and
their anti-particles) with high energy resolution, while distinguishing well
between electrons and protons. ATIC (right panel in Fig. 1) presented its
primary cosmic ray electron ($e^{-}$\+ $e^{+}$) spectrum between the energies
3 GeV to about 2.5 TeV202020The cosmic ray electrons follow a power law
spectrum, the index being $\sim$ $-3.0$. Thus it is normalized by a factor
$E^{3.0}$ .. The results show that the spectrum while agreeing with the
GALPROP expectations up to 100 GeV, show a sharp increase above 100 GeV. The
total flux increases till about 600 GeV where it peaks and then sharply falls
till about 800 GeV. Thus, ATIC sees an excess of the primary cosmic ray
($e^{-}$\+ $e^{+}$) spectrum between the energy range $300-800$ GeV. The rest
of the spectrum is consistent with the expectations within the errors. What is
interesting about such peaks in the spectrum is that, if they are confirmed
they could point towards a Breit-Wigner resonance in dark matter annihilation
cross section with a life time as given by its width. As we will discuss in
the next section, this possibility is severely constrained by the data from
the FERMI experiment.

Another ground based experiment sensitive to cosmic rays within this energy
range is H.E.S.S which can measure gamma rays from few hundred GeV to few TeV.
This large reflecting array telescope operating from Namibia has presented
data (shown in figure 2) from $600$ GeV to about 5 TeV. It could confirm
neither the ‘peaking’ like behavior at 600 GeV nor the sharp cut-off at 800
GeV of the ATIC data. The ATIC results can be made consistent with those of
HESS. This would require a $15\%$ overall normalisation of the HESS data. Such
a normalisation is well within the uncertainty of the energy resolution of
HESS. However notice that HESS data does not have a sharp fall about and after
800 GeV.

The Large Area Telescope (LAT) is one of the main components of the Fermi
Gamma Ray Space Telescope, which was launched in June 2008. Due to its high
resolution and high statistical capabilities, it has been one of the most
anticipated experiments in the recent times. Fermi can measure Gamma rays
between 20 MeV and 300 GeV with high accuracy and primary cosmic ray electron
($e^{-}$\+ $e^{+}$) flux between 20 GeV and 1 TeV. The energy resolution
averaged over the LAT acceptance is 11% FWHM (Full-Width-at-Half-Maximum) for
20-100 GeV, increasing to 13% FWHM for 150-200 GeV. The photon angular
resolution is less than 0.1° over the energy range of interest (68%
containment). The FERMI-LAT collaboration has recently published its six month
data on the primary cosmic ray electron flux. More than 4 million electron
events above 20 GeV were selected in survey (sky scanning) mode from 4 August
2008 to 31 January 2009. The systematic error on the absolute energy of the
LAT was determined to be ${}^{-10\%}_{+5\%}~{}$ for 20-300 GeV. Please see
Table I for more details on the errors in Abdo:2009zk . In Fig. 2 we reproduce
the result produced by the FERMI collaboration. They find that the primary
cosmic ray electron spectrum more or less goes along the expected lines up to
100 GeV (its slightly below the expected flux between 10 and 50 GeV), however
above 100 GeV, there is strong signal for an excess of the flux ranging up to
1 TeV. The FERMI data thus confirms the excess in the electron spectrum which
was seen by ATIC, the excess however has a much flatter profile with respect
to the peak seen by ATIC. Thus, ATIC could in principle signify a ‘resonance’
in the spectrum, whereas FERMI cannot. However, in comparing both the spectra
from the figures presented above, one should keep in mind that the FERMI
excess is in the total electron spectrum ($e^{+}+e^{-}$ ) whereas the ATIC
data is presented in terms of positron excess only. If the excess in FERMI is
caused by the excess only through excess positrons, one should expect that the
FERMI spectra to also have similar ‘peak’ like behavior at 600 GeV. From
Fig.(2), where both FERMI and ATIC data are presented, we see that the ATIC
data points are far above that of FERMI’s.

##  IV The Interpretations

Lets now summarise the experimental observations strumia  which would require
an interpretation :

  * •

The excess in the flux of positron fraction
$\left(\tfrac{\phi(e^{+})}{\phi(e^{-})+\phi(e^{+})}\right)$ measured by PAMELA
up to 100 GeV.

  * •

The lack of excess in the anti-proton fraction measured by PAMELA up to 100
GeV.

  * •

The excess in the total flux $\left(\phi(e^{-})+\phi(e^{+})\right)$ in the
spectrum above 100 GeV seen by FERMI, HESS etc. While below 100 GeV, the
measurements have been consistent with GALPROP expectations.

  * •

The absence of ‘peaking’ like behavior as seen by ATIC, which indicates a long
lived particle, in the total electron spectrum measured by FERMI.

