$f(Q,L_m)$ gravity, and its cosmological implications

TL;DR

This paper introduces a new $f(Q, ext{L}_m)$ gravity theory that incorporates explicit geometry-matter coupling, derives its field equations, and explores its cosmological implications, offering potential alternatives to standard cosmology.

Contribution

It proposes a generalized $f(Q, ext{L}_m)$ gravity model with explicit matter coupling, deriving field equations and analyzing cosmological solutions beyond existing $f(Q)$ theories.

Findings

Derived generalized field equations for $f(Q, ext{L}_m)$ gravity.

Obtained modified Friedmann equations for FLRW universe.

Compared specific models with $ ext{Lambda CDM}$ and discussed observational implications.

Abstract

Symmetric teleparallel gravity and its $f(Q)$ extensions have emerged as promising alternatives to General Relativity (GR), yet the role of explicit geometry-matter couplings remains largely unexplored. In this work, we address this gap by proposing a generalized $f(Q,\mathcal{L}_m)$ theory, where the gravitational Lagrangian density depends on both the non-metricity scalar $Q$ and the matter Lagrangian $\mathcal{L}_m$. This formulation naturally includes Coincident GR and the Symmetric Teleparallel Equivalent of GR as special cases. Working in the metric formalism, we derive the corresponding field equations, which generalize those of the standard $f(Q)$ gravity, and obtain the modified Klein-Gordon equation for scenarios involving scalar fields. The cosmological implications of the theory are explored in the context of the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. As a first step, we obtain the modified Friedmann equations for $f(Q,\mathcal{L}_m)$ gravity in full generality. We then investigate specific cosmological models arising from both linear and non-linear choices of $f(Q,\mathcal{L}_m)$, performing detailed comparisons with the standard $\Lambda$CDM scenario and examining their observational consequences.