# Geometric Inflation

## TL;DR

This paper demonstrates that higher-curvature corrections to Einstein's gravity naturally lead to an inflationary epoch without extra fields, replacing the Big Bang with a singularity-free exponential expansion compatible with standard cosmology.

## Contribution

It shows that a specific class of higher-curvature theories inherently produce a viable inflationary phase and possess properties similar to Einstein gravity, without introducing additional degrees of freedom.

## Key findings

- Higher-curvature corrections induce a singularity-free inflationary epoch.
- The theories admit Schwarzschild-like black holes without hair.
- Only standard graviton degrees of freedom propagate on vacuum.

## Abstract

We argue that the presence of an inflationary epoch is a natural, almost unavoidable, consequence of the existence of a sensible effective action involving an infinite tower of higher-curvature corrections to the Einstein-Hilbert action. No additional fields besides the metric are required. We show that a family of such corrections giving rise to a well-posed cosmological evolution exists and automatically replaces the radiation-dominated early-universe Big Bang by a singularity-free period of exponential growth of the scale factor, which is gracefully connected with standard late-time $\Lambda$CDM cosmology. The class of higher-curvature theories giving rise to sensible cosmological evolution share additional remarkable properties such as the existence of Schwarzschild-like non-hairy black holes, or the fact that, just like for Einstein gravity, the only degrees of freedom propagated on the vacuum are those of the standard graviton.