Consistent cosmological modifications to the Einstein equations

Abstract

General Relativity (GR) is a phenomenologically successful theory that rests on firm foundations, but has not been tested on cosmological scales. The advent of dark energy (and possibly even the requirement of cold dark matter), has increased the need for testing modifications to GR, as the inference of such otherwise undetected fluids, depends crucially on the theory of gravity. In this work I outline a general scheme for constructing consistent and covariant modifications to the Einstein equations. This framework is such that there is a clear connection between the modification and the underlying field content that produces it. I conclude by a simple metric based modification of the fluctuation equations for which the background is exact Lambda-CDM and present its impact on observations of the cosmic microwave background radiation.

Figures (1)

• Figure 1: Upper panel: The CMB spectrum for the simple modified gravity model in the text. The solid curve is the plain $\Lambda CMD$ model ($\beta = 0$), while the dotted, dashed and dot-dashed curves are with $\beta = \{0.1, 0.5, 1\}$ respectively. Lower panel : The time evolution of $g = \frac{\hat{\Phi} - \hat{\Psi}}{\hat{\Phi} +\hat{\Psi}}$ (as in HSHu) at $k=10^{-3}Mpc^{-1}$ for the same set of models.