Testing distance duality with CMB anisotropies

Abstract

We constrain deviations of the form T ∝ (1+z)1+ϵ from the standard redshift-temperature relation, corresponding to modifying distance duality as DL = (1+z)2(1+ϵ) DA. 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 ϵ ≥ 0. The Planck 2015 release high multipole temperature plus low multipole data give the limit ϵ < 4.5 × 10−3 at 95% C.L. The main obstacle to improving this CMB-only result is strong degeneracy between ϵ and the physical matter densities ωb and ωc. A constraint on deuterium abundance improves the limit to ϵ < 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 ϵ < 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 Neff, and consider the impact of dark radiation perturbations and allowing ϵ < 0 on the results.