Second-order matter density perturbations and skewness in scalar-tensor modified gravity models

TL;DR

This paper investigates second-order matter density perturbations and skewness in scalar-tensor modified gravity models, showing that skewness remains nearly unchanged from LCDM, serving as a model-independent test of gravitational instability.

Contribution

It derives equations for second-order perturbations in scalar-tensor models and demonstrates the skewness's robustness as a test for gravity models.

Findings

Skewness differs from LCDM by less than a few percent.

Second-order perturbations can be approximated neglecting first-order scalar field fluctuations.

Skewness is a model-independent probe of gravitational instability.

Abstract

We study second-order cosmological perturbations in scalar-tensor models of dark energy that satisfy local gravity constraints, including f(R) gravity. We derive equations for matter fluctuations under a sub-horizon approximation and clarify conditions under which first-order perturbations in the scalar field can be neglected relative to second-order matter and velocity perturbations. We also compute the skewness of the matter density distribution and find that the difference from the LCDM model is only less than a few percent even if the growth rate of first-order perturbations is significantly different from that in the LCDM model. This shows that the skewness provides a model-independent test for the picture of gravitational instability from Gaussian initial perturbations including scalar-tensor modified gravity models.