Coupling matter in modified $Q$-gravity

TL;DR

This paper introduces a new class of modified gravity theories with nonminimal coupling between nonmetricity and matter, exploring their cosmological implications and potential to explain late-time acceleration.

Contribution

It develops a novel extension of symmetric teleparallel gravity with nonminimal nonmetricity-matter coupling and analyzes its cosmological solutions.

Findings

Models exhibit late-time accelerating expansion.

Nonconservation of energy-momentum due to coupling.

Potential for more viable gravity theories with matter coupling.

Abstract

We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity $Q$ is nonminimally coupled to the matter Lagrangian. More specifically, we consider a Lagrangian of the form $L \sim f_1(Q) + f_2(Q) L_M$, where $f_1$ and $f_2$ are generic functions of $Q$, and $L_M$ is the matter Lagrangian. This nonminimal coupling entails the nonconservation of the energy-momentum tensor, and consequently the appearance of an extra force. The motivation is to verify whether the subtle improvement of the geometrical formulation, when implemented in the matter sector, would allow more universally consistent and viable realisations of the nonminimal curvature-matter coupling theories. Furthermore, we consider several cosmological applications by presenting the evolution equations and imposing specific functional forms of the functions $f_1(Q)$ and $f_2(Q)$, such as power-law and exponential dependencies of the nonminimal couplings. Cosmological solutions are considered in two general classes of models, and found to feature accelerating expansion at late times.