A First Detection of the Acoustic Oscillation Phase Shift Expected from the Cosmic Neutrino Background

TL;DR

A first detection of the resulting shifts in the temporal phase of the oscillations is reported, which is inferred from their signature in the cosmic microwave background temperature power spectrum.

Abstract

The unimpeded relativistic propagation of cosmological neutrinos prior to recombination of the baryon-photon plasma alters gravitational potentials and therefore the details of the time-dependent gravitational driving of acoustic oscillations. We report here a first detection of the resulting shifts in the temporal phase of the oscillations, which we infer from their signature in the Cosmic Microwave Background (CMB) temperature power spectrum.

Figures (3)

• Figure 1: Undamped power spectra ${\cal K}_l$ (defined in Eq. \ref{['eq:kell']}) with different values of $N_\nu$. In all panels the baryon density $\omega_b$, the ratio of matter to radiation density $\rho_m/(\rho_\gamma + \rho_\nu)$ and the angular size of the sound horizon $\theta_s$ are held fixed as these are well-determined by CMB data fairly independently of the assumed value of $N_\nu$. In the top panel the dominant source of variation is the change in the damping scale $\theta_D$ caused by the changes in $N_\nu$. In the middle panel we fix $\theta_D$ by varying the primordial fraction of baryonic mass in Helium appropriately, leaving the dominant source of power spectrum variation as the change in oscillation amplitude $A^\prime$. Finally in the bottom panel, with the spectra normalized to remove the effect of $A^\prime$ variation, one can see the subtle impact of the shifts in temporal phase $\phi$. The data points are the 2013 Planck data.
• Figure 2: Posterior reconstructions of the phase shift template $f_l=\alpha \ln(l) + \beta$ under the $\Lambda$CDM + $N_{\nu}$ + $N_{\nu}^{\delta \phi}$ model, normalized to give the amplitude of the relative shift between the fiducial 3.046 neutrino species and a single specie, along with numerically obtained phase shifts obtained from 100 different simulated cosmologies with varying neutrino species drawn from $N_{\nu} = \left[1,6\right]$ relative to the fiducial cosmology, rescaled by the amplitude parameter given in equation \ref{['eq:phiamp']}. Also included is the analytic approximation given by bashinsky_signatures_2004, which they also found to be $\sim 25\%$ higher than the numerical result at $\ell \simeq 3000$.
• Figure 3: Top: 2D constraints on the jointly varying $\Lambda$CDM+$N_{\nu}$+$N_{\nu}^{\delta\phi}$ parameter space. The constraints on $N_{\nu}$ (damping) and $N_{\nu}^{\delta\phi}$ (phase shift) are essentially orthogonal. Bottom: Constraints from March 2013 ${\it Planck}$ temperature power spectrum measurements on the number of neutrino species from (1) blue/solid: varying $N_{\nu}^{\delta\phi}$ while holding $N_{\nu}$ fixed at three and (2) green/dashed: varying along the physical direction $N_{\nu} = N_{\nu}^{\delta\phi}$. The constraints assume a Gaussian $\tau$ prior of mean $\mu = 0.085$ and width $\sigma = 0.015$.