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 which show similar cosmic acceleration at z ~ 1, can produce quite different normalization for large scale density fluctuations, ie sigma_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 Omega_M ~ 0.22, DGP and standard Cardassian cosmologies predict about 2 and 3 times more clusters respectively than the standard Lambda model at z=1.5. When normalized to CMB fluctuations the sigma_8 amplitude turns out to be lower by a few tens of a percent. We also find that, for a limited red-shift range, the linear growth rate can be faster in some models (eg modified polytropic Cardassian with q>1) than in the Einstein-deSitter universe. The value of the skewness S_3 is found to have up to ~10 percent variations (up or down) from model to model.