Scalars, Vectors and Tensors from Metric-Affine Gravity

TL;DR

This paper demonstrates that metric-affine gravity theories based on non-metricity, torsion, and curvature can be decomposed into scalar, vector, and tensor fields, providing a versatile framework for cosmological models.

Contribution

It introduces a decomposition of metric-affine gravity into scalar, vector, and tensor fields, linking it to various cosmological and modified gravity theories.

Findings

Model accommodates TeVeS gravity and vector inflation.

Provides a unified framework for scalar, vector, and tensor fields.

Enables detailed analysis of cosmological phenomena within metric-affine gravity.

Abstract

The metric-affine gravity provides a useful framework for analyzing gravitational dynamics since it treats metric tensor and affine connection as fundamentally independent variables. In this work, we show that, a metric-affine gravity theory composed of the invariants formed from non-metricity, torsion and curvature tensors can be decomposed into a theory of scalar, vector and tensor fields. These fields are natural candidates for the ones needed by various cosmological and other phenomena. Indeed, we show that the model accommodates TeVeS gravity (relativistic modified gravity theory), vector inflation, and aether-like models. Detailed analyses of these and other phenomena can lead to a standard metric-affine gravity model encoding scalars, vectors and tensors.