Two main interpretations have been put forward: (a) A nearby astrophysical
source which has a mechanism to accelerate particles to high energies and (b)
A dark matter particle which decays or annihilates leading to excess of
electron and positron flux. Which of the interpretations is valid will be
known within the coming years with enhanced data from both PAMELA and FERMI.
Let us now turn to both the interpretations:

Pulsars and supernova shocks have been proposed as likely astrophysical local
sources of energetic particles that could explain the observed excess of the
positron fraction Hooper:2008kg ; Blasi:2009hv . In the high magnetic fields
present in the pulsar magnetosphere, electrons can be accelerated and induce
an electromagnetic cascade through the emission of curvature
radiation212121The curvature radiation arises due to relativistic, charged
particles moving around curved magnetic field lines, see for details Gil et
al.Gil:2003ug .. This can lead to a production of high energy photons above
the threshold for pair production; and on combining with the number density of
pulsars in the Galaxy, the resulting emission can explain the observed
positron excess Hooper:2008kg . The energy of the positrons tell us about the
site of their origin and their propagation history coutu99 . The cosmic ray
positrons above 1 TeV could be primary and arise due to a source like a young
plusar within a distance of 100 pc ato95 . This would also naturally explain
the observed anisotropy, as argued for two of the nearest pulsars, namely
$B0656+14$ and the $Geminga$ bue08 ; Yuksel:2008rf . On a similar note,
diffusive shocks as in a supernova remnant hardens the spectrum, hence this
process can explain the observed positron excess above 10 GeV as seen from
PAMELA Ahlers09 .

Another possible astrophysical source that has been proposed is the pion
production during acceleration of hadronic cosmic rays in the local sources
Blasi:2009hv . It has been argued Mertsch:2009ph  that the measurement of
secondary nuclei produced by cosmic ray spallation can confirm whether this
process or pulsars are more important as the production mechanism. It has been
show that the present data from ATIC-II supports the hadronic model and can
account for the entire positron excess observed.

If the excess observed by PAMELA, HESS and FERMI is not due to some yet not
fully-understood astrophysics but is a signature of the dark matter, then
there are two main processes through which such an excess can occur:

  1. (i)

The annihilation of dark matter particles into Standard Model (SM) particles
and

  2. (ii)

The decay of the dark matter particle into SM particles.

Interpretation in terms of annihilating dark matter, however, leads to
conflicts with cosmology. The observed excesses in the PAMELA/FERMI data would
set a limit on the product of annihilation cross section and the velocity of
the dark matter particle in the galaxy (for a known dark matter density
profile). Annihilation of the dark matter particles also happens in the early
universe with the same cross section but at much larger velocities for
particles (about 1000 times the particle velocities in galaxies). The
resultant relic density is not compatible with observations. The factor $\sim
1000$ difference in the velocities should some how be compensated in the cross
sections. This can be compensated by considering “boost” factors for the
particles in the galaxy which can enhance the cross section by several orders
of magnitude. The boost factors essentially emanate from assuming local
substructures for the dark matter particles, like clumps of dark matter and
are typically free parameters of the model (see however, delahaye1 ). Another
mechanism which goes by the name Sommerfeld mechanism can also enhance the
annihilation cross sections. For very heavy dark matter ( with masses much
greater than the relevant gauge boson masses) trapped in the galactic
potential, non-perturbative effects could push the annihilation cross-sections
to much larger values. For SU(2) charged dark matter, the masses of dark
matter particles should be $\gg M_{W}$ hisano . The Sommerfeld mechanism is
more general and applicable to other (new) interactions alsohannestead .
Another way of avoiding conflict with cosmology would be to consider non-
thermal production of dark matter in the early universe222222Non-thermal
production typically refers to production mechanisms through decays of very
heavy particles like inflaton. See for example riotto1 .. Before the release
of FERMI data, the annihilating dark matter model with a very heavy dark
matter $\sim\mathcal{O}(2-3)\ $TeV was much in favour to explain the
“resonance peak” of the ATIC and the excess in PAMELA data. Post FERMI, whose
data does not have sharp raise and fall associated with a resonance, the
annihilating dark matter interpretation has been rendered incompatible.
However, considering possible variations in the local astro physical
background profile due to presence of local cosmic ray accelerator, it has
been shown that it is still possible to explain the observed excess, along
with FERMI data with annihilating dark matter. The typical mass of the dark
matter particle could lie even within sub-TeV region Dodelson:2009ih ;
Belikov:2009cx ; Cholis:2009gv ; Hooper:2009cs  and as low as $30-40$ GeV
Goodenough:2009gk . Some more detailed analysis can be found in Pato:2009fn .

