Cosmography beyond standard candles and rulers

Abstract

We perform a cosmographic analysis using several cosmological observables such as the luminosity distance moduli, the volume distance, the angular diameter distance and the Hubble parameter. These quantities are determined using different data sets: Supernovae type Ia and Gamma Ray Bursts, the Baryonic Acoustic Oscillations, the cosmic microwave background power spectrum and the Hubble parameter as measured from surveys of galaxies. This data set allows to put constraints on the cosmographic expansion with unprecedented precision. We also present forecasts for the coefficients of the kinematic expansion using future but realistic data sets: constraints on the coefficients of the expansions are likely to improve by a factor ten with the upcoming large scale structure probes. Finally, we derive the set of the cosmographic parameters for several cosmological models (including $\Lambda$CDM) and compare them with our best fit set. While distance measurements are unable to discriminate among these models, we show that the inclusion of the Hubble data set leads to strong constraints on the lowest order coefficients and in particular it is incompatible with $\Lambda$CDM at 3-$\sigma$ confidence level. We discuss the reliability of this determination and suggest further observations which might be of crucial importance for the viability of cosmographic tests in the next future.Comment: 15 pages, 2 figures, 2 tables, Accepted for publication in PR