Hamiltonian perturbation theory in f(R) gravity

TL;DR

This paper applies Hamiltonian perturbation theory to analyze the stability of f(R) gravity models, identifying potential instabilities that can rule out certain formulations based on their behavior under perturbations.

Contribution

It introduces a Hamiltonian framework for perturbation analysis in f(R) gravity, focusing on metric and momentum conjugate variables in the presence of matter.

Findings

Instabilities depend on the form of f(R)

Perturbations perpendicular to R reveal stability issues

Method can exclude unstable f(R) models

Abstract

Hamiltonian perturbation theory is used to analyse the stability of f(R) models. The Hamiltonian equations for the metric and its momentum conjugate are written for f(R) Lagrangian in the presence of perfect fluid matter. The perturbations examined are perpendicular to R. As perturbations are added to the metric and momentum conjugate to the induced metric instabilities are found, depending on the form of f(R). Thus the examination of these instabilities is a way to rule out certain f(R) models.