$f(Q,T)$ gravity

Understand

We propose an extension of the symmetric teleparallel gravity, in which the gravitational action $L$ is given by an arbitrary function $f$ of the nonmetricity $Q$ and of the trace of the matter energy-momentum tensor $T$, so that $L=f(Q,T)$.

• The field equations of the theory are obtained by varying the gravitational action with respect to both metric and connection.
• The covariant divergence of the field equations is obtained, with the geometry-matter coupling leading to the nonconservation of the energy-momentum tensor.
• We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of general relativity.