Modified Gravity and the CMB

TL;DR

This paper investigates how simple models of modified gravity, involving a massive scalar field, can alter the CMB peak structure through effects on perturbations, sound speed, and potential contributions, offering new ways to constrain gravity theories.

Contribution

It demonstrates how different couplings of a massive scalar field to matter can independently modify CMB peaks, and shows how to design models with specific scalar field evolutions for testing gravity.

Findings

Large scalar-CDM coupling increases peak amplitudes.

Moderate scalar-baryon coupling shifts peaks to higher momenta.

Combined couplings add a Newton potential term, boosting peak heights.

Abstract

We consider the effect of modified gravity on the peak structure of the Cosmic Microwave Background (CMB) spectrum. We focus on simple models of modified gravity mediated by a massive scalar field coupled to both baryons and cold dark matter. This captures the features of chameleon, symmetron, dilaton and $f(R)$ models. We find that the CMB peaks can be affected in three independent ways provided the Compton radius of the massive scalar is not far-off the sound horizon at last scattering. When the coupling of the massive scalar to Cold Dark Matter (CDM) is large, the anomalous growth of the CDM perturbation inside the Compton radius induces a change in the peak amplitudes. When the coupling to baryons is moderately large, the speed of sound is modified and the peaks shifted to higher momenta. Finally when both couplings are non-vanishing, a new contribution proportional to the Newton potential appears in the Sachs-Wolfe temperature and increases the peak amplitudes. We also show how, given any temporal evolution of the scalar field mass, one can engineer a corresponding modified gravity model of the chameleon type. This opens up the possibility of having independent constraints on modified gravity from the CMB peaks and large scale structures at low redshifts.