Cosmology of Quadratic Metric-Affine Gravity

TL;DR

This paper explores the cosmological implications of the most general quadratic Metric-Affine Gravity theory, deriving modified Friedmann equations and exact solutions for specific hyperfluid sources, highlighting the roles of torsion and non-metricity.

Contribution

It provides the first comprehensive derivation of cosmological equations in the full quadratic Metric-Affine Gravity framework with explicit solutions for key hyperfluid cases.

Findings

Derived the most general modified Friedmann equations for quadratic Metric-Affine Gravity.

Obtained exact cosmological solutions for dilation and spin hypermomentum sources.

Highlighted the significant influence of torsion and non-metricity in cosmological evolution.

Abstract

We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lema\^itre-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of torsion and non-metricity vectors. In this setup, studying the modified Friedmann equations along with the conservation laws of the perfect cosmological hyperfluid, we provide exact solutions both for purely dilation and for purely spin hypermomentum sources. We then discuss the physical consequences of our model and the prominent role of torsion and non-metricity in this cosmological setup.