Testing the mapping between redshift and cosmic scale factor

The canonical redshift−scale factor relation, 1/a = 1 + z, is a key element in the standard ΛCDM model of the big bang cosmology. Despite its fundamental role, this relation has not yet undergone any observational tests since Lemaı̂tre and Hubble established the expansion of the Universe. It is strictly based on the assumption of the Friedmann–Lemaı̂tre–Robertson–Walker metric describing a locally homogeneous and isotropic universe and that photons move on null geodesics of the metric. Thus any violation of this assumption, within general relativity or modified gravity, can yield a different mapping between the model redshift z = 1/a − 1 and the actually observed redshift zobs, i.e. zobs 6= z. Here we perform a simple test of consistency for the standard redshift−scale factor relation by determining simultaneous observational constraints on the concordance ΛCDM cosmological parameters and a generalized redshift mapping z = f(zobs). Using current baryon acoustic oscillations (BAO) and Type Ia supernova (SN) data we demonstrate that the generalized redshift mapping is strongly degenerated with dark energy. Marginalization over a class of monotonic functions f(zobs) changes substantially degeneracy between matter and dark energy density: the density parameters become anticorrelated with nearly vertical axis of degeneracy. Furthermore, we show that current SN and BAO data, analysed in a framework with the generalized redshift mapping, do not constrain dark energy unless the BAO data include the measurements from the Lyα forest of high-redshift quasars.