How Massless Neutrinos Affect the Cosmic Microwave Background Damping Tail

TL;DR

The paper analyzes how massless relativistic species, parametrized by Neff, alter the CMB damping tail. It shows that the dominant effect is the expansion-rate change prior to recombination, which modifies the ratio between the Silk damping scale and the sound horizon, rather than neutrino perturbations or the early ISW effect. The authors quantify the damping via the rd/rs ratio and demonstrate how Y_P introduces degeneracies that BB N consistency can alleviate, while also highlighting the limited role of post-decoupling physics. They further discuss implications for low-redshift distance measures and potential improvements with future CMB data.

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.

Figures (2)

• Figure 1: Top panel:WMAP and SPT power spectrum measurements, and theoretical power spectra normalized at $\ell = 200$. The black (central) curve is for the best-fit $\Lambda$CDM + $N_{\rm eff}$ model assuming BBN consistency. The other model curves are for $N_{\rm eff}$ varying from 2 to 6 with $\rho_b$, $\theta_s$, and $z_{\rm EQ}$ held fixed. Larger $N_{\rm eff}$ corresponds to lower power. Central panel: Same as above except normalized at $\ell = 400$ where the ISW contribution is negligible. We see most of the variation remains. Bottom panel: The same as the central panel except we vary $Y_{\rm P}$ to keep $\theta_d$ fixed. The lack of scatter in these spectra compared to those in the middle panel demonstrates that the effect of $N_{\rm eff}$ on small-scale data is largely captured by its impact on the damping scale. We can also begin to see more subtle effects of the neutrinos, most noticeably a phase shift in the acoustic oscillations bashinsky04.
• Figure 2: Probability distribution of $N_{\rm eff}$ using just WMAP data, WMAP + SPT, and WMAP + constraints on $\theta_d/\theta_s$ from WMAP + SPT (see Tab. \ref{['tab:neff_bbn']}).