In this paper, using a significantly improved version of the model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ, 614, 1), we address an important question: Was there a decelerating past for the universe? To answer this, the Bayes's probability theory is employed, which is the most appropriate tool for quantifying our knowledge when it changes through the acquisition of new data. The cosmographic approach helps to sort out the models in which the universe was always accelerating from those in which it decelerated for at least some time in the period of interest. Bayesian model comparison technique is used to discriminate these rival hypotheses with the aid of recent releases of supernova data. We also attempt to provide and improve another example of Bayesian model comparison, performed between some Friedmann models, using the same data. Our conclusion, which is consistent with other approaches, is that the apparent magnitude-redshift data alone cannot discriminate these competing hypotheses. We also argue that the lessons learnt using Bayesian theory are extremely valuable to avoid frequent U-turns in cosmology.

Using the Bayesian theory of model comparison, a new cosmological model due to John and Joseph [M. V. John and K. Babu Joseph, Phys. Rev. D 61, 87304 (2000)] is compared with the standard \Omega_{\Lambda} \neq 0 cosmological model. Their analysis based on the recent apparent magnitude-redshift data of Type Ia supernovas found evidence against the new model; our more careful analysis finds instead that this evidence is not strong. On the other hand, we find that the angular size-redshift data from compact (milliarcsecond) radio sources do not discriminate between the two models. Our analysis serves as an example of how to compare the relative merits of cosmological models in general, using the Bayesian approach.Comment: Accepted for publication in Physical Review

The apparent magnitude-redshift data of SNe Ia call for modifications in the standard model energy densities. Under the circumstance that this modification cannot be limited to the addition of a mere cosmological constant, a serious situation has emerged in cosmology, in which the energy densities in the universe have become largely speculative. In this situation, an equation of state of the form p = wρ itself is not well-motivated. In this paper, we argue that the reasonable option left is to make a model-independent analysis of SNe data, without reference to the energy densities. In this basically kinematic approach, we limit ourselves to the observationally justifiable assumptions of homogeneity and isotropy; i.e., to the assumption that the universe has a RW metric. This cosmographic approach is historically the original one to cosmology. We perform the analysis by expanding the scale factor into a polynomial of order 5, which assumption can be further generalised to any order. The present expansion rates h, q 0 , r 0 etc. are evaluated by computing the marginal likelihoods for these parameters. These values are relevant, since any cosmological solution would ultimately need to explain them.

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Recent measurements require modifications in conventional cosmology by way of introducing components other than ordinary matter into the total energy density in the universe. On the basis of some dimensional considerations in line with quantum cosmology, Chen and Wu [W. Chen and Y. Wu, Phys. Rev. D 41, 695 (1990)] have argued that an additional component, which corresponds to an effective cosmological constant Λ must vary as a −2 in the classical era. Their decaying-Λ model assumes inflation and yields a value for q 0 , which is not compatible with observations. We generalize this model by arguing that the Chen-Wu ansatz is applicable to the total energy density of the universe and not to Λ alone. The resulting model, which has a coasting evolution (i.e., a ∝ t), is devoid of the problems of horizon, flatness, monopole, cosmological constant, size, age and generation of density perturbations. However, to avoid serious contradictions with big bang nucleosynthesis, the model has to make the predictions Ω m = 4/3 and Ω Λ = 2/3, which in turn are at variance with current observational values.