Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid

TL;DR

This paper investigates how galaxy bispectrum multipoles can detect deviations from General Relativity in modified gravity models, specifically within the context of Euclid-like surveys, using perturbation theory.

Contribution

It introduces a detailed perturbation theory calculation of the redshift-space galaxy bispectrum multipoles in Hu-Sawicki f(R) gravity, including nonlinear screening effects and forecasts their detectability.

Findings

Monopole and quadrupole bispectrum multipoles show 2-8% deviations at z=0.7 for f_{R0}=10^{-5}.

Forecasted signal-to-noise ratios are up to 30 for the monopole and 15 for the quadrupole in Euclid-like surveys.

Bispectrum multipoles can effectively break degeneracies and improve constraints on modified gravity.

Abstract

We study the galaxy bispectrum multipoles in the Hu-Sawicki $f(R)$ gravity model, where a scalar degree of freedom mediates a fifth force that is screened in high-density environments. The model is specified by $f_{R0}$, the present-day background value of the scalar field, which controls the strength of deviations from General Relativity (GR). Using perturbation theory, we compute the redshift-space galaxy bispectrum with the full scale- and time-dependent second-order kernels, incorporating corrections from the scale-dependent growth rate and nonlinear screening. Expanding the bispectrum in spherical harmonics, we analyze the sensitivity of the multipoles to modified gravity and forecast their detectability in a \textit{Euclid}-like survey. The monopole ($B_0^0$) and quadrupole ($B_2^0$) show the strongest signatures, with relative deviations of $2\%$--$8\%$ at $z=0.7$ and $k_1\simeq0.3\,h\,{\rm Mpc}^{-1}$ (largest side of the triangle) for $f_{R0}=10^{-5}$. Higher multipoles provide weaker but complementary signals. For \textit{Euclid}, we forecast signal-to-noise ratios up to $\sim30$ for the monopole and $\sim15$ for the quadrupole including the Finger-of-God damping and shot noise effect. These results demonstrate that bispectrum multipoles are a powerful probe of gravity, capable of breaking degeneracies with bias and velocity effects and strengthening constraints on deviations from $\Lambda$CDM.