How Massless Neutrinos Affect the Cosmic Microwave Background Damping Tail

Abstract

We explore the physical origin and robustness of constraints on the energy density in relativistic species prior to and during recombination, often expressed as constraints on an effective number of neutrino species, Neff. Constraints from current data combination of Wilkinson Microwave Anisotropy Probe (WMAP) and South Pole Telescope (SPT) are almost entirely due to the impact of the neutrinos on the expansion rate, and how those changes to the expansion rate alter the ratio of the photon diffusion scale to the sound horizon scale at recombination. We demonstrate that very little of the constraining power comes from the early Integrated Sachs-Wolfe (ISW) effect, and also provide a first determination of the amplitude of the early ISW effect. Varying the fraction of baryonic mass in Helium, Yp, also changes the ratio of damping to sound-horizon scales. We discuss the physical effects that prevent the resulting near-degeneracy between Neff and Yp from being a complete one. Examining light element abundance measurements, we see no significant evidence for evolution of Neff and the baryon-to-photon ratio from the epoch of big bang nucleosynthesis to decoupling. Finally, we consider measurements of the distance-redshift relation at low to intermediate redshifts and their implications for the value of Neff.