Large-scale structure in non-standard cosmologies

Abstract

We study the growth of large‐scale structure in two recently proposed non‐standard cosmological models: the ‘brane’ induced gravity model of Dvali, Gabadadze and Porrati (DGP) and the ‘Cardassian’ models of Freese and Lewis. A general formalism for calculating the growth of fluctuations in models with a non‐standard Friedman equation and a normal continuity equation of energy density is discussed. Both linear and non‐linear growth are studied, together with their observational signatures on higher‐order statistics and abundance of collapsed objects. In general, models that show similar cosmic acceleration at z≃ 1 can produce quite different normalization for large‐scale density fluctuations, i.e. σ8, cluster abundance or higher‐order statistics, such as the normalized skewness S3, which is independent of the linear normalization. For example, for a flat universe with ΩM≃ 0.22, DGP and standard Cardassian cosmologies predict about two and three times more clusters respectively than the standard Λ model at z= 1.5. When normalized to cosmic microwave background fluctuations, the σ8 amplitude turns out to be lower by a few tens of per cent. We also find that, for a limited redshift range, the linear growth rate can be faster in some models (e.g. modified polytropic Cardassian with q > 1) than in the Einstein–de Sitter universe. The value of the skewness S3 is found to have up to ≃10 per cent variations (up or down) from model to model.

Large scale structure and the generalized Chaplygin gas as dark energy

“…Within the spherical collapse approximation one can show that in a matter dominated universe (i.e. the collapsing matter has no pressure) [32,33] …”

“…The linear and non-linear growth can be related to observations and hence lead to observational constraints like galaxy number counts (see [32]). Our approach is similar to [32,33], where other non-standard cosmologies have been considered (also see [35] for related discussions). In Section 2 we review and study properties of GCg cosmology.…”

Latest observational constraints on Cardassian models

“…As we know, many observational constraints have been placed on Cardassian models, including those from the angular size of high-z compact radio sources [21], the SNe Ia [22,23,24,25,26,27,28,29,30,31,32], the shift parameter of the CMB [23,28,32,33], the baryon acoustic peak from the SDSS [23,33], the gravitational lensing [34], the x-ray gas mass fraction of clusters [29,35], the large scale structure [32,36,37], and the Hubble parameter versus redshift data [33,38].…”

Modifying gravity: you cannot always get what you want

“…Consider a uniform overdensity in a localized spherical region such that 10) wherer is the background matter density that follows cosmological evolution. Parametrizing time evolution using x = 8pGr/3H 2 0 , the growing perturbation mode d(x) goes as [53,55],…”