1.3. Inflation and perturbations
A complete description of the Universe should include a description of deviations from homogeneity, at least in a statistical way. Indeed, some of the most powerful probes of the parameters described above come from
1.3. Inflation and perturbations
A complete description of the Universe should include a description of deviations from homogeneity, at least in a statistical way. Indeed, some of the most powerful probes of the parameters described above come from studying the evolution of perturbations, so their study is naturally intertwined in the determination of cosmological parameters.
There are many different notations used to describe the perturbations, both in terms of the quantity used to describe the perturbations and the definition of the statistical measure. We use the dimensionless power spectrum 2 as defined in Olive and Peacock (also denoted in some of the literature). If the perturbations obey Gaussian statistics, the power spectrum provides a complete description of their properties.
From a theoretical perspective, a useful quantity to describe the perturbations is the curvature perturbation, which measures the spatial curvature of a comoving slicing of the space-time. A case of particular interest is the Harrison-Zel'dovich spectrum, which corresponds to a constant spectrum 2. More generally, one can approximate the spectrum by a pow