Galaxy clustering in 3D and modified gravity theories

Dipak Munshi (1) , Geraint Pratten (1) , Patrick Valageas (2, 3) , Peter Coles (1) , Philippe Brax (2, 3)

1 Astronomy Centre, University of Sussex
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 CNRS - Centre National de la Recherche Scientifique

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.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Dipak Munshi, Geraint Pratten, Patrick Valageas, Peter Coles, Philippe Brax. Galaxy clustering in 3D and modified gravity theories. Monthly Notices of the Royal Astronomical Society, 2016, 456, pp.1627-1644. ⟨10.1093/mnras/stv2724⟩. ⟨cea-01199525⟩