**4. Generalized exponential power-law inflation**

The scheme for constructing models of the early universe based on the evolution of the scalar field in the context of the inflationary paradigm can be represented as follows:

To build cosmological models corresponding to observational data, we propose the principle of constructing the inflationary models with generalized exponential power-law expansion. For this aim we consider any exact solutions f g *ϕ; H;V* of Eqs. (3)–(5) for which the substitution of the slow-roll parameters (8)–(10) into Eqs. (13)–(17) doesn't correspond to observational constraints (17)–(18).

After the following transformations

$$
\overline{H} = \mathfrak{n}H + \lambda \tag{21}
$$

$$\overline{a}(t) = \mathbf{C}a^n(t)e^{\lambda t}, \mathbf{C} = \overline{a}\_0/a\_0^n \tag{22}$$

$$
\varphi = \sqrt{n}\phi\tag{23}
$$

$$
\overline{V}(\phi) = 3n^2H^2 + 6\lambda nH - nH\_{\phi}^{\prime 2} + 3\lambda^2,\\
\overline{V}(\phi) = \overline{V}(\phi(\varphi))\tag{24}
$$

one has new exact solutions *φ; H;V* � � with new slow-roll parameters

$$\overline{\epsilon} = n\epsilon \left( n + \frac{\lambda}{H(\epsilon)} \right)^{-2} \tag{25}$$

$$\overline{\delta} = \delta \left( n + \frac{\lambda}{H(\epsilon)} \right)^{-1} \tag{26}$$

and with the conformity to observational constraints which can be achieved by choosing the values of free constant parameters *n* and *λ*.

The proposed approach has two limitations:

a. The original scale factor *a t*ð Þ doesn't violate the law of accelerated expansion.

*The Early Universe as a Source of Gravitational Waves DOI: http://dx.doi.org/10.5772/intechopen.87946*

b.The potential *V*ð Þ *φ* corresponding to the scale factor (20) implies the evolution of the scalar field *φ*, according to the inflationary paradigm.

Transformations (21)–(24) define a class of models with the generalized exponential power-law dynamics, and the original scale factor *a t*ð Þ may not correspond to the condition of accelerated expansion *a*€>0; however, the resulting scale factor *a t*ð Þ implies a combination of the de Sitter solution (for *n* ¼ 0) and the power-law expansion (for *λ* ¼ 0), which corresponds to the basic feature of the inflationary paradigm implying a graceful exit from the stage of accelerated expansion to the power-law non-accelerated expansion.

#### **5. Relic gravitational waves**

Also, we note that the relic gravitational waves were not directly observed, which leads to a large number of theoretical models of cosmological inflation, which provide an explanation of the origin and evolution of the large-scale structure

The scheme for constructing models of the early universe based on the evolution of the scalar field in the context of the inflationary paradigm can be represented

a. The generating solutions of background dynamic equations (excluding quantum fluctuations of the scalar field) for a given potential, the law of accelerated expansion of the early universe, or the evolution of a scalar field.

b.Analysis of the quantum fluctuations of a scalar field and the corresponding metric perturbations on the basis of the theory of cosmological perturbation for the previously obtained background solutions. The result of this analysis is the values of the spectral parameters of cosmological perturbations

c. Comparison of the obtained spectral parameters of cosmological perturbations

To build cosmological models corresponding to observational data, we propose the principle of constructing the inflationary models with generalized exponential power-law expansion. For this aim we consider any exact solutions f g *ϕ; H;V* of Eqs. (3)–(5) for which the substitution of the slow-roll parameters (8)–(10) into Eqs. (13)–(17) doesn't correspond to observational constraints (17)–(18).

*λt*

*φ* ¼ ffiffiffi

*, C* ¼ *a*0*=an*

*ϕ* þ 3*λ*2

*λ H*ð Þϵ � ��2

*λ H*ð Þϵ � ��1

and with the conformity to observational constraints which can be achieved by

a. The original scale factor *a t*ð Þ doesn't violate the law of accelerated expansion.

*H* ¼ *nH* þ *λ* (21)

*n* p *ϕ* (23)

0 (22)

*,V*ð Þ¼ *φ V*ð Þ *ϕ φ*ð Þ (24)

(25)

(26)

of the universe and correspond to the observational constraints.

**4. Generalized exponential power-law inflation**

which can be calculated from Eqs. (13)–(17).

After the following transformations

*V*ð Þ¼ *ϕ* 3*n*2

with the corresponding observational data (18)–(20).

