# Affine Inflation

## TL;DR

This paper explores affine gravity, a metric-less gravity theory, demonstrating its ability to support inflationary dynamics and highlighting its unique features compared to general relativity, with potential for future observational tests.

## Contribution

It constructs an affine gravity framework for inflation, compares it with general relativity, and reveals a unique frame in affine gravity distinct from Einstein and Jordan frames.

## Key findings

- Affine gravity supports scalar field inflation without a metric.
- Non-minimally coupled inflaton can be transformed into a minimally-coupled form with a modified potential.
- Affine gravity has a unique frame, unlike the multiple frames in general relativity.

## Abstract

Affine gravity, a gravity theory based on affine connection with no notion of metric, supports scalar field dynamics only if scalar fields have non-vanishing potential. The non-vanishing vacuum energy ensures that the cosmological constant is non-vanishing. It also ensures that the energy-momentum tensor of vacuum gives the dynamically generated metric tensor. We construct this affine setup and study primordial inflation in it. We study inflationary dynamics in affine gravity and general relativity, comparatively. We show that non-minimally coupled inflaton dynamics can be transformed into a minimally-coupled one with a modified potential. We also show that there is one unique frame in affine gravity, as opposed to the Einstein and Jordan frames in general relativity. Future observations with higher accuracy may be able to test the affine gravity.