The resilience of the Etherington-Hubble relation

The Etherington reciprocity theorem, or distance duality relation (DDR), relates the mutual scaling of cosmic distances in any metric theory of gravity where photons are massless and propagate on null geodesics. In this paper, we make use of the DDR to build a consistency check based on its degeneracy with the Hubble constant, H-0. We parametrize the DDR using the form eta(z) = 1 + epsilon z, thus only allowing small deviations from its standard value. We use a combination of late-time observational data to provide the first joint constraints on the Hubble parameter and epsilon with percentage accuracy: H-0 = 68.6 +/- 2.5 km s(-1) Mpc(-1) and epsilon = 0.001(-0.026)(+0.023). We build our consistency check using these constraints and compare them with the results obtained in extended cosmological models using cosmic microwave background data. We find that extensions to Lambda cold dark matter (Lambda CDM) involving massive neutrinos and/or additional dark radiation are in perfect agreement with the DDR, while models with non-zero spatial curvature show a preference for DDR violation, i.e. epsilon not equal 0 at the level of similar to 1.5 sigma. Most importantly, we find a mild 2 sigma discrepancy between the validity of the DDR and the latest publicly available Cepheid-calibrated Type Ia supernova (SNIa) constraint on H-0. We discuss the potential consequences of this for both the Etherington reciprocity theorem and the H-0 tension.

Automated summary

The Etherington reciprocity theorem is used to build a consistency check and provides new results about cosmological models. Using late-time observational data, joint constraints on the Hubble parameter and epsilon are obtained and compared with other cosmological models. Additionally, a discrepancy between the validity of the DDR and the latest publicly available Cepheid-calibrated Type Ia supernova constraint on H-0 is identified.