Validity of the 'conservation law' in the evolution of cosmological perturbations

It is shown that the 'conservation law' for metric fluctuations with long wavelengths is indeed applicable for growing modes of perturbations, which are of interest in cosmology, in spite of recent criticism. This is demonstrated both by general arguments and by presenting an explicitly solvable toy model for the evolution of metric perturbations during inflation.     

Formulae for growth factors in expanding universes containing matter and a cosmological constant

Formulae are presented for the linear growth factor D a and its logarithmic derivative d ln  D /d ln a in expanding Friedmann–Robertson–Walker universes with arbitrary matter and vacuum densities. The formulae permit rapid and stable numerical evaluation. A fortran program is available at http://casa.colorado.edu/~ajsh/growl/.     

CDM models with a BSI step-like primordial spectrum and a cosmological constant

A class of spatially flat models with cold dark matter (CDM), a cosmological constant and a broken-scale-invariant (BSI) step-like primordial (initial) spectrum of adiabatic perturbations, generated in an exactly solvable inflationary model where the inflaton potential has a rapid change of its first derivative at some point, is confronted with existing observational data on angular fluctuations of the CMB temperature, galaxy clustering and peculiar velocities of galaxies. If we locate the step in the initial spectrum at k  ≃ 0.05  h Mpc⁻¹, where a feature in the spectrum of Abell clusters of galaxies was found that could reflect a property of the initial spectrum, and if the large-scale flat plateau of the spectrum is normalized according to the COBE data, the only remaining parameter of the spectrum is p — the ratio of amplitudes of the metric perturbations between the small-scale and large-scale flat plateaux. Allowed regions in the plane of parameters (Ω = 1 − Ω_Λ,  H ₀) satisfying all data have been found for p lying in the region (0.8–1.7). Especially good agreement of the form of the present power spectrum in this model with the form of the cluster power spectrum is obtained for the inverted step ( p  < 1,  p  = 0.7–0.8), when the initial spectrum has slightly more power on small scales.     

Phase information and the evolution of cosmological density perturbations

The Fourier transform of cosmological density perturbations can be represented in terms of amplitudes and phases for each Fourier mode. We investigate the phase evolution of these modes using a mixture of analytical and numerical techniques. Using a toy model of one-dimensional perturbations evolving under the Zel'dovich approximation as an initial motivation, we develop a statistic that quantifies the information content of the distribution of phases. Using numerical simulations beginning with more realistic Gaussian random-phase initial conditions, we show that the information content of the phases grows from zero in the initial conditions, first slowly and then rapidly when structures become non-linear. This growth of phase information can be expressed in terms of an effective entropy. Gaussian initial conditions are a maximum entropy realization of the initial power spectrum; gravitational evolution decreases the phase entropy. We show that our definition of phase entropy results in a statistic that explicitly quantifies the information stored in the phases of density perturbations (rather than their amplitudes), and that this statistic displays interesting scaling behaviour for self-similar initial conditions.     

Scalar perturbations in two-temperature cosmological plasmas

We study the properties of density perturbations of a two-component plasma with a temperature difference on a homogeneous and isotropic background. For this purpose, we extend the general relativistic gauge-invariant and covariant (GIC) perturbation theory to include a multifluid with a particular equation of state (ideal gas) and imperfect fluid terms due to the relative energy flux between the two species. We derive closed sets of GIC vector and subsequently scalar evolution equations. We then investigate solutions in different regimes of interest. In particular, we study long-wavelength and arbitrary-wavelength Langmuir and ion-acoustic perturbations. The harmonic oscillations are superposed on a Jeans-type instability. We find a generalized Jeans criterion for collapse in a two-temperature plasma, which states that the species with the largest sound velocity determines the Jeans wavelength. Furthermore, we find that within the limit for gravitational collapse, initial perturbations in either the total density or charge density lead to a growth in the initial temperature difference. These results are relevant for the basic understanding of the evolution of inhomogeneities in cosmological models.     

Evolution of the cosmological density distribution function

We present a new calculation for the evolution of the one-point probability distribution function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman–Kolmogorov equation and second-order Eulerian perturbation theory we propagate the initial density distribution into the non-linear regime. Our calculations yield the moment generating function, allowing a straightforward derivation of the skewness of the PDF to second order. We find a new dependence on the initial perturbation spectrum. We compare our results with other approximations to the one-point PDF, and with N -body simulations. We find that our distribution accurately models the evolution of the one-point PDF of dark matter.     