*a t*ðÞ¼ *Can*ð Þ*t e*

*H*2 þ 6*λnH* � *nH*02

one has new exact solutions *φ; H;V* � � with new slow-roll parameters

ϵ ¼ *n*ϵ *n* þ

*δ* ¼ *δ n* þ

choosing the values of free constant parameters *n* and *λ*. The proposed approach has two limitations:

as follows:

*Progress in Relativity*

**228**

As an additional verification tool for cosmological models, we consider the possibility of direct detection of the relic gravitational waves. The detection of relic gravitational waves is extremely important for determining the parameters of the models of early universe. Additionally, such a detection enhances the position of the inflationary paradigm compared to alternative scenarios, for example, the models with a rebound from singularity in which cosmological gravitational waves are absent [19].

As the main observational characteristic of relic gravitational waves, we consider the energy density, which is usually determined by the dimensionless quantity [20]:

$$
\Omega\_{GW}(f) = \frac{1}{\rho\_c} \frac{d\rho\_{GW}}{d\ln f} \tag{27}
$$

where *f* is the linear frequency, *ρc* ¼ 3*H*2 0 is the critical energy density, *H*0 is the value of the Hubble parameter in the modern era, and *ρGW* is the energy density of gravitational waves.

Also, the energy density of relic gravitational waves can be represented in terms of the power spectrum:

$$
\Omega\_{GW}(k) = \frac{k^2}{12H\_0^2} P\_T(k) \tag{28}
$$

The frequency and energy density of relic gravitational waves are limited by the following conditions [20]:

a. The energy density of relic gravitational waves should not exceed

$$\int\_{f\_0}^{\infty} \Omega\_{GW} d\ln f \le \mathbf{1.1} \times \mathbf{10}^{-5} \tag{29}$$

where *f* 0≈10�9 Hz.

a. The temperature of the scalar field *T*∗ and the frequency of gravitational waves *f* at the end of the inflation stage are

$$T\_\* = 5.85 \times 10^6 \left(\frac{f}{Hz}\right) \left(\frac{g\_\*}{106.75}\right)^{1/6} \text{GeV} \tag{30}$$

$$f = 1.71 \times 10^{-7} \left(\frac{T\_\*}{\text{GeV}}\right) \left(\frac{\text{g}\_\*}{106.75}\right)^{-1/6} Hz \tag{31}$$

**6. Conclusion**

observational constraints.

**Author details**

**231**

Vladimir Gladyshev\* and Igor Fomin

provided the original work is properly cited.

Bauman Moscow State Technical University, Moscow, Russia

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to<EMAIL_ADDRESS>
exponential power-law dynamics are proposed.

*The Early Universe as a Source of Gravitational Waves DOI: http://dx.doi.org/10.5772/intechopen.87946*

low-frequency optical resonance proposed in [23, 24].

We considered the basis of building and verifying of the inflationary models of early universe. As the method for constructing the exact cosmological solutions corresponding to observational constraints, the models with generalized

The verification of the relevance of such models is related to the estimation of the contribution of relic gravitational waves to the anisotropy and polarization of the cosmic microwave background radiation. Therefore, there are a lot of infla-

The most obvious way to significantly reduce the number of theoretical models

The most promising methods in this area of experimental research are using the

interferometers as detectors. The interesting direction of the observation is the detection of high-frequency relic gravitational waves using the effect of

tionary models with different scalar field potentials that will satisfy the

of cosmological inflation is direct detection of relic gravitational waves.

where *g* ∗ is the effective number of the degrees of freedom (in standard model of elementary particles *g* ∗ ¼ 106*:*75).

Therefore, conditions (18) and (21)–(23) impose restrictions on the parameters of relic gravitational waves.

The application to the analysis of the models of the early universe only of the slow-roll approximation implies a low-frequency spectrum of relic gravitational waves in the range of 10�18 � 10�16 Hz [20]. However, the predominance of the kinetic energy of the scalar field during the evolution of the early universe provides a theoretical justification for the existence of high-frequency relic gravitational waves in models with one scalar field in the range of 102 � 104 Hz [21] which can be used as affordable means of verification of models of the early universe in the presence of physical effects that increase the sensitivity of the detector to the required level.

Currently, the most productive method of direct detection of gravitational waves is the use of interferometers as detectors, which was proposed in the article by Gertsenshtein and Pustovoit [22]. This principle is widely used in modern laser interference gravitational antennas, the main element of which is the Fabry-Perot interferometer. These are broadband gravitational antennas, which offer a lot of opportunities as to the methods of recording of gravitational waves and extracting signals, as well as the use of quantum non-perturbative measurements and the inclusion of gravitational antennas in the network. The main element of laser interference gravitational antennas, as a rule, is Fabry-Perot multipath free-mass resonator, on whose properties the sensitivity and noise immunity of the entire gravitational antenna largely depend [4, 23, 24].