Several existing BSM physics models of annihilating dark matter become highly
constrained or ruled out if one requires to explain PAMELA/ATIC and FERMI
data. The popular supersymmetric DM candidate neutralino with its annihilating
partners such as chargino, stop, stau etc., can explain the cosmological relic
density but not the excess observed by PAMELA/ATIC. Novel models involving a
new ‘dark force’, with a gauge boson having mass of about 1 GeV
ArkaniHamed:2008qn , which predominantly decays to leptons, together with the
so-called Sommerfeld enhancement seem to fit the data well. The above class of
models, which are extensions of standard model with an additional $U(1)$ gauge
group, caught the imagination of the theorists Katz:2009qq ; Cholis:2008vb ;
Cholis:2008hb ; Cholis:2008qq . A similar supersymmetric version of this
mechanism where the neutralinos in the MSSM can annihilate to a scalar
particle, which can then decay the observed excess in the cosmic ray data
Hooper:2009gm . Models involving Type II seesaw mechanism Gogoladze:2009gi
have also been considered recently where neutrino mass generation is linked
with the positron excess. In addition to the above it has been shown that
extra dimensional models with KK gravitions can also produce the excess
Hooper:2009fj 232323Some of the first simulations using PYTHIA and DARK SUSY
for the KK gravition has been done in hooperkribs . Similar study for SUSY can
be found in susy01 . These have been done when HEAT results have shown an
excess though in a less statistically significant way.. Models with Nambu-
Goldstone bosons as dark matter have been studied in murayama .

In the case of decaying dark matter, the relic density constraint of the early
universe is not applicable, however, the lifetime of the dark matter particle
(typically of a mass of $\mathcal{O}(1)$ TeV) should be much much larger than
($\sim 10^{9}$ times) the age of the universestrumia . Such a particle can fit
the data well. A crucial difference in this picture with respect to the
annihilation picture is that the decay rate is directly proportional to the
density of the dark matter ($\rho$), whereas the annihilation rate is
proportional to its square, ($\rho^{2}$). The most promising candidates in the
decaying dark matter seem to be a fermion (scalar) particle decaying in to
$W^{\pm}l^{\pm}$ etc. ($W^{+}W^{-}$ etc.) Ibarra:2009dr ; Ibarra:2009nw ;
Ibarra:2008jk ; Nardi:2008ix . In terms of the BSM physics, supersymmetric
models with a heavy gravitino and small R-parity violation have been proposed
as candidates for decaying dark matter Buchmuller:2007ui . A heavy neutralino
with $R$-parity violation can also play a similar role Gogoladze:2009kv
stated above. A recent more general model independent analysis has shown that,
assuming the GALPROP background, gravitino decays cannot simultaneously
explain both PAMELA and FERMI excess. However, the presence of additional
astrophysical sources can change the situation Buchmuller:2009xv . Independent
of the gravitino model, it has been pointed out that, the decays of the Dark
Matter particle could be new signals for unification where the Dark Matter
candidate decays through dimension six operators suppressed by two powers of
GUT scale Arvanitaki:2008hq ; Arvanitaki:2009yb ; Buckley:2009kw . Finally,
there has also been some discussion about the possibilities of dark matter
consisting of not one particle but two particles, of which one is the decaying
partner. This goes under the name of ‘two-component dark matter’ and analysis
of this scenario has been presented by Fairbairn:2008fb .

We have so far mentioned just a sample of the theoretical ideas proposed in
the literature. Several other equally interesting and exciting ideas have been
put forward, which have not been presented to avoid the article becoming too
expansive.

##  V Outlook and Remarks

An interesting aspect about the present situation is that, future data from
PAMELA and FERMI could distinguish whether the astrophysical interpretation
i.e. in terms of pulsars or the particle physics interpretation in terms of
dark matter is valid Malyshev:2009tw . PAMELA is sensitive to up to 300 GeV in
its positron fraction and this together with the measurement of the total
electron spectrum can strongly effect the dark matter interpretations. FERMI
with its improved statistics, can on the other hand look for anisotropies
within its data Grasso:2009ma  which can exist if the pulsars are the origin
of this excess. Further measurements of the anti-Deuteron could possibly gives
us a hint why there is no excess in the anti-Proton channel Kadastik:2009ts .
Similarly neutrino physics experiments could give us valuable information on
the possible modelshisano2 . Finally, the Large Hadron collider could also
give strong hints on the nature of dark matter through direct production LHCdm
.

As we have been preparing this note, there has been news from one the
experiments called CDMS-II (Cryogenic Dark Matter Search Experiment)cdms2 . As
mentioned before this experiment conducts direct searches for WIMP dark matter
by looking at collisions of WIMPs on super-cooled nuclear target material. The
present and final analysis of this experiment have shown two events in the
signal region, with the probability of observing two or more background events
in that region being close to $23\%$. Thus, while these results are positive
and encouraging, they are not conclusive. However these results already set a
stringent upper bound on the WIMP-nucleus cross section for a WIMP mass of
around 70 GeV. The exclusion plots in the parameter space of WIMP cross
section and WIMP mass are presented in the paper cdms2 . The interpretations
of this positive signal are quite different compared to the signal of PAMELA
and FERMI. While PAMELA and FERMI as we have seen would require severe
modifications for the existing beyond standard model (BSM) models of Dark
Matter, CDMS results if confirmed would prefer the existing BSM dark matter
candidates like neutralino of the supersymmetry. There are ways of making both
PAMELA/FERMI and CDMS-II consistent through dark matter interpretations,
however, we will not discuss it further here. Finally, it has been shown that
it is possible to make CDMS-II results consistent with DAMA annual modulation
results by assuming a spin-dependent inelastic scattering of WIMP on Nuclei
koppzupan .

