# Metastability in Quadratic Gravity

## TL;DR

This paper demonstrates that quadratic gravity, a UV completion of general relativity, exhibits metastable solutions that avoid classical instabilities at cosmologically relevant energies, with implications for early universe cosmology.

## Contribution

It shows that quadratic gravity's classical solutions are metastable rather than unstable, providing a consistent framework compatible with cosmology and inflation.

## Key findings

- Metastability replaces instability in quadratic gravity.
- Bounded energies prevent runaway solutions.
- Implications for early universe and homogeneous cosmology.

## Abstract

Quadratic gravity is a UV completion of general relativity, which also solves the hierarchy problem. The presence of 4 derivatives implies via the Ostrogradsky theorem that the $classical$ Hamiltonian is unbounded from below. Here we solve this issue by showing that the relevant solutions are not unstable but metastable. When the energies are much below a threshold (that is high enough to describe the whole cosmology) runaways are avoided. Remarkably, the chaotic inflation theory of initial conditions ensures that such bound is satisfied and we work out testable implications for the early universe. The possible instability occurring when the bound is violated not only is compatible with cosmology but would also explain why we live in a homogeneous and isotropic universe.