Phenomenology of dark energy: general features of large-scale perturbations

TL;DR

This paper systematically explores dark energy and modified gravity models with a scalar field, revealing generic features of large-scale perturbations and providing constraints on their behavior using an effective field theory approach.

Contribution

It introduces a comprehensive EFT framework to analyze large-scale perturbations in scalar-tensor dark energy models, deriving generic predictions and physical constraints.

Findings

Linear growth rate is suppressed at intermediate redshifts compared to ΛCDM.

A super-growth period occurs at higher redshifts with faster matter fluctuation growth.

The gravitational slip parameter η is bounded, exceeding unity only under specific conditions.

Abstract

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $\Lambda$CDM at intermediate redshifts ($0.5 \lesssim z \lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $\Lambda$CDM. (3) The gravitational slip parameter $\eta$ - the ratio of the space part of the metric perturbation to the time part - is bounded from above. For Brans-Dicke-type theories $\eta$ is at most unity. For more general theories, $\eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.