In the present note, we have tried to convey exciting developments which have
been happening recently within the interface of astrophysics and particle
physics, especially on the one of the most intriguing subjects of our time,
namely, the Dark Matter. Though it has been proposed about sixty years ago, so
far we have not have any conclusive evidence of its existence other than
through gravitational interactions, or we do not of its fundamental
composition. Experimental searches which have been going on for decades have
not bore fruit in answering either of these questions. For these reasons, the
present indications from PAMELA and FERMI have presented us with a unique
opportunity of unraveling at least some of mystery surrounding the dark
matter. These experimental results, if they hold and get confirmed as due to
dark matter, would strongly modify the way dark matter was perceived in the
scientific community. As a closing point, let us note that there are several
new experiments being planned to explore the dark matter either directly or
indirectly and thus some information about the nature of the dark matter might
just around the corner.

###### Acknowledgements.

We thank PAMELA collaboration, ATIC collaboration and FERMI-LAT collaboration
for giving us permission to reproduce their figures. We thank Diptiman Sen for
a careful reading of this article and useful comments. C. J. would like to
thank Gary Mamon for illuminating discussions regarding the search for dark
matter in elliptical galaxies and clusters. We thank A. Iyer for bringing to
our notice a reference. Finally, we thank the anonymous referee for
suggestions and comments which have contributed in improving the article.

## References

  * (1) V. Rubin, Scientific American 248, 96 (1983).
  * (2) Y. Sofue and V. Rubin, Ann. Rev. Astron. Astrophys. 39, 137 (2001) [arXiv:astro-ph/0010594].
  * (3) J. Binney and S. Tremaine, “Galactic Dynamics”, Princeton University Press (1987).
  * (4) A. Dekel, F. Stoehr, G.A. Mamon, T.J. Cox, G.S. Novak and J.R. Primack 2005, Nature, 437, 707.
  * (5) G. Mamon, In the meeting on “Mass Unveiling the mass: Extracting and Interpreting Galaxy Masses”, held in Kingston, Canada in June 2009.
  * (6) Zwicky, F. Helvetica Physica Acta, 6, 110 (1933); also see Binney, J. & Tremaine, S. D. Galactic Dynamics, $2^{nd}$ edition, Princeton University Press (2007).
  * (7) C. L. Bennett et al., Astrophys. J. 464, L1 (1996) [arXiv:astro-ph/9601067]. See Also, J. R. Bond, G. Efstathiou and M. Tegmark, Mon. Not. Roy. Astron. Soc. 291, L33 (1997) [arXiv:astro-ph/9702100].
  * (8) M. Kowalski et al. [Supernova Cosmology Project Collaboration], Astrophys. J. 686, 749 (2008) arXiv:0804.4142 [astro-ph].
  * (9) G. Hinshaw et al. [WMAP Collaboration], Astrophys. J. Suppl. 180 (2009) 225 [arXiv:0803.0732 [astro-ph].
  * (10) Komatsu, E. et al. preprint at arXiv:0803.0547v2 [astro-ph].
  * (11) See for example, S. Dodelson, “Modern Cosmology,” Amsterdam, Netherlands: Academic Pr. (2003)
V. Sahni, Lect. Notes Phys. 653 (2004) 141 [arXiv:astro-ph/0403324] ;
T. Padmanabhan, Phys. Rept. 380 (2003) 235 [arXiv:hep-th/0212290] ;
E. J. Copeland, M. Sami and S. Tsujikawa, Int. J. Mod. Phys. D 15 (2006) 1753
[arXiv:hep-th/0603057].

