Cosmography and constraints on the equation of state of the Universe in various parametrizations

TL;DR

This paper employs cosmography to constrain the Universe's kinematics and equation of state without relying on specific models, introducing new parameterizations and higher-order parameters to improve fit accuracy and consistency with observational data.

Contribution

It introduces a sixth order cosmographic parameter, new viable redshift variables, and methods to directly fit the equation of state, enhancing model-independent cosmological analysis.

Findings

Results are consistent with the mbda CDM model.

Alternative fluid models without a cosmological constant fit the data well.

Re-parameterization improves numerical fits to cosmological distances.

Abstract

We use cosmography to present constraints on the kinematics of the Universe, without postulating any underlying theoretical model. To this end, we use a Monte Carlo Markov Chain analysis to perform comparisons to the supernova Ia Union 2 compilation, combined with the Hubble Space Telescope measurements of the Hubble constant, and the Hubble parameter datasets. We introduce a sixth order cosmographic parameter and show that it does not enlarge considerably the posterior distribution when comparing to the fifth order results. We also propose a way to construct viable parameter variables to be used as alternatives of the redshift $z$. These can overcome both the problems of divergence and lack of accuracy associated with the use of $z$. Moreover, we show that it is possible to improve the numerical fits by re-parameterizing the cosmological distances. In addition, we constrain the equation of state of the Universe as a whole by the use of cosmography. Thus, we derive expressions which can be directly used to fit the equation of state and the pressure derivatives up to fourth order. To this end, it is necessary to depart from a pure cosmographic analysis and to assume the Friedmann equations as valid. All our results are consistent with the $\Lambda$CDM model, although alternative fluid models, with nearly constant pressure and no cosmological constant, match the results accurately as well.