The Cosmology of Quadratic Torsionful Gravity

TL;DR

This paper explores a quadratic torsionful gravity theory's cosmology, deriving exact solutions and analyzing how torsion influences the universe's expansion within a modified Einstein-Cartan framework.

Contribution

It introduces a quadratic torsionful gravity model with exact analytic solutions in cosmology, extending Einstein-Cartan theory with quadratic torsion scalars and connection-dependent matter.

Findings

Derived torsion-modified Friedmann equations

Obtained exact analytic cosmological solutions

Analyzed conservation laws in torsionful gravity

Abstract

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-Lema\^itre-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.