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 temperature power spectrum. A First Detection of the Acoustic Oscillation Phase Shift Expected from the Cosmic Neutrino Background Brent Follin, 1 Lloyd Knox, 1 Marius Millea, 1 and Zhen Pan 1 1University of California, Davis ∗ 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. These same hot and dense conditions led to a cosmic neutrino background (CNB) that contributes nearly as much as photons to the total energy density in the early universe. The neutrinos began to stream freely at kBT∼ MeV, and continue to stream freely through the cosmos to this day. Unlike with photons, direct detection of the CNB is exceedingly difficult [1]. We have had indirect, though highly significant, evi- dence for the CNB for decades, starting with determina- tions of the primordial abundance of Helium, an abun- dance affected by the contribution of neutrinos to the ex- pansion rate (see Steigman [2]). Bashinsky and Seljak [6] analytically found that the propagation of neutrino perturbations at speeds faster than the speed of sound in the plasma alters the time- dependent gravitational driving of the acoustic oscilla- tions. Altering the driving of a harmonic oscillator has two effects: it changes the amplitude and the temporal phase of the oscillations. To date, no one has isolated these two distinct effects. Although the influence of neu- trino perturbations has been detected [4, 7], it remains an open question whether the phase shift plays a significant role in these determinations. Isolating the phase shift effect clarifies the amount of model dependence in our inferences of the CNB. If we knew d, we could use this effect alone to measure the energy density in the CNB. However, d depends on the (otherwise unknown) value of the cosmological constant. In Fig. 1 we show a series of plots where we vary Nν while holding certain other quantities fixed, in order to demonstrate the observable consequences of various ef- fects of neutrinos. Because θs, baryon density ωb, and the ratio of matter to radiation density ρm/(ργ + ρν) are well determined by the data, in all rows we show variations with these parameters fixed. In the top row one can see the impact of Nν on the typical distance a photon diffuses prior to last scattering, rd. The values ofA′/A andφ depend on the details of the potential de- cay, and in particular on the fraction of the radiation that can freely stream out of over densities at the speed 3 of light. We can see in the middle row that increasing Nν decreases A′/A. Finally, in the bottom row we normalize the spectra to remove the effect of changingA′/A so that the change in values of φ is more evident. As φ changes, the value of k =kp for which kprs(t∗) +φ =pπ changes so ℓp≃kpd changes. The net result is δℓp =−δφ/θs. In this Letter we show that these subtle shifts are detectable with the Planck data. Template fitting: To quantify the sensitivity of the data to the expected phase shift we must be able to artificially increase or decrease it, independent of other effects of the CNB. Since the phase shift effects are most observ- able deep in the We sample 100 different cosmology pairs, and find that in the region of parameter space explored by these mod- els, the phase shift is well captured by a linear response proportional to the fraction of radiation density in free- streaming neutrinos. The multipole dependence is well described by a logarithmic template, which is jointly sam- pled with cosmology against both the March 2013 Planck temperature data and the measured phase shifts in the 100 cosmology pairs. Posterior samples of the template are shown in Fig. We found that the min- imum χ2 (≡− 2 lnL) decreased by 19.9 when switching from a ΛCDM model withNδφ ν = 0 to the ΛCDM +Nδφ ν model. A χ2 difference this large or larger will occur, as- sumingNδφ ν = 0, with the same probability, 8× 10−6, as a 4.5σ Gaussian fluctuation. While letting Nν and Nδφ ν vary independently (top of Fig. 3), the width of the constraint on Nν is dominated by an ns- Nν degeneracy: fixing ns results in roughly a halving of the characteristic width of the posterior in the Nν direction. Finally, we note that there is a slight dependence on priors for the 2D posterior shown in Fig. 3. If we switch from uniform priors on the number of neutrino speciesNν andNδφ ν to their corresponding neutrino fractionsR(Nν) and R(Nδφ ν ), the average value of the posterior shifts down by ( ∆Nν = 0.3, ∆Nδφ ν = 0.5 ) , a shift of slightly more than 0.5σ in both directions. This is predominantly due to a contraction in the high probability region at high Nν or Nδφ ν . Regardless of prior, Nδφ ν = 0 is heavily dis- favored. [15] A Fisher matrix analysis shows that using the τ prior instead of the “WP” of The Planck Collaboration [9] does not lose any information relevant to the phase shift [16] https://github.com/marius311/cosmoslik.git [17] This approximation results in a ∼ 10% widening of the constraint onNν in the standard model extended to arbi- trary number of neutrino species when compared to the full CMB likelihood, which includes WMAP9 polariza- tion. [18] For a summary of existing constraints on “secret neutrino interactions” see Ng and Beacom [13].