# Bayesian model comparison of alternative cosmologies

Abstract

In this work, we make a statistical comparison of some known cosmological models: The cosmological constant ($$\Lambda$$CDM) model, the constant equation-of-state ($$w$$CDM) model, the CPL dark energy parameterization, the Dvali-Gabadadze-Porrati (DGP) model, a vacuum-decay ($$\Lambda(t)$$CDM) model and also the power-law $$f(R)$$ model in the metric formalism. For this purpose, we perform a Bayesian model selection analysis using the Affine-Invariant Ensemble Sampler Monte-Carlo method. In order to obtain the parametric space and the posterior distribution for the parameters of each model, we use the more up-to-date type Ia supernova (SNe Ia) data, the Joint Lightcurve Analysis (JLA) compilation, containing 740 events between $$0.01<z<1.3$$. The model selection is then performed by obtaining the Bayesian evidence of each model and computing the Bayes factor between two models. The results indicate that the JLA data only cannot distinguish the standard $$\Lambda$$CDM from the $$\Lambda(t)$$CDM, power-law metric $$f(R)$$ and DGP alternatives, but to make more strong conclusions, a more robust analysis including combining the SNe Ia data with other kind of observables is necessary.

## Introduction

\label{sec:introduction}

More than a decade ago, the late time accelerated expansion had been discovered by the distance-redshift measurement of Type Ia supernovae (Riess 1998, Perlmutter 1999). Since then, a wide variety of theories have been advanced in the literature to explain such accelerated expansion but its underlying physical cause is still an ambiguous to the community. Though, other cosmological observations namely the Cosmic Microwave Background radiation (CMB) anisotropic measurements (Komatsu 2009, Planck Collaboration 2015, Planck Collaboration 2015a), the baryon acoustic oscillations (BAO) (Eisenstein 2005, Cole 2005, Percival 2007, Percival 2010), the recent observation from type Ia Supernovae (Riess 2004, Riess 2006, Astier 2006, Wood-Vasey 2007, Kessler 2009) and the observation of matter distribution over very large length scales from galaxy redshift survey (Mantz 2010, Mantz 2010a, Rozo 2010, Vikhlinin 2009) have already confirmed its existence. The main challenge left behind is “how to quantify and discriminate these numerous theoretical models with the standard case, among each others”.

In general, this phenomenon of cosmic acceleration is explored in two different ways: either introduce an exotic fluid, “dark energy” (DE), with a large negative pressure in the framework of general relativity (GR) or modify the Einstein’s general theory of relativity (GR) at very large scales. The dark energy models range from a simple constant energy density field model with equation-of-state $$w=p/\rho=-1$$, so called $$\Lambda$$CDM to a slowly varying with time and in space “the dynamical scalar field models”.

So far, the cosmological constant $$\Lambda$$CDM remains the most consistent DE model with a large number of observational datasets. However, its theoretical issues (e.g. fine tuning and cosmic coincidence problems (Weinberg 1989, Carroll 2001, Sahni 2000) allow many alternative mechanisms to formulate in the literature (see (Peebles 2003, Padmanabhan 2003, Copeland 2006, Armendariz-Picon 2000, Amendola 2013) for recent reviews). The dynamical DE models consist of the parametrization of EoS, quintessence, phantom, K-essence, among others. An attempt has also been made to interact the dark energy field with the dark matter, for example “vacuum decay models” (Wetterich 1995, Amendola 2000). In the framework of modify GR: $$f(R)$$ gravity, scalar tenser theories (Brans 1961, Amendola 1999)