Phases of New Physics in the CMB

TL;DR

The paper uses analytic insights into the CMB phase shift of acoustic peaks to diagnose beyond-Standard Model physics, focusing on free-streaming radiation and isocurvature perturbations as key sources. It develops a Green's-function framework to derive conditions under which a phase shift arises and connects these to observable consequences in $N_{ m eff}$, $N_{ m fluid}$, and $Y_p$. Planck 2015 data provide robust constraints on free-streaming versus non-free-streaming components, and future CMB-S4 forecasts show potential to reach $\sigma(N_{ m eff})$ at the $\sim 10^{-2}$ level, enabling precise tests of dark radiation and related BSM scenarios. The work highlights the critical role of polarization and delensing in breaking degeneracies and extracting the phase-shift signal, with implications for time evolution of radiation densities and a broad class of models including decays, isocurvature, and modified gravity.

Abstract

Fluctuations in the cosmic neutrino background are known to produce a phase shift in the acoustic peaks of the cosmic microwave background. It is through the sensitivity to this effect that the recent CMB data has provided a robust detection of free-streaming neutrinos. In this paper, we revisit the phase shift of the CMB anisotropy spectrum as a probe of new physics. The phase shift is particularly interesting because its physical origin is strongly constrained by the analytic properties of the Green's function of the gravitational potential. For adiabatic fluctuations, a phase shift requires modes that propagate faster than the speed of fluctuations in the photon-baryon plasma. This possibility is realized by free-streaming relativistic particles, such as neutrinos or other forms of dark radiation. Alternatively, a phase shift can arise from isocurvature fluctuations. We present simple models to illustrate each of these effects. We then provide observational constraints from the Planck temperature and polarization data on additional forms of radiation. We also forecast the capabilities of future CMB Stage IV experiments. Whenever possible, we give analytic interpretations of our results.

Figures (10)

• Figure 1: Particles beyond the Standard Model can be classified according to their masses $M$ and their mean free paths $\lambda_{\rm mfp}$ (both normalized relative to the Hubble rate at recombination, $H_{\rm rec}$). Particles with $M > H_{\rm rec}$ contribute to the cold dark matter of the universe, while particles with $M < H_{\rm rec}$ are relativistic at recombination. Massive, strongly interