Complete density perturbations in the Jordan-Fierz-Brans-Dicke theory

TL;DR

This paper derives exact density perturbation equations in Jordan-Fierz-Brans-Dicke scalar-tensor theories within a Lambda-CDM background, comparing their evolution to standard cosmology and highlighting the impact of coupling variations.

Contribution

It provides a general method to obtain the exact fourth-order differential equation for density contrast evolution in scalar-tensor theories, applicable to all modes and coupling values.

Findings

Exact fourth-order differential equation derived for density contrast.

Differences observed between scalar-tensor and standard Lambda-CDM evolution.

Comparison shows coupling influences perturbation growth.

Abstract

In the context of scalar-tensor theories we study the evolution of the density contrast for Jordan-Fierz-Brans-Dicke theories in a Friedmann-Lemaitre-Robertson-Walker Universe. Calculations are performed in the Einstein Frame with the cosmological background described as Lambda-Cold Dark Matter (Lambda-CDM) and supplemented by a Jordan-Fierz-Brans-Dicke field. By using a completely general procedure valid for all scalar-tensor theories, we obtain the exact fourth-order differential equation for the density contrast evolution in modes of arbitrary size. In the case of sub-Hubble modes, the expression reduces to a simpler but still fourth-order equation that is then compared with the standard (quasistatic) approximation. Differences with respect to the evolution as predicted by the standard Concordance Lambda-CDM model are observed depending on the value of the coupling.