Cosmological Constraints on the Undulant Universe

TL;DR

This paper uses multiple cosmological data sets to constrain parameters of the Undulant Universe model, finding that combined data significantly improve constraints and that the model closely resembles the Lambda-CDM model.

Contribution

It introduces a comprehensive analysis of the Undulant Universe using diverse observational data and demonstrates the importance of combined data sets in constraining cosmological parameters.

Findings

$H(z)$ data are as effective as SNe Ia in cosmological constraints.

BAO and CMB data help break parameter degeneracies.

The Undulant Universe closely resembles the $\\Lambda$CDM model.

Abstract

We use the redshift Hubble parameter $H(z)$ data derived from relative galaxy ages, distant type Ia supernovae (SNe Ia), the Baryonic Acoustic Oscillation (BAO) peak, and the Cosmic Microwave Background (CMB) shift parameter data, to constrain cosmological parameters in the Undulant Universe. We marginalize the likelihood functions over $h$ by integrating the probability density $P\propto e^{-\chi^2/2}$. By using the Markov Chain Monte Carlo (MCMC) technique, we obtain the best fitting results and give the confidence regions on the $b-\Omega_{\rm m0}$ plane. Then we compare their constraints. Our results show that the $H(z)$ data play a similar role with the SNe Ia data in cosmological study. By presenting the independent and joint constraints, we find that the BAO and CMB data play very important roles in breaking the degeneracy compared with the $H(z)$ and SNe Ia data alone. Combined with the BAO or CMB data, one can improve the constraints remarkably. The SNe Ia data sets constrain $\Omega_{\rm m0}$ much tighter than the $H(z)$ data sets, but the $H(z)$ data sets constrain $b$ much tighter than the SNe Ia data sets. All these results show that the Undulant Universe approaches the $\Lambda \rm$CDM model. We expect more $H(z)$ data to constrain cosmological parameters in future.