Equation of state of dark energy in f(R) gravity

TL;DR

This paper investigates the equation of state of dark energy in f(R) gravity, demonstrating that the thin-shell mechanism allows for deviations from w = -1 when the Klein-Gordon equation is correctly applied, challenging previous static assumptions.

Contribution

It corrects the application of the Poisson equation in f(R) gravity, showing that the dark energy equation-of-state parameter can differ from -1.

Findings

Thin-shell solutions exist even with w significantly different from -1.

Correct perturbative Klein-Gordon equation reveals more flexible dark energy behavior.

Challenges previous claims based on static Poisson equation assumptions.

Abstract

f(R) gravity is one of the simplest generalizations of general relativity, which may explain the accelerated cosmic expansion without introducing a cosmological constant. Transformed into the Einstein frame, a new scalar degree of freedom appears and it couples with matter fields. In order for f(R) theories to pass the local tests of general relativity, it has been known that the chameleon mechanism with a so-called thin-shell solution must operate. If the thin-shell constraint is applied to a cosmological situation, it has been claimed that the equation-of-state parameter of dark energy w must be extremely close to -1. We argue this is due to the incorrect use of the Poisson equation which is valid only in the static case. By solving the correct Klein-Gordon equation perturbatively, we show that a thin-shell solution exists even if w deviates appreciably from -1.