Galaxy Clustering in 3D and Modified Gravity Theories

Abstract

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 ${\mathcal{C}}_{\ell }^s(k_1,k_2)$ 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 $\phi (r)\propto \exp (-r^2/r_0^2)$, $r_0=150h^{-1}\text{Mpc}$, and number density of galaxies $\bar{\text{N}}=10^{-4}{\text{Mpc}}^{-3}$, we use a ${\chi }^2$ analysis, and find that the lower-order $(\ell \le 25)$ multipoles of ${\mathcal{C}}_{\ell }^s(k,k^{\prime })$ (with radial modes restricted to $k<0.2h{\text{Mpc}}^{-1}$) 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.

21 pages, 15 Figures, 1 Table, Submitted to MNRAS

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• SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition
• The Integrated Bispectrum and Beyond
• Extracting the late-time kinetic Sunyaev-Zel'dovich effect
• The Integrated Bispectrum in Modified Gravity Theories
• Lensing-induced morphology changes in CMB temperature maps in modified gravity theories
• Consistency Relations in Effective Field Theory
• Flat-sky Angular Power Spectra Revisited
• Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
• Fast Generation of Weak Lensing Maps in Modified Gravity with COLA
• Fisher matrix for the angular power spectrum of multi-tracer galaxy surveys