After creating the first laser interferometer for detecting gravitational waves, systematic work began on the creation and improvement of such devices in various laboratories around the world. The experience of gravitational antenna projects by VIRGO (Italy, France), LIGO (USA), TAMA (Japan), CLIO (Japan), GEO-600 (Germany), and OGRAN (Russia) will certainly be used to create more compact and highly sensitive antennas of new generation [4]. Also, as the most promising project for the direct detection of gravitational waves, work on the creation of a space interferometer in a helio-stationary orbit should be noted, in which the distance between the mirrors will be about 1 million kilometers. This project is called Laser Interferometer Space Antenna (LISA) [25]. The implementation of the LISA project is scheduled for 2029.

One of the promising methods for increasing the sensitivity of gravitational antennas in the high-frequency region of the spectrum is to use the phenomenon of low-frequency optical resonance, which distinguishes this approach from other projects on the detection of gravitational waves. The presence of this effect in Fabry-Perot interferometers was first considered in [23, 24]. At the moment, there is a high-frequency gravitational wave detector, which was built at the University of Birmingham, United Kingdom [26]. Also, it is planned to build the high-frequency gravitational wave detectors in Japan [27].

Thus, at the moment there are a large number of promising methods for direct observation of gravitational waves, which correspond to the ability to measure the characteristics of relic gravitational waves for a better understanding of the physical processes occurring in the early universe.


*Supporting open minds since 2005*

Thymus http://dx.doi.org/10.5772/intechopen.73777 Edited by Nima Rezaei

#### Contributors

Dragoș Cătălin Jianu, Silviana Nina Jianu, Claudia Birsan, Rachel Thomas, Dong-Ming Su, Sarai Belchi-Navarro, Ana-Belen Sabater-Jara, María Pina Funes, Maria A. Pedreño, Ali Kouhi, Saeed Sohrabpour, Krisztian Kvell, Ildikó Bódi, Krisztina H.-Minkó, Zsolt Prodán, Imre Oláh, Robin Cornelissen, Arbab Sikandar, Shahzaib Shahzaib, Naeem Ullah, Teresa Fortoul, Martha Ustarroz-Cano, Nelly López-Valdez, Isabel García-Peláez, Marisol Lopea-Angel, Nima Rezaei, Amene Saghazadeh

#### © The Editor(s) and the Author(s) 2020

The rights of the editor(s) and the author(s) have been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights to the book as a whole are reserved by INTECHOPEN LIMITED. The book as a whole (compilation) cannot be reproduced, distributed or used for commercial or non-commercial purposes without INTECHOPEN LIMITED's written permission. Enquiries concerning the use of the book should be directed to INTECHOPEN LIMITED rights and permissions department (permissions@intechopen.com).

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Individual chapters of this publication are distributed under the terms of the Creative Commons Attribution 3.0 Unported License which permits commercial use, distribution and reproduction of the individual chapters, provided the original author(s) and source publication are appropriately acknowledged. If so indicated, certain images may not be included under the Creative Commons license. In such cases users will need to obtain permission from the license holder to reproduce the material. More details and guidelines concerning content reuse and adaptation can be found at http://www.intechopen.com/copyright-policy.html.

#### Notice

Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book.

First published in London, United Kingdom, 2020 by IntechOpen IntechOpen is the global imprint of INTECHOPEN LIMITED, registered in England and Wales, registration number: 11086078, 7th floor, 10 Lower Thames Street, London, EC3R 6AF, United Kingdom Printed in Croatia

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Paraffin - an Overview

## *Edited by Fathi Samir Soliman*

Published in London, United Kingdom

## *Supporting open minds since 2005*

Paraffin - an Overview http://dx.doi.org/10.5772/intechopen.75234 Edited by Fathi Samir Soliman

#### Contributors

Keshawa Shukla, Mayank Vishal Labh, Amir Reza Vakhshouri, Erika C.A. Nunes Chrisman, Márcio N. Souza, Angela C. P. Duncke, Marcia C.K. Oliveira, Wenye Lin, Zhenjun Ma, Haoshan Ren, Jingjing Liu, Kehua Li, Fathi Samir Soliman

#### © The Editor(s) and the Author(s) 2020

The rights of the editor(s) and the author(s) have been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights to the book as a whole are reserved by INTECHOPEN LIMITED. The book as a whole (compilation) cannot be reproduced, distributed or used for commercial or non-commercial purposes without INTECHOPEN LIMITED's written permission. Enquiries concerning the use of the book should be directed to INTECHOPEN LIMITED rights and permissions department (permissions@intechopen.com).

Violations are liable to prosecution under the governing Copyright Law.

Individual chapters of this publication are distributed under the terms of the Creative Commons Attribution 3.0 Unported License which permits commercial use, distribution and reproduction of the individual chapters, provided the original author(s) and source publication are appropriately acknowledged. If so indicated, certain images may not be included under the Creative Commons license. In such cases users will need to obtain permission from the license holder to reproduce the material. More details and guidelines concerning content reuse and adaptation can be found at http://www.intechopen.com/copyright-policy.html.