  * (12) Navarro, J.F., Frenk, C.S. & White, S.D.M. Astrophys. J. 490, 493 (1997).
  * (13) de Blok, W. J. G., McGaugh, S. S., Bosma, A. & Rubin, V. C. Astrophys. J., 552, L23 (2001).
  * (14) M. Milgrom, Astrophys. J. 270, 365 (1983).
  * (15) O. Tiret and F. Combes, Astronomy and Astrophysics, 464, 2, 517 (2007) [arXiv:astro-ph/0701011].
  * (16) F. Combes and O. Tiret, Invited paper presented at “The Invisible Universe International Conference”, ed. J-M. Alimi, A. Fuzfa, P-S. Corasaniti, AIP publications, arXiv:0908.3289 [astro-ph.CO].
  * (17) D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch, S. W. Randall, C. Jones and D. Zaritsky, Astrophys. J. 648, L109 (2006) [arXiv:astro-ph/0608407].
  * (18) M. Valluri and C. J. Jog, Astrophys. J. 357, 367 (1990).
  * (19) J. D. Bekenstein, Phys. Rev. D 70, 083509 (2004) [Erratum-ibid. D 71, 069901 (2005)] [arXiv:astro-ph/0403694].
  * (20) J. D. Bekenstein, Nucl. Phys. A 827, 555C (2009) [arXiv:0901.1524 [astro-ph]].
  * (21) Trimble, V. Existence and nature of dark matter in the universe, ARAA,25, 425 (1987).
  * (22) D’ Amico, G., Kamionkowski, M. & Sigurdson, K. arXiv: 0907.1912 [astro-ph] (2009).
  * (23) Pfenniger, D., Combes, F. & Martinet, L. A & A, 285, 79 (1994).
  * (24) E. Witten, Phys. Rev. D 30 (1984) 272.
  * (25) J. e. Alam, S. Raha and B. Sinha, Astrophys. J. 513, 572 (1999) [arXiv:astro-ph/9704226].
  * (26) For an earlier discussion on this topic, see, A. Bhattacharyya, J. e. Alam, S. Sarkar, P. Roy, B. Sinha, S. Raha and P. Bhattacharjee, Nucl. Phys. A 661, 629 (1999) [arXiv:hep-ph/9907262] , and references there in.
  * (27) See for example, S. Banerjee, S. K. Ghosh, S. Raha and D. Syam, Phys. Rev. Lett. 85 (2000) 1384 [arXiv:hep-ph/0006286] ; J. E. Horvath, Astrophys. Space Sci. 315 (2008) 361 [arXiv:0803.1795 [astro-ph]]. For a recent summary on this topic, please see, S. K. Ghosh, arXiv:0808.1652 [astro-ph].
  * (28) T. Schwetz, M. A. Tortola and J. W. F. Valle, New J. Phys. 10, 113011 (2008) [arXiv:0808.2016 [hep-ph]].
  * (29) J. A. Peacock, “Cosmological physics”, Cambridge, UK: Univ. Pr. (1999).
  * (30) A. Strumia and F. Vissani, arXiv:hep-ph/0606054.
  * (31) M. Viel, J. Lesgourgues, M. G. Haehnelt, S. Matarrese and A. Riotto, Phys. Rev. Lett. 97, 071301 (2006) [arXiv:astro-ph/0605706].
  * (32) J. Lesgourgues and S. Pastor, Phys. Rept. 429 (2006) 307 [arXiv:astro-ph/0603494].
  * (33) A. Palazzo, D. Cumberbatch, A. Slosar and J. Silk, Phys. Rev. D 76, 103511 (2007) [arXiv:0707.1495 [astro-ph]].
  * (34) G. Gelmini, S. Palomares-Ruiz and S. Pascoli, Phys. Rev. Lett. 93, 081302 (2004) [arXiv:astro-ph/0403323].
  * (35) G. Gelmini, E. Osoba, S. Palomares-Ruiz and S. Pascoli, JCAP 0810 (2008) 029 [arXiv:0803.2735 [astro-ph]].
  * (36) M. A. Acero and J. Lesgourgues, Phys. Rev. D 79 (2009) 045026 [arXiv:0812.2249 [astro-ph]].
  * (37) C. Boehm and P. Fayet, Nucl. Phys. B 683, 219 (2004) [arXiv:hep-ph/0305261].
  * (38) P. Fayet, Phys. Rev. D 75, 115017 (2007) [arXiv:hep-ph/0702176].
  * (39) S. Gopalakrishna, S. J. Lee and J. D. Wells, Phys. Lett. B 680, 88 (2009) [arXiv:0904.2007 [hep-ph]].
  * (40) N. Borodatchenkova, D. Choudhury and M. Drees, Phys. Rev. Lett. 96, 141802 (2006) [arXiv:hep-ph/0510147].
  * (41) R. Barbieri and L. J. Hall, arXiv:hep-ph/0510243.
  * (42) Q. H. Cao, E. Ma and G. Rajasekaran, Phys. Rev. D 76, 095011 (2007) [arXiv:0708.2939 [hep-ph]].
  * (43) R. Barbieri, L. J. Hall and V. S. Rychkov, Phys. Rev. D 74, 015007 (2006) [arXiv:hep-ph/0603188].
  * (44) R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
