Tracking the Local Group Dynamics by Extended Gravity

TL;DR

This paper investigates the dynamics of the Local Group within extended gravity theories, deriving constraints on Yukawa-like interactions and exploring if modified gravity can replace dark matter, with implications for cosmological models.

Contribution

It introduces constraints on Yukawa couplings in $f(R)$ gravity and examines the potential of $f(R) ightarrow R^{1+ ext{small } extepsilon}$ theories to mimic dark matter effects in the Local Group.

Findings

Constraints on Yukawa coupling $ ext{alpha} < 0.581$ and $m_{grav} < 5.095 imes 10^{-26} eV/c^2$.

Identification of a parameter $eta$ that minimizes the Local Group mass in $f(R)$ models.

Potential to falsify MOND-like theories based on the dark matter to baryonic matter ratio.

Abstract

The Local Group (LG) of galaxies, modeled as a two body problem, is sensitive to cosmological contributions like those related to the presence of a cosmological constant $\Lambda$ into dynamics. Here we study the LG dynamics in the context of Extended Theories of Gravity like $f(R)$ gravity considered as dark energy and dark matter contributions. In the first approach, we perturb the dark energy effect considering a Yukawa-like interaction that naturally emerges from $f(R)$ gravity in the weak field limit. We assume the mass of LG from simulations and, from this, derive constraints on the Yukawa couplings: $\alpha < 0.581$ and $m_{grav} < 5.095 \cdot 10^{-26} \, eV/c^2$. In the second part, considering a minimal extension of General Relativity, i.e. $f(R) \sim R^{1+\epsilon}$, with $|\epsilon|\ll 1$, we investigate the possibility that it replaces dark matter as a MOND-like theory. We find that there is a value of the parameter $\beta$ (derived starting from $\epsilon$) which gives a minimal value for the LG mass. Moreover, this particular potential allows to calculate the ratio of dark matter and baryonic matter for the LG to be. We show that this ratio could falsify MOND-like theories.