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.
