On the prior dependence of cosmological constraints on some dark matter interactions

We explore the issue of prior dependence in the context of one-sided constraints on the dark matter-photon and dark matter-neutrino elastic scattering cross-sections derived from cosmic microwave background (CMB) anisotropies measurements. Testing in particular the linear flat, Jeffreys, and logarithmic flat priors, we find that the former two yield upper limits on the cross-sections that are mutually consistent to within 20%. In contrast, bounds derived under the assumption of the logarithmic flat prior are strongly sensitive to the choice of the lower prior boundary. Indeed, surveying the recent literature, we find that this pathology of the logarithmic prior has resulted in published constraints that are up to an order of magnitude artificially tighter than they should objectively be. Our revised "objective" constraints from the 2015 data of the Planck CMB mission on the present-day scattering cross-sections are σ_DM-γ < 1.72 × 10^-6 σ_T (m_DM/GeV) and σ_DM-γ < 2.74 × 10^-15 σ_T (m_DM/GeV) for dark matter-photon interactions scaling as a⁰ and a^-2 respectively, where a is the scale factor, and σ_T the total Thomson scattering cross-section. Their dark matter-neutrino counterparts read σ_DM-ν < 2.14 × 10^-6 σ_T (m_DM/GeV) and σ_DM-ν< 2.46 × 10^-15 σ_T (m_DM/GeV). All have been computed assuming the Jeffreys prior.