Observational Constraints on Redshift Remapping

There are two redshifts in cosmology: $z_{obs}$, the observed redshift computed via spectral lines, and the model redshift, $z$, defined by the effective FLRW scale factor. In general these do not coincide. We place observational constraints on the allowed distortions of $z$ away from $z_{obs}$ - a possibility we dub redshift remapping. Remapping is degenerate with cosmic dynamics for either $d_L(z)$ or $H(z)$ observations alone: for example, the simple remapping $z = \alpha_1 z_{obs} +\alpha_2 z_{obs}^2$ allows a decelerating Einstein de Sitter universe to fit the observed supernova Hubble diagram as successfully as $\Lambda$CDM, highlighting that supernova data alone cannot prove that the universe is accelerating. We show however, that redshift remapping leads to apparent violations of cosmic distance duality that can be used to detect its presence even when neither a specific theory of gravity nor the Copernican Principle are assumed. Combining current data sets favours acceleration but does not yet rule out redshift remapping as an alternative to dark energy. Future surveys, however, will provide exquisite constraints on remapping and any models -- such as backreaction -- that predict it.