The growth of matter perturbations in some scalar-tensor DE models

TL;DR

This paper investigates scalar-tensor dark energy models with specific asymptotic behaviors, analyzing their impact on matter perturbation growth and identifying distinctive signatures that differentiate them from General Relativity.

Contribution

It introduces and analyzes scalar-tensor dark energy models with unique growth of matter perturbations, highlighting their differences from standard models and potential observational constraints.

Findings

Growth of matter perturbations at high redshift is close to standard behavior.

Large values of mbda'_0 can occur, affecting growth predictions.

Distinctive growth signatures can discriminate these models from GR.

Abstract

We consider asymptotically stable scalar-tensor dark energy (DE) models for which the equation of state parameter $w_{DE}$ tends to zero in the past. The viable models are of the phantom type today, however this phantomness is milder than in General Relativity if we take into account the varying gravitational constant when dealing with the SNIa data. We study further the growth of matter perturbations and we find a scaling behaviour on large redshifts which could provide an important constraint. In particular the growth of matter perturbations on large redshifts in our scalar-tensor models is close to the standard behaviour $\delta_m \propto a$, while it is substantially different for the best-fit model in General Relativity for the same parametrization of the background expansion. As for the growth of matter perturbations on small redshifts, we show that in these models the parameter $\gamma'_0\equiv \gamma'(z=0)$ can take absolute values much larger than in models inside General Relativity. Assuming a constant $\gamma$ when $\gamma'_0$ is large would lead to a poor fit of the growth function $f$. This provides another characteristic discriminative signature for these models.