Constraining alternatives to a cosmological constant: Generalized couplings and scale invariance

Abstract

We present a comparative analysis of observational low-redshift background constraints on three candidate models for explaining the low-redshift acceleration of the universe. The generalized coupling model by Feng and Carloni and the scale invariant model by Maeder (both of which can be interpreted as bimetric theories) are compared to the traditional parametrization of Chevallier, Polarski and Linder. In principle the generalized coupling model, which in vacuum is equivalent to General Relativity, contains two types of vacuum energy: the usual cosmological constant plus a second contribution due to the matter fields. We show that the former is necessary for the model to agree with low-redshift observations, while there is no statistically significant evidence for the presence of the second. On the other hand the scale invariant model effectively has a time-dependent cosmological constant. In this case we show that a matter density ${\Omega }_m\sim 0.3$ is a relatively poor fit to the data, and the best-fit model would require a fluid with a much smaller density and a significantly positive equation of state parameter.

Introduction

The search for the physical mechanism underlying the observed low-redshift acceleration of the universe is the most compelling goal of modern fundamental cosmology. A number of theoretical possibilities can be envisaged in principle, whose observational consequences are being explored [1], [2], [3].

The simplest possibility is a cosmological constant: this has the minimal number of additional parameters and indeed is, broadly speaking, in agreement with the currently available data (despite several recent observational hints of inconsistencies). Nevertheless, the observationally inferred value is theoretically unexpected, and reconciling the two would require fine-tuning or some other radical departure from current knowledge. The next-to-simplest possibility would be one (or more) additional dynamical degrees of freedom—particularly scalar fields, which are known to be among Nature’s building blocks. Indeed, many (perhaps most) phenomenological dark energy studies explicitly or implicitly assume that the source of the dark energy is a canonical scalar field. Finally, more radical (or, arguably, epicyclic) approaches rely on modifications of the behaviour of gravity. Each of these alternative paradigms will have its observational fingerprints, which one can look for in the ever-improving available data [4].

Our goal in this work is to present a comparative study of the observational constraints on three classes of models. Two of these are recently proposed models: the generalized coupling model by Feng and Carloni [5] and the scale invariant model by Maeder [6]. Both of these models can be interpreted as bimetric theories. As a benchmark for the more standard models we use the traditional phenomenological parametrization of Chevallier, Polarski and Linder (henceforth CPL) [7], [8]. All three models have common parameters (specifically, the matter density parameter, ${\Omega }_m$) but also some specific ones, and a comparative analysis using a common data set is therefore interesting.

In this work we take all three models at face value and phenomenologically constrain them using low-redshift background cosmology data, further described in the next section. The plan of the rest of the paper is as follows. We start in Section 2 with a brief summary of the data and statistical analysis methodology we use. After this, in the following three sections we introduce each of the three models and present the constraints obtained from the aforementioned data sets, under various assumptions. Specifically, the CPL model is discussed in Section 3, the generalized coupling model in Section 4, and the scale invariant model in Section 5. Finally in Section 6 we discuss our results and present some conclusions.