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A comparison of cosmological models using recent supernova data

S. Nesseris, L. Perivolaropoulos

TL;DR

This study assesses how well a range of cosmological models reproduce Type Ia supernova observations to $z\approx1.75$ by fitting $H(z)$ parametrizations to a 194 point SnIa data set. It uses a flat prior with $Ω_{0m}=0.3$ and maximum-likelihood fits to compare models via $χ^2_{min}$, identifying LCDM as broadly consistent while SCDM is strongly disfavored, and finding an oscillating $H(z)$ (OA) as the best fit among the considered models. A common implication across good fits is a dark-energy equation of state $w(z)$ that remains near $-1$ at low redshift but becomes positive at higher redshift, suggesting metamorphosis or oscillations constrained by nucleosynthesis and structure formation. The results motivate a systematic search for simple, data-informed $H(z)$ ansatze that capture potential oscillations in dark energy and expansion history.

Abstract

We study the expansion history of the universe up to a redshift of z=1.75 using the 194 recently published SnIa data by Tonry et. al. and Barris et. al. In particular we find the best fit forms of several cosmological models and $H(z)$ ansatze, determine the best fit values of their parameters and rank them according to increasing value of $χ_{min}^2$ (the minimum value of $χ^2$ for each $H(z)$ ansatz). We use a prior of $Ω_{0m} = 0.3$ and assume flat geometry of the universe. No prior assumptions are made about validity of energy conditions. The fitted models are fourteen and include SCDM, LCDM, dark energy with constant equation of state parameter $w$ (quiessence), third order polynomial for $H(1+z)$, Chaplygin gas, Cardassian model, $w(z)=w_0 + w_1 z$, $w(z)=w_0 + z w_1/(1+z)$, an oscillating ansatz for $H(z)$ etc. All these models with the exception of SCDM are consistent with the present data. However, the quality of the fit differs significantly among them and so do the predicted forms of $w(z)$ and $H(z)$ at best fit. The worst fit among the data-consistent models considered corresponds to the simplest model LCDM ($χ_{min}^2 = 198.7$ for $Ω_{0m} = 0.34$) while the best fit is achieved by the three parameter oscillating ansatz ($χ_{min}^2 = 194.1$). Most of the best fit ansatze have an equation of state parameter $w(z)$ that varies between $w(z) \simeq -1$ for $z<0.5$ to $w(z) > 0$ for $z>1$. This implies that the sign of the pressure of the dark energy may be alternating as the redshift increases. The goodness of fit of the oscillating $H(z)$ ansatz lends further support to this possibility.

A comparison of cosmological models using recent supernova data

TL;DR

This study assesses how well a range of cosmological models reproduce Type Ia supernova observations to by fitting parametrizations to a 194 point SnIa data set. It uses a flat prior with and maximum-likelihood fits to compare models via , identifying LCDM as broadly consistent while SCDM is strongly disfavored, and finding an oscillating (OA) as the best fit among the considered models. A common implication across good fits is a dark-energy equation of state that remains near at low redshift but becomes positive at higher redshift, suggesting metamorphosis or oscillations constrained by nucleosynthesis and structure formation. The results motivate a systematic search for simple, data-informed ansatze that capture potential oscillations in dark energy and expansion history.

Abstract

We study the expansion history of the universe up to a redshift of z=1.75 using the 194 recently published SnIa data by Tonry et. al. and Barris et. al. In particular we find the best fit forms of several cosmological models and ansatze, determine the best fit values of their parameters and rank them according to increasing value of (the minimum value of for each ansatz). We use a prior of and assume flat geometry of the universe. No prior assumptions are made about validity of energy conditions. The fitted models are fourteen and include SCDM, LCDM, dark energy with constant equation of state parameter (quiessence), third order polynomial for , Chaplygin gas, Cardassian model, , , an oscillating ansatz for etc. All these models with the exception of SCDM are consistent with the present data. However, the quality of the fit differs significantly among them and so do the predicted forms of and at best fit. The worst fit among the data-consistent models considered corresponds to the simplest model LCDM ( for ) while the best fit is achieved by the three parameter oscillating ansatz (). Most of the best fit ansatze have an equation of state parameter that varies between for to for . This implies that the sign of the pressure of the dark energy may be alternating as the redshift increases. The goodness of fit of the oscillating ansatz lends further support to this possibility.

Paper Structure

This paper contains 4 sections, 38 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Cosmic Expansion History
  3. Conclusion
  4. Appendix

Figures (3)

  • Figure 1: The observed 194 SnIa Hubble free luminocity distances along with the theoretically predicted curves in the context of SCDM (continuous line) and LCDM (dashed line).
  • Figure 2: The redshift dependence of the equation of state parameter $w(z)$ for the $q-\Lambda$ ansatze. The thick curve is the best fit and the light (dark) shaded regions represent the $1\sigma$ ($2\sigma$) error regions.
  • Figure 4: The reduced Hubble parameter for some of the best and the worst fits of the cosmological ansatze of Table 1. The number in the parenthesis shows the rank $(1-13)$ of the corresponding ansatz in terms of goodness of fit. The LCDM curve is not flat at zero because in its construction we used the best fit value $\Omega_{0m}=0.34$ while the $H_{LCDM}$ on the axis assumes the prior $\Omega_{0m}=0.30$.