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 \simeq 1 , can produce quite different normalization for large scale density fluctuations , i.e . \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 } \simeq 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 \simeq 10 \% percent variations ( up or down ) from model to model .