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The canonical redshift-scale factor relation, 1/a=1+z, is a key element inthe standard LambdaCDM model of the big bang cosmology. Despite its fundamentalrole, this relation has not yet undergone any observational tests sinceLemaitre and Hubble established the expansion of the Universe. It is strictlybased on the assumption of the Friedmann-Lemaitre-Robertson-Walker metricdescribing a locally homogeneous and isotropic universe and that photons moveon null geodesics of the metric. Thus any violation of this assumption, withingeneral relativity or modified gravity, can yield a different mapping betweenthe model redshift z=1/a-1 and the actually observed redshift z_obs, i.e. z_obsneq z. Here we perform a simple test of consistency for the standardredshift-scale factor relation by determining simultaneous observationalconstraints on the concordance LambdaCDM cosmological parameters and ageneralized redshift mapping z=f(z_obs). Using current baryon acousticoscillations (BAO) and Type Ia supernova (SN) data we demonstrate that thegeneralized redshift mapping is strongly degenerated with dark energy.Marginalization over a class of monotonic functions f(z_obs) changessubstantially degeneracy between matter and dark energy density: the densityparameters become anti correlated with nearly vertical axis of degeneracy.Furthermore, we show that current SN and BAO data, analysed in a framework withthe generalized redshift mapping, do not constrain dark energy unless the BAOdata include the measurements from the Ly-alpha forest of high-redshiftquasars.

Testing the mapping between redshift and cosmic scale factor