Galaxy clustering in 3D and modified gravity theories

We study Modified Gravity (MG) theories by modelling the redshifted matter power spectrum in a spherical Fourier-Bessel (sFB) basis. We use a fully non-linear description of the real-space matter power-spectrum and include the lowest-order redshift-space correction (Kaiser effect), taking into account some additional non-linear contributions. Ignoring relativistic corrections, which are not expected to play an important role for a shallow survey, we analyse two different modified gravity scenarios, namely the generalised Dilaton scalar-tensor theories and the f(R) models in the large curvature regime. We compute the 3D power spectrum C s l (k 1 ,k 2 ) for various such MG theories with and without redshift space distortions, assuming precise knowledge of background cosmological parameters. Using an all-sky spectroscopic survey with Gaussian selection function f(r)?exp(-r 2 /r 2 0 ) , r 0 =150h -1 Mpc , and number density of galaxies N ¯ =10 -4 Mpc -3 , we use a ? 2 analysis, and find that the lower-order (l=25) multipoles of C s l (k,k ' ) (with radial modes restricted to k<0.2hMpc -1 ) can constraint the parameter f R 0 at a level of 2×10 -5 (3×10 -5 ) with 3s confidence for n=1(2) . Combining constraints from higher l>25 modes can further reduce the error bars and thus in principle make cosmological gravity constraints competitive with solar system tests. However this will require an accurate modelling of non-linear redshift space distortions. Using a tomographic ß(a) -m(a) parameterization we also derive constraints on specific parameters describing the Dilaton models of modified gravity.