#### Notice

Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book.

First published in London, United Kingdom, 2020 by IntechOpen IntechOpen is the global imprint of INTECHOPEN LIMITED, registered in England and Wales, registration number: 11086078, 5 Princes Gate Court, London, SW7 2QJ, United Kingdom Printed in Croatia

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library

Additional hard and PDF copies can be obtained from<EMAIL_ADDRESS>
Paraffin - an Overview Edited by Fathi Samir Soliman p. cm. Print ISBN 978-1-83880-594-4 Online ISBN 978-1-83880-595-1 eBook (PDF) ISBN 978-1-83880-596-8


**1. Introduction**

Information-psychological impact (IPI) is the informational influence on people's minds, which alters their perception of the reality, behavioural functions and, in some cases, even the functioning of their inner organs and body systems [1–3]. Information-psychological impact (IPI) may affect individuals, groups of people, communities and the whole society. IPI can be either positive or negative, depending on the intended purpose. Positive IPI is used for medical treatment purposes, rehabilitation, improvement of behavioural patterns and creative purposes. It can also be used to unite people for a good cause. Negative IPI is used for manipulating—directly or indirectly—individuals, groups of people or the whole society into actions that violate either their own interests or interests of others. Negative IPI may cause emotional, psychological and social tensions, deterioration of moral standards and behavioural norms, as well as moral and political disorientation. This, in turn, leads to dramatic changes in individual, group and public

conscience and alterations in the moral, political, social and psychological environment within the society [1–3].

Information-psychological impact is implemented by means of various tools and techniques. At the moment, negative information-psychological impacts are more common. They influence individuals, groups of people or the society by means of telecommunication systems, mass media and social networks. Negative IPIs are used to control the society, force certain opinions on various issues, recruit members to religious cults and terrorist groups and to alter people's mental state. Among the examples of such IPIs are colour revolutions, the so-called "death groups" on social networking sites, as well as active recruitment campaigns to terrorist groups, which are based on films or video games aimed primarily at young people.

subject are presented as vector *yt* and change under the influence of other

ferromagnetism, Ising model is often used to verify the results of numerical modelling. When studying the diffusion of IPI in social networks, the model helps to describe the changes in the behaviour of a large social group caused by the nearest neighbours. The influence of the nearest neighbours plays a key role, and the willingness of the group to accept a new idea serves as the

4. Influence models based on Markov chains. Such models employ corresponding mathematical tools to represent the activities of every subject and the group as a whole. They are used to analyse social dynamics and determine the patterns of the group behaviour. The authors [22–24] consider the similarity of opinions of the subject, the authors [7, 24] focus on the time over which the opinions become similar, and the authors [7, 25] study the conditions under

All the above-mentioned models represent the rules of interaction between the subjects or groups of subjects. However, they either do not at all represent the specifics and characteristics of the network influence and the interaction process or

When a social network is considered as a set of agents [4, 26–28], we assume

therefore necessary to determine a small group of agents with the maximal level of influence, that is, to solve the influence maximisation problem [4, 10, 29]. These agents can be used as key nods for influencing other subjects of the social network

that every agent has a certain degree of influence on the other agents. It is

or to monitor the social network in order to reveal the presence of IPI. The influence maximisation problem has been considered in papers focusing on the

• Viral marketing [29], where a social network is represented by a Markov chain with each agent A having his own value that depends on the profit from

• Influence maximisation in the models of innovations' diffusion [10]. They include a set of active agents, and at a certain point in time, a new active agent

• Voting process modelling [9], where every agent can, at any stage, change his opinion by accidentally voting for one of his neighbours and adapting their opinion. The agent is more likely to adapt the opinion supported by the

Besides analysing the influence, management and confrontation, there is also a problem of diffusion of information-psychological impact in the information space [5]. Information may spread in the following directions [5, 30]: from a subject to another subject, from a subject to a group, from the information production centre

The authors [5, 26–28, 31] suggest a multi-agent model of information diffusion. The model takes into account the growth of the number of agents over time. Agents

.

subjects according to the so-called influence matrix *W*: *yt*þ1 ¼ *Wyt*

3. Ising models [20, 21]. Invented for studying the phenomenon of

*Modelling the Information-Psychological Impact in Social Networks*

analogue of the temperature.

*DOI: http://dx.doi.org/10.5772/intechopen.88252*

do this inadequately.

following issues.

which a uniform final opinion is formed.

sales to other agents influenced by agent A.

majority of his neighbours.

to an individual subject or a group.

**295**

can activate his neighbours with a set probability.

It is thus very important to model IPIs in social networks in order to analyse and select the most effective methods of using positive IPIs and combating negative IPIs [1, 2, 4].