Large-scale structure in non-standard cosmologies

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. 8 , cluster abundance or higher-order statistics, such as the normalized skewness S 3 , which is independent of the linear normalization. For example, for a flat universe with M 0.22, DGP and standard Cardassian cosmologies predict about two and three times more clusters respectively than the standard model at z = 1.5. When normalized to cosmic microwave background fluctuations, the 8 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 S 3 is found to have up to 10 per cent variations (up or down) from model to model.