Cosmographic Evaluation of the Deceleration Parameter Using Type Ia Supernova Data

The apparent magnitude-redshift data of Type Ia supernovae (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 remaining option 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 Robertson-Walker metric. This cosmographic approach is historically the original one in cosmology. We perform the analysis by expanding the scale factor into a fifth-order polynomial, an assumption that can be further generalized to any order. The present expansion rates h, q0, r0, 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.