  * (45) R. D. Peccei, Lect. Notes Phys. 741, 3 (2008) [arXiv:hep-ph/0607268].
  * (46) G. Bertone, D. Hooper and J. Silk, Phys. Rept. 405, 279 (2005) [arXiv:hep-ph/0404175].
  * (47) S. P. Martin, “A Supersymmetry Primer,” arXiv:hep-ph/9709356.
  * (48) M. Drees, R. Godbole and P. Roy, “Theory and phenomenology of sparticles: An account of four-dimensional $\mathcal{N}=1$ supersymmetry in high energy physics,” Hackensack, USA: World Scientific (2004).
  * (49) Jungman, G., Kamionkowski, M. & Griest, K. Phys. Rept. 267, 195-373 (1996).
  * (50) N. Arkani-Hamed, A. Delgado and G. F. Giudice, Nucl. Phys. B 741, 108 (2006) [arXiv:hep-ph/0601041].
  * (51) A. Djouadi, M. Drees and J. L. Kneur, JHEP 0603, 033 (2006) [arXiv:hep-ph/0602001].
  * (52) See for example, L. Covi and J. E. Kim, New J. Phys. 11, 105003 (2009) [arXiv:0902.0769 [astro-ph.CO]] and references there in.
  * (53) N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B 429, 263 (1998) [arXiv:hep-ph/9803315].
  * (54) N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Rev. D 59, 086004 (1999) [arXiv:hep-ph/9807344].
  * (55) L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999) [arXiv:hep-ph/9905221].
  * (56) L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999) [arXiv:hep-th/9906064].
  * (57) G. Servant and T. M. P. Tait, Nucl. Phys. B 650, 391 (2003) [arXiv:hep-ph/0206071].
  * (58) D. Hooper and S. Profumo, Phys. Rept. 453, 29 (2007) [arXiv:hep-ph/0701197].
  * (59) Cheng, H. C., Feng, J. L. & Matchev, K. T. Kaluza-Klein dark matter. Phys. Rev. Lett. 89, 211301-211304 (2002).
  * (60) G. Bertone, G. Servant and G. Sigl, Phys. Rev. D 68, 044008 (2003) [arXiv:hep-ph/0211342].
  * (61) J. Hubisz and P. Meade, Phys. Rev. D 71, 035016 (2005) [arXiv:hep-ph/0411264].
  * (62) G. Belanger, A. Pukhov and G. Servant, JCAP 0801 (2008) 009 [arXiv:0706.0526 [hep-ph]].
  * (63) I. F. M. Albuquerque, L. Hui and E. W. Kolb, Phys. Rev. D 64 (2001) 083504 [arXiv:hep-ph/0009017].
  * (64) D. J. H. Chung, E. W. Kolb and A. Riotto, Phys. Rev. Lett. 81 (1998) 4048 [arXiv:hep-ph/9805473]; E. W. Kolb, D. J. H. Chung and A. Riotto, arXiv:hep-ph/9810361.
  * (65) I. F. M. Albuquerque and C. Perez de los Heros, Phys. Rev. D 81 (2010) 063510 [arXiv:1001.1381 [astro-ph.HE]].
  * (66) K. Sigurdson, M. Doran, A. Kurylov, R. R. Caldwell and M. Kamionkowski, Phys. Rev. D 70, 083501 (2004) [Erratum-ibid. D 73, 089903 (2006)] [arXiv:astro-ph/0406355].
  * (67) P. Bhattacharjee and G. Sigl, Phys. Rept. 327, 109 (2000) [arXiv:astro-ph/9811011].
  * (68) For a discussion of this effects please see, D. Hooper, arXiv:0901.4090 [hep-ph].
  * (69) P. Jean et al., Astron. Astrophys. 407 (2003) L55 [arXiv:astro-ph/0309484].
  * (70) G. Weidenspointner et al., Nature 451, 159 (2008).
  * (71) R. Bernabei et al. [DAMA Collaboration], Eur. Phys. J. C 56 (2008) 333 [arXiv:0804.2741 [astro-ph]].
  * (72) R. Bernabei et al., Eur. Phys. J. C 67 (2010) 39 [arXiv:1002.1028 [astro-ph.GA]].
  * (73) J. Angle et al. [XENON Collaboration], Phys. Rev. Lett. 100, 021303 (2008) [arXiv:0706.0039 [astro-ph]].
  * (74) E. Aprile et al. [XENON100 Collaboration], Phys. Rev. Lett. 105 (2010) 131302 [arXiv:1005.0380 [astro-ph.CO]].
  * (75) Z. Ahmed et al. [CDMS Collaboration], Phys. Rev. Lett. 102 (2009) 011301 [arXiv:0802.3530 [astro-ph]].
  * (76) C. E. Aalseth et al. [CoGeNT Collaboration], Phys. Rev. Lett. 101 (2008) 251301 [Erratum-ibid. 102 (2009) 109903] [arXiv:0807.0879 [astro-ph]].
  * (77) C. E. Aalseth et al. [CoGeNT collaboration], arXiv:1002.4703 [astro-ph.CO].
