Model-independent determination of the cosmic growth factor

Abstract

The two most important functions describing the evolution of the universe and its structures are the expansion function E(a)E(a) and the linear growth factor D_+(a)D+(a). It is desirable to constrain them based on a minimum of assumptions in order to avoid biases from assumed cosmological models. The expansion function has been determined in previous papers in a model-independent way using distance moduli to type-Ia supernovae and assuming only a metric theory of gravity, spatial isotropy and homogeneity. Here, we extend this analysis in three ways: (1) We enlarge the data sample by combining measurements of type-Ia supernovae with measurements of baryonic acoustic oscillations; (2) we substantially simplify and generalise our method for reconstructing the expansion function; and (3) we use the reconstructed expansion function to determine the linear growth factor of cosmic structures, equally independent of specific assumptions on an underlying cosmological model other than the usual spatial symmetries. In this approach, the present-day matter-density parameter \Omega_\mathrm{m0}Ωm0 is the only relevant parameter for an otherwise purely empirical and accurate determination of the growth factor. We further show how our method can be used to derive a possible time evolution of the dark energy as well as the growth index directly from distance measurements. Deviations from \LambdaΛCDM that we see in some of our results may be due to possibly insufficient flexibility of our method that could be cured by larger data samples, a real departure from \LambdaΛCDM at a\lesssim0.3a≲0.3, or hidden systematics in the data. The latter could be a matter of concern for all type-Ia supernovae analyses based on \LambdaΛCDM fitting approaches, especially in view of the current dispute on the value of H_0H0. These results illustrate the applicability of our approach as a diagnostic tool.