# Metric-affine Gravity and Inflation

## TL;DR

This paper classifies metric-affine gravity theories with independent metric and connection, showing they reduce to Einstein gravity in certain cases, and explores their implications for inflation with scalar fields, including potential observational viability.

## Contribution

It provides a systematic classification of metric-affine gravity models and analyzes their inflationary dynamics with scalar fields, including Galileon fields.

## Key findings

- Connections are non-dynamical under Einstein-Hilbert action, simplifying to Riemannian geometry.
- Certain parameters in scalar field models satisfy observational constraints.
- Galileon scalar fields in metric-affine gravity can lead to G-inflation.

## Abstract

We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the equations for the distortion tensor (torsion and non-metricity) become algebraic, which means that those variables are not dynamical. As a result, we can rewrite the basic equations in the form of Riemannian geometry. Although all classified models recover the Einstein gravity in the Palatini formalism (in which we assume there is no coupling between matter and the connections), but when matter field couples to the connections, the effective Einstein equations include an additional hyper energy-momentum tensor obtained from the distortion tensor. Assuming a simple extension of a minimally coupled scalar field in metric-affine gravity, we analyze an inflationary scenario. Even if we adopt a chaotic inflation potential, certain parameters could satisfy observational constraints. Furthermore, we find that a simple form of Galileon scalar field in metric-affine could cause G-inflation.