The cosmology of quadratic torsionful gravity

We study the cosmology of a quadratic metric-compatible torsionful gravity theory in the presence of a perfect hyperfluid. The gravitational action is an extension of the Einstein-Cartan theory given by the usual Einstein-Hilbert contribution plus all the admitted quadratic parity even torsion scalars and the matter action also exhibits a dependence on the connection. The equations of motion are obtained by regarding the metric and the metric-compatible torsionful connection as independent variables. We then consider a Friedmann-Lemaitre-Robertson-Walker background, analyze the conservation laws, and derive the torsion modified Friedmann equations for our theory. Remarkably, we are able to provide exact analytic solutions for the torsionful cosmology.

Automated summary

This study examines a quadratic metric-compatible torsionful gravity theory in the presence of a perfect hyperfluid, providing exact analytic solutions for torsionful cosmology and deriving torsion modified Friedmann equations. The gravitational action extends the Einstein-Cartan theory, while the matter action depends on the connection, with the equations of motion obtained by considering the metric and torsionful connection as independent variables.