Testing distance duality with CMB anisotropies

Abstract

We constrain deviations of the form T proportional to (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 x 10(-3) at 95% C.L. The main obstacle to improving this CMB-only result is strong degeneracy between and the physical matter densities omega(b) and omega(c). A constraint on deuterium abundance improves the limit to epsilon <1.8 x 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 x 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.