Testing distance duality with CMB anisotropies

Abstract

We constrain deviations of the form T propto (1+z)^1+epsilon from the standard redshift-temperature relation, corresponding to modifying distance duality as D_L = (1+z)^2(1+epsilon) D_A. We consider a consistent model, in which both the background and perturbation equations are changed. For this purpose, we introduce a species of dark radiation particles to which photon energy density is transferred, and assume epsilon >= 0. The Planck 2015 release high multipole temperature plus low multipole data give the limit epsilon < 4.5 × 10^-3 at 95% C.L. The main obstacle to improving this CMB-only result is strong degeneracy between epsilon and the physical matter densities ω_b and ω_c. A constraint on deuterium abundance improves the limit to epsilon < 1.8 × 10^-3. Adding the Planck high-multipole CMB polarisation and BAO data leads to a small improvement; with this maximal dataset we obtain epsilon < 1.3 × 10^-3. This dataset constrains the present dark radiation energy density to at most 12% of the total photon plus dark radiation density. Finally, we discuss the degeneracy between dark radiation and the effective number of relativistic species N_eff, and consider the impact of dark radiation perturbations and allowing epsilon < 0 on the results.