Evidence for extra radiation? Profile likelihood versus Bayesian posterior

Understand

A number of recent analyses of cosmological data have reported hints for the presence of extra radiation beyond the standard model expectation.

• In order to test the robustness of these claims under different methods of constructing parameter constraints, we perform a Bayesian posterior-based and a likelihood profile-based analysis of current data.
• We confirm the presence of a slight discrepancy between posterior- and profile-based constraints, with the marginalised posterior preferring higher values of the effective number of neutrino species N_eff.
• This can be traced back to a volume effect occurring during the marginalisation process, and we demonstrate that the effect is related to the fact that cosmic microwave background (CMB) data constrain N_eff only indirectly via the redshift of matter-radiation equality.