  * (78) S. Chang, J. Liu, A. Pierce, N. Weiner and I. Yavin, JCAP 1008 (2010) 018 [arXiv:1004.0697 [hep-ph]].
  * (79) J. Kopp, T. Schwetz and J. Zupan, JCAP 1002 (2010) 014 [arXiv:0912.4264 [hep-ph]].
  * (80) O. Adriani et al. [PAMELA Collaboration], Nature 458, 607 (2009) [arXiv:0810.4995 [astro-ph]].
  * (81) J. Chang et al., Nature 456, 362 (2008).
  * (82) F. Aharonian et al. [H.E.S.S. Collaboration], Phys. Rev. Lett. 101, 261104 (2008) [arXiv:0811.3894 [astro-ph]].
  * (83) A. A. Abdo et al. [The Fermi LAT Collaboration], Phys. Rev. Lett. 102, 181101 (2009) [arXiv:0905.0025 [astro-ph.HE]].
  * (84) Moskalenko, I. V. & Strong, A. W. Astrophys. J. 493, 694(1998).
  * (85) A. W. Strong and I. V. Moskalenko, Adv. Space Res. 27, 717 (2001) [arXiv:astro-ph/0101068].
  * (86) M. Aguilar et al. [AMS Collaboration], Phys. Rept. 366, 331 (2002) [Erratum-ibid. 380, 97 (2003)].
  * (87) S. W. Barwick et al., Astrophys. J. 498, 779 (1998) [arXiv:astro-ph/9712324].
  * (88) S. Torii et al., Astrophys. J. 559, 973 (2001).
  * (89) S. Torii et al. [PPB-BETS Collaboration], arXiv:0809.0760 [astro-ph].
  * (90) A. W. Strong, I. V. Moskalenko and O. Reimer, Astrophys. J. 613, 962 (2004) [arXiv:astro-ph/0406254].
  * (91) http://galprop.stanford.edu/web_galprop/galprop_home.html.
  * (92) http://www-ekp.physik.uni-karlsruhe.de/~zhukov/GalProp/galpropanal.html.
  * (93) http://apcauger.in2p3.fr/CRPropa/index.php
  * (94) C. Evoli, D. Gaggero, D. Grasso and L. Maccione, JCAP 0810 (2008) 018 [arXiv:0807.4730 [astro-ph]].
  * (95) http://crt.osu.edu/
  * (96) http://wwwasd.web.cern.ch/wwwasd/geant/
  * (97) L. Desorgher, E. O. Fluckiger, M. R. Moser and R. Butikofer, Prepared for 28th International Cosmic Ray Conferences (ICRC 2003), Tsukuba, Japan, 31 Jul - 7 Aug 2003
  * (98) See for example, A. Strumia, Talk at presented at Planck 2009, http://www.pd.infn.it/planck09/Talks/Strumia.pdf, and P. Meade, M. Papucci, A. Strumia and T. Volansky, arXiv:0905.0480 [hep-ph].
  * (99) P. Gondolo, J. Edsjo, P. Ullio, L. Bergstrom, M. Schelke and E. A. Baltz, JCAP 0407, 008 (2004) [arXiv:astro-ph/0406204].
  * (100) T. Delahaye, F. Donato, N. Fornengo, J. Lavalle, R. Lineros, P. Salati and R. Taillet, Astron. Astrophys. 501, 821 (2009) [arXiv:0809.5268 [astro-ph]].
  * (101) D. Hooper, P. Blasi and P. D. Serpico, JCAP 0901, 025 (2009) [arXiv:0810.1527 [astro-ph]].
  * (102) P. Blasi, arXiv:0903.2794 [astro-ph.HE].
  * (103) J. Gil, Y. Lyubarsky and G. I. Melikidze, Astrophys. J. 600, 872 (2004) [arXiv:astro-ph/0310621].
  * (104) S. Coutu et al. 1999, Astroparticle Physics, 11, 429
  * (105) Atoian, A. M., Aharonian, F. A., & Volk, H. J. Phys. Rev. D 52, 3265-3275 (1995).
  * (106) H. Yuksel, M. D. Kistler and T. Stanev, Phys. Rev. Lett. 103, 051101 (2009) [arXiv:0810.2784 [astro-ph]].
  * (107) Büsching, I., de Jager, O. C., Potgieter, M. S. & Venter, C. Astrophys. J. 78, L39-L42 (2008).
  * (108) M. Ahlers, P. Mertsch and S. Sarkar arXiv: 0909.4060 [astro-ph.HE]
  * (109) P. Mertsch and S. Sarkar, arXiv:0905.3152 [astro-ph.HE].
  * (110) J. Lavalle, Q. Yuan, D. Maurin and X. J. Bi, Astron. Astrophys. 479, 427 (2008) [arXiv:0709.3634 [astro-ph]].
  * (111) J. Hisano, S. Matsumoto and M. M. Nojiri, Phys. Rev. Lett. 92 (2004) 031303 [arXiv:hep-ph/0307216] ; J. Hisano, S. Matsumoto, M. M. Nojiri and O. Saito, Phys. Rev. D 71 (2005) 063528 [arXiv:hep-ph/0412403].
  * (112) For a recent discussion, please see, S. Hannestad and T. Tram, arXiv:1008.1511 [astro-ph.CO].
  * (113) D. J. H. Chung, E. W. Kolb and A. Riotto, Phys. Rev. D 60, 063504 (1999) [arXiv:hep-ph/9809453].
