Cosmological Large-scale Structures beyond Linear Theory in Modified Gravity

TL;DR

This paper investigates how modified gravity theories affect the second-order growth of large-scale cosmic structures, revealing subtle changes in mode coupling and identifying transition scales in scalar field models.

Contribution

It provides explicit formulas for the effects of modified gravity on second-order perturbations and analyzes transition scales in scalar field models like chameleons and dilatons.

Findings

Modified gravity alters mode coupling amplitudes in density and velocity fields.

Transition scales exist where scalar fields significantly change cosmic field couplings.

Effects in dilaton models are comparable to those in DGP at tree level.

Abstract

We consider the effect of modified gravity on the growth of large-scale structures at second order in perturbation theory. We show that modified gravity models changing the linear growth rate of fluctuations are also bound to change, although mildly, the mode coupling amplitude in the density and reduced velocity fields. We present explicit formulae which describe this effect. We then focus on models of modified gravity involving a scalar field coupled to matter, in particular chameleons and dilatons, where it is shown that there exists a transition scale around which the existence of an extra scalar degree of freedom induces significant changes in the coupling properties of the cosmic fields. We obtain the amplitude of this effect for realistic dilaton models at the tree-order level for the bispectrum, finding them to be comparable in amplitude to those obtained in the DGP model.