Constraining alternatives to a cosmological constant: Generalized couplings and scale invariance
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, ) 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.
Section snippets
Data and methods
We start with a short description of our analysis methodology and of the data sets that we will be used in the analysis. We follow a standard likelihood analysis (see for example [9]), with the likelihood defined as As has already been mentioned, we use low-redshift background cosmology data, specifically from supernovas and Hubble parameter data. The two data sets are independent, so the total chi-square is the sum of the two, . Our main observable in both cases
Standard cosmology: the CPL model
In the CPL parametrization the dark energy equation of state parameter is assumed to have the form [7], [8] where is its present value while quantifies its possible evolution in time (or, explicitly, redshift). This is a phenomenological approach, in the sense that it is not intended to mimic a particular dark energy model, but aims to describe generic departures from the CDM behaviour, which naturally corresponds to and . In principle it allows for both
Generalized couplings: the Feng-Carloni model
The precise nature of the coupling between matter and the metric in the Einstein equations is one of the most questionable assumptions of the theory. One may therefore explore the possibility that this coupling is nontrivial. In Feng and Carloni’s generalized coupling model [5] one assumes a coupling of the form where is a nonsingular fourth-order tensor, subject to the constraint that in vacuum , where for future convenience we have defined . This ensures
Scale invariance: the Maeder model
The recently proposed scale invariant model [6] draws heavily on previous work on scale-covariant theories by Canuto et al. [17], [18]. Although it is well known that the effects of scale invariance are expected to disappear upon the presence of matter, the assumption underlying scale invariant models is that at large (i.e., cosmological) scales empty space should still be scale invariant. This assumption ultimately leads to a bimetric theory, with a function (not to be confused with the
Outlook
We have compared three classes of models for the low- redshift acceleration of the universe against background low-redshift cosmological observations. Specifically, we used the traditional CPL phenomenological parametrization as a benchmark for the generalized coupling model of Feng and Carloni [5] and the specific scale invariant model by Maeder [6]. Both of these can be interpreted as bimetric theories, but stem from very different underlying assumptions and, as we have seen, are subject to
CRediT authorship contribution statement
C.B.D. Fernandes: Data curation, Formal analysis, Investigation, Software, Validation, Visualization, Writing - original draft. C.J.A.P. Martins: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing. B.A.R. Rocha: Data curation, Formal analysis, Investigation, Software, Validation, Visualization, Writing -
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was financed by FEDER—Fundo Europeu de Desenvolvimento Regional funds through the COMPETE 2020— Operational Programme for Competitiveness and Internationalisation (POCI), and by Portuguese funds through FCT - Fundação para a Ciência e a Tecnologia in the framework of the project POCI-01-0145-FEDER-028987 and PTDC/FIS-AST/28987/2017.
References (24)
- et al.
Low-redshift constraints on homogeneous and isotropic universes with torsion
Phys. Dark Univ.
(2020) - et al.
Dynamics of dark energy
Internat. J. Modern Phys. D
(2006) - et al.
Dark energy and the accelerating universe
Ann. Rev. Astron. Astrophys.
(2008) - et al.
Dark energy versus modified gravity
Ann. Rev. Nucl. Part. Sci.
(2016) - et al.
Dark energy two decades after: Observables, probes, consistency tests
Rep. Progr. Phys.
(2018) - et al.
New class of generalized coupling theories
Phys. Rev. D
(2020) An alternative to the CDM model: The case of scale invariance
Astrophys. J.
(2017)- et al.
Accelerating universes with scaling dark matter
Internat. J. Modern Phys. D
(2001) Exploring the expansion history of the universe
Phys. Rev. Lett.
(2003)Statistical methods in cosmology
Lecture Notes in Phys.
(2010)
Type ia supernova distances at redshift 1.5 from the hubble space telescope multi-cycle treasury programs: The early expansion rate
Astrophys. J.
Effects of supernova redshift uncertainties on the determination of cosmological parameters
Astrophys. J.
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