Constraints on kinematic parameters at z≠0

Abstract

The standard cosmographic approach consists in performing a series expansion of a cosmological observable around z=0 and then using the data to constrain the cosmographic (or kinematic) parameters at present time. Such a procedure works well if applied to redshift ranges inside the z-series convergence radius (z<1), but can be problematic if we want to cover redshift intervals that fall outside the z−series convergence radius. This problem can be circumvented if we work with the y−redshift, y=z/(1+z), or the scale factor, a=1/(1+z)=1−y, for example. In this paper, we use the scale factor a as the variable of expansion. We expand the luminosity distance and the Hubble parameter around an arbitrary ã and use the Supernovae Ia (SNe Ia) and the Hubble parameter data to estimate H, q, j and s at z≠0 (ã≠1). We show that the last relevant term for both expansions is the third. Since the third order expansion of dL(z) has one parameter less than the third order expansion of H(z), we also consider, for completeness, a fourth order expansion of dL(z). For the third order expansions, the results obtained from both SNe Ia and H(z) data are incompatible with the ΛCDM model at 2σ confidence level, but also incompatible with each other. When the fourth order expansion of dL(z) is taken into account, the results obtained from SNe Ia data are compatible with the ΛCDM model at 2σ confidence level, but still remains incompatible with results obtained from H(z) data. These conflicting results may indicate a tension between the current SNe Ia and H(z) data sets.