Coupling matter in modified<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>gravity

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 $L\ensuremath{\sim}{f}_{1}(Q)+{f}_{2}(Q){L}_{M}$, 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 formulation of the gravity sector in terms of the $Q$ instead of the curvature may result in subtle improvements of the theory. In the context of nonminimal matter couplings, we are therefore motivated to explore whether the new geometrical formulation in terms of the $Q$, when implemented also in the matter sector, would allow more universally consistent and viable realizations of the nonminimal coupling. 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.