# Einstein-Hilbert actions with torsion

## TL;DR

This paper explores Einstein-Hilbert actions incorporating torsion and non-symmetric metrics, deriving formulas for pressure, density, and energy-momentum tensor, and generalizing cosmological models to include torsion effects.

## Contribution

It introduces general formulas for pressure, density, and energy-momentum tensor in the context of non-symmetric metrics with torsion, extending cosmological models.

## Key findings

- Derived formulas for pressure and density based on non-symmetric metrics.
- Obtained the energy-momentum tensor expression for non-symmetric metrics.
- Generalized Bianchi type-I cosmological model to include torsion effects.

## Abstract

In this paper, we studied the full Einstein-Hilbert actions with respect to non-symmetric metrics and the corresponding torsion. The first concrete result in this paper are the general formulae for pressure and density with respect to the Madsen's article (the equation (3.1), in [10]). Based on these results, we obtained the expression of energy-momentum tensor with respect to non-symmetric metrics. We started the generalization of the Bianchi type-I model of cosmology with respect to the corresponding non-symmetric metrics.