  * (114) S. Dodelson, A. V. Belikov, D. Hooper and P. Serpico, Phys. Rev. D 80, 083504 (2009) [arXiv:0903.2829 [astro-ph.CO]].
  * (115) A. V. Belikov and D. Hooper, arXiv:0906.2251 [astro-ph.CO].
  * (116) I. Cholis, G. Dobler, D. P. Finkbeiner, L. Goodenough, T. R. Slatyer and N. Weiner, arXiv:0907.3953 [astro-ph.HE].
  * (117) D. Hooper and K. M. Zurek, arXiv:0909.4163 [hep-ph].
  * (118) L. Goodenough and D. Hooper, arXiv:0910.2998 [hep-ph].
  * (119) M. Pato, L. Pieri and G. Bertone, arXiv:0905.0372 [astro-ph.HE].
  * (120) N. Arkani-Hamed, D. P. Finkbeiner, T. R. Slatyer and N. Weiner, Phys. Rev. D 79 (2009) 015014 [arXiv:0810.0713 [hep-ph]].
  * (121) See for example, A. Katz and R. Sundrum, JHEP 0906, 003 (2009) [arXiv:0902.3271 [hep-ph]].
  * (122) I. Cholis, L. Goodenough and N. Weiner, Phys. Rev. D 79, 123505 (2009) [arXiv:0802.2922 [astro-ph]].
  * (123) I. Cholis, L. Goodenough, D. Hooper, M. Simet and N. Weiner, arXiv:0809.1683 [hep-ph].
  * (124) I. Cholis, D. P. Finkbeiner, L. Goodenough and N. Weiner, arXiv:0810.5344 [astro-ph].
  * (125) D. Hooper and T. M. P. Tait, Phys. Rev. D 80, 055028 (2009) [arXiv:0906.0362 [hep-ph]].
  * (126) I. Gogoladze, N. Okada and Q. Shafi, Phys. Lett. B 679, 237 (2009) [arXiv:0904.2201 [hep-ph]].
  * (127) D. Hooper and K. M. Zurek, Phys. Rev. D 79, 103529 (2009) [arXiv:0902.0593 [hep-ph]].
  * (128) D. Hooper and G. D. Kribs, Phys. Rev. D 70, 115004 (2004) [arXiv:hep-ph/0406026].
  * (129) E. A. Baltz and J. Edsjo, Phys. Rev. D 59 (1998) 023511 [arXiv:astro-ph/9808243].
  * (130) M. Ibe, H. Murayama, S. Shirai and T. T. Yanagida, JHEP 0911, 120 (2009) [arXiv:0908.3530 [hep-ph]].
  * (131) A. Ibarra, D. Tran and C. Weniger, arXiv:0906.1571 [hep-ph].
  * (132) A. Ibarra, D. Tran and C. Weniger, Fermi LAT,” arXiv:0909.3514 [hep-ph].
  * (133) A. Ibarra and D. Tran, JCAP 0902, 021 (2009) [arXiv:0811.1555 [hep-ph]].
  * (134) E. Nardi, F. Sannino and A. Strumia, JCAP 0901, 043 (2009) [arXiv:0811.4153 [hep-ph]].
  * (135) W. Buchmuller, L. Covi, K. Hamaguchi, A. Ibarra and T. Yanagida, JHEP 0703, 037 (2007) [arXiv:hep-ph/0702184].
  * (136) I. Gogoladze, R. Khalid, Q. Shafi and H. Yuksel, Phys. Rev. D 79, 055019 (2009) [arXiv:0901.0923 [hep-ph]].
  * (137) W. Buchmuller, A. Ibarra, T. Shindou, F. Takayama and D. Tran, JCAP 0909, 021 (2009) [arXiv:0906.1187 [hep-ph]].
  * (138) A. Arvanitaki, S. Dimopoulos, S. Dubovsky, P. W. Graham, R. Harnik and S. Rajendran, Phys. Rev. D 79, 105022 (2009) [arXiv:0812.2075 [hep-ph]].
  * (139) A. Arvanitaki, S. Dimopoulos, S. Dubovsky, P. W. Graham, R. Harnik and S. Rajendran, Phys. Rev. D 80, 055011 (2009) [arXiv:0904.2789 [hep-ph]].
  * (140) M. R. Buckley, K. Freese, D. Hooper, D. Spolyar and H. Murayama, arXiv:0907.2385 [astro-ph.HE].
  * (141) M. Fairbairn and J. Zupan, arXiv:0810.4147 [hep-ph].
  * (142) D. Malyshev, I. Cholis and J. Gelfand, Phys. Rev. D 80, 063005 (2009) [arXiv:0903.1310 [astro-ph.HE]].
  * (143) D. Grasso et al. [FERMI-LAT Collaboration], arXiv:0905.0636 [astro-ph.HE].
  * (144) M. Kadastik, M. Raidal and A. Strumia, arXiv:0908.1578 [hep-ph].
  * (145) J. Hisano, M. Kawasaki, K. Kohri and K. Nakayama, Phys. Rev. D 79 (2009) 043516 [arXiv:0812.0219 [hep-ph]].
  * (146) J. Goodman, M. Ibe, A. Rajaraman, W. Shepherd, T. M. P. Tait and H. B. P. Yu, arXiv:1005.1286 [hep-ph]; J. Goodman, M. Ibe, A. Rajaraman, W. Shepherd, T. M. P. Tait and H. B. P. Yu, arXiv:1008.1783 [hep-ph].
  * (147) Z. Ahmed et al. [The CDMS-II Collaboration], arXiv:0912.3592 [astro-ph.CO].