Instabilities in field theories: Lecture notes with a view into modified gravity

TL;DR

This paper discusses the common instabilities in modified gravity theories, their detection methods, and the implications of these instabilities for constructing viable models.

Contribution

It introduces the main types of instabilities in field theories, provides techniques for their detection, and applies these concepts specifically to modified gravity theories.

Findings

Identification of key instabilities in modified gravity

Techniques for detecting dynamical instabilities

Implications for model viability

Abstract

Modified theories of gravity usually present new degrees of freedom, as well as higher order derivatives, wrong signs in certain terms and complicated couplings already present in the Lagrangian from the beginning or originated by the field redefinitions needed to reach an Einstein frame. As a consequence, they are very prone to present dynamical instabilities that could spoil any attempt to construct viable models within these frameworks. In these three lectures we introduce the most common types of instabilities that appear in field theory as well as some techniques to detect them, and supplement these contents with several examples. The goal is to understand the implications of having such pathological behaviors and the application of these notions to modified theories of gravity.