Towards the nonlinear regime in extensions to GR: assessing possible options

TL;DR

This paper investigates methods to control mathematical pathologies in extended theories of gravity, demonstrating that modifying equations to manage higher-order gradients is a robust approach for exploring nonlinear regimes.

Contribution

It introduces a model problem to analyze pathologies in gravity extensions and validates a modification method for controlling higher-order gradients effectively.

Findings

The modification approach is robust and efficient.

Controlling higher-order gradients mitigates mathematical pathologies.

The method facilitates exploration of nonlinear gravitational regimes.

Abstract

Testing General Relativity and exploring possible departures has received further input with the possibility to do so through gravitational waves emitted in strongly gravitating/highly dynamical scenarios and also through the availability of exquisitely sensitive cosmological observations. However, most extensions suffer from severe pathologies at the mathematical level which have stymied a thorough exploration of putative theories. With the aid of a model problem which captures typical pathologies, we explore suggested methods to control them. We find that the approach that modifies the equations to control higher-order gradients is both robust and efficient.