Model-Independent Reconstruction of the Expansion Rate of the Universe Through Combination of Different Cosmological Probes

Abstract

This work proposes a method to constrain the cosmic expansion rate and the linear growth factor for structure formation from different cosmological measurements, without reference to a specific Friedmann model and its parameters. First, a model-independent reconstruction technique to estimate the expansion rate from luminosity distance data has been developed: it converts the integral relation between the expansion function and the luminosity distance into a Volterra integral equation, which is known to have a unique solution in terms of a Neumann series. Expanding observables such as the luminosity distances to type-Ia supernovae into a series of orthonormal functions, the integral equation can be solved and the cosmic expansion rate recovered within the limits allowed by the accuracy of the data. The performance of the method is demonstrated through application to synthetic data sets of increasing complexity, including a toy model with a sudden transition in the expansion rate. With the additional assumption of local Newtonian dynamics, the growth rate for linear structure formation can be calculated from the estimate of the expansion rate, in the redshift interval over which supernovae are available, and employed in the analysis of cosmic shear data: combined to a traditional, Lambda-CDM analysis of the same data set, this approach allows to tighten the constraints on the matter density parameter, Omega_m, and the normalisation of the power spectrum, sigma_8. Furthermore, the method to reconstruct the expansion rate can be applied to angular-diameter distance data from baryon acoustic oscillation experiments; an optimisation of the orthonormal function set employed in the algorithm has also been performed, by means of a principal component analysis.