Delineating cosmic expansion history with recent supernova data: A Bayesian model-independent approach

Abstract

Marginal likelihoods for the cosmic expansion rates are evaluated using the recent `Constitution' data of 397 supernovas, thereby updating the results in some previous works. Even when beginning with a very strong prior probability that favors an accelerated expansion, we end up with a marginal likelihood for the deceleration parameter $q_0$ peaked around zero in the spatially flat case. This is in agreement with some other analysis of the Constitution data. It is also found that the new data significantly constrains the cosmic expansion rates, when compared to the previous analysis. Here again we adopt the model-independent approach in which the scale factor is expanded into a Taylor series in time about the present epoch; for practical purposes, it is truncated to polynomials of various orders, in different trials. Though one cannot regard the polynomials thus obtained as models, in this paper we evaluate the total likelihoods (Bayesian evidences) for them to find the order of the polynomial having the largest likelihood. Analysis using the Constitution data shows that the largest likelihood occurs for the fourth order polynomial and is of value $\approx 0.77 \times 10^{-102}$. It is argued that this value, which we call the likelihood for the model-independent approach, may be used to calibrate the performance of realistic models.