Virialization of cosmological structures in models with time-varying equation of state

We study the virialization of the cosmic structures in the framework of flat cosmological models where the dark energy component plays an important role in the global dynamics of the Universe. In particular, our analysis focuses on the study of the spherical matter perturbations, as the latter decouple from the background expansion, start to 'turn around' and finally collapse. We generalize this procedure, taking into account models with an equation of state which vary with time, and provide a complete formulation of the cluster virialization attempting to address the non-linear regime of structure formation. In particular, assuming that clusters have collapsed prior to the epoch of z _f≃ 1.4, in which the most distant cluster has been found, we show that the behaviour of the spherical collapse model depends on the functional form of the equation of state.     

Parameter information from non-linear cosmological fields

We develop a general formalism for analysing parameter information from non-Gaussian cosmic fields. The method can be adapted to include the non-linear effects in galaxy redshift surveys, weak lensing surveys and cosmic velocity field surveys as part of parameter estimation. It can also be used as a test of non-Gaussianity of the cosmic microwave background. Generalizing maximum-likelihood analysis to second order, we calculate the non-linear Fisher information matrix and likelihood surfaces in parameter space. To this order we find that the information content is always increased by including non-linearity. Our methods are applied to a realistic model of a galaxy redshift survey, including non-linear evolution, galaxy bias, shot-noise and redshift-space distortions to second order. We find that including non-linearities allows all of the degeneracies between parameters to be lifted. Marginalized parameter uncertainties of a few per cent will then be obtainable using forthcoming galaxy redshift surveys.     

The spherical infall model in a cosmological background density field

We discuss the influence of the cosmological background density field on the spherical infall model. The spherical infall model has been used in the PressSchechter formalism to evaluate the number abundance of clusters of galaxies, as well as to determine the density parameter of the Universe from the infalling flow. Therefore, the understanding of collapse dynamics plays a key role for extracting cosmological information. Here, we consider a modified version of the spherical infall model. We derive the mean field equations from the Newtonian fluid equations, in which the influence of cosmological background inhomogeneity is incorporated into the averaged quantities as the backreaction . By calculating the averaged quantities explicitly, we obtain simple expressions and find that, in the case of a scale-free power spectrum, density fluctuations with a negative spectral index make the infalling velocities slow. This suggests that we underestimate the density parameter when using the simple spherical infall model. In cases with the index n >0, the effect of background inhomogeneity could be negligible and the spherical infall model becomes a good approximation for infalling flows. We also present a realistic example with a cold dark matter power spectrum. In this case, the mean infall tends to be slow owing to the anisotropic random velocity.     

Linear redshift distortions and power in the IRAS Point Source Catalog Redshift Survey

We present a state-of-the-art linear redshift distortion analysis of the recently published IRAS Point Source Catalog Redshift Survey (PSC z ). The procedure involves linear compression into 4096 KarhunenLoève (signal-to-noise) modes culled from a potential pool of 310⁵ modes, followed by quadratic compression into three separate power spectra, the galaxygalaxy, galaxyvelocity and velocityvelocity power spectra. Least squares-fitting to the decorrelated power spectra yields a linear redshift distortion parameter     

Voids in a ΛCDM universe

We study the formation and evolution of voids in the dark matter distribution using various simulations of the popular Λ cold dark matter cosmogony. We identify voids by requiring them to be regions of space with a mean overdensity of −0.8 or less – roughly the equivalent of using a spherical overdensity group finder for haloes. Each of the simulations contains thousands of voids. The distribution of void sizes in the different simulations shows good agreement when differences in particle and grid resolution are accounted for. Voids very clearly correspond to minima in the smoothed initial density field. Apart from a very weak dependence on the mass resolution, the rescaled mass profiles of voids in the different simulations agree remarkably well. We find a universal void mass profile of the form  ρ(< r )/ρ( r _eff) ∝ exp[( r / r _eff)^α]  , where r _eff is the effective radius of a void and  α∼ 2  . The mass function of haloes in voids is steeper than that of haloes that populate denser regions. In addition, the abundances of void haloes seem to evolve somewhat more strongly between redshifts ∼1 and 0 than the global abundances of haloes.     

The growth of linear perturbations in generic defect models for structure formation

We study the growth of linear perturbations induced by a generic causal scaling source as a function of the cosmological parameters h ,     and     . We show that for wavenumbers k ≳0.01  h  Mpc⁻¹ the spectrum of density and velocity perturbations scales in a similar way to that found in inflationary models with primordial perturbations. We show that this result is independent of the more-or-less incoherent nature of the source, the small-scale power spectrum of the source and of deviations from scaling that naturally occur at late times if     .