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 \({\cal C}^s_{\ell}(k_1,k_2)\) 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 \(\varphi(r)\propto \exp(-{r^2 / r^2_0})\), \(r_0 = 150 \, h^{-1} \, {\textrm{Mpc}}\), and number density of galaxies \(\bar {\textrm{N}} =10^{-4}\;{\textrm{Mpc}}^{-3}\), we use a \(\chi^2\) analysis, and find that the lower-order \((\ell \leq 25)\) multipoles of \({\cal C}^s_\ell(k,k')\) (with radial modes restricted to \(k < 0.2 \, h \,{\textrm{Mpc}}^{-1}\)) can constraint the parameter \(f_{R_0}\) at a level of \(2\times 10^{-5} (3\times 10^{-5})\) with \(3 \sigma\) confidence for \(n=1(2)\). Combining constraints from higher \(\ell > 25\) 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 \(\beta(a)\)-\(m(a)\) parameterization we also derive constraints on specific parameters describing the Dilaton models of modified gravity.