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 LambdaCDM model of the big bang cosmology. Despite its fundamental
role, this relation has not yet undergone any observational tests since
Lemaitre and Hubble established the expansion of the Universe. It is strictly
based on the assumption of the Friedmann-Lemaitre-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 z_obs, i.e. z_obs
neq z. Here we perform a simple test of consistency for the standard
redshift-scale factor relation by determining simultaneous observational
constraints on the concordance LambdaCDM cosmological parameters and a
generalized redshift mapping z=f(z_obs). 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(z_obs) changes
substantially degeneracy between matter and dark energy density: the density
parameters become anti correlated 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 Ly-alpha forest of high-redshift
quasars.
