A cosmological model in Weyl-Cartan spacetime: I. Field equations and solutions

TL;DR

This paper introduces an extended cosmological model in Weyl-Cartan spacetime that generalizes previous work, deriving field equations and solutions, and demonstrating the decay of non-Riemannian quantities over time.

Contribution

It presents a new generalized cosmological model in Weyl-Cartan spacetime with explicit field equations and solutions, expanding the framework of metric-affine gravity.

Findings

Non-Riemannian quantities can decay over time.

Explicit solutions for a broad parameter class.

Model fits within metric-affine gravity framework.

Abstract

In this first article of a series on alternative cosmological models we present an extended version of a cosmological model in Weyl-Cartan spacetime. The new model can be viewed as a generalization of a model developed earlier jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e. torsion $T^{\alpha}$ and nonmetricity $Q_{\alpha \beta}$, are proportional to the Weyl 1-form. The hypermomentum $\Delta_{\alpha \beta}$ depends on our ansatz for the nonmetricity and vice versa. We derive the explicit form of the field equations for different cases and provide solutions for a broad class of parameters. We demonstrate that it is possible to construct models in which the non-Riemannian quantities die out with time. We show how our model fits into the more general framework of metric-affine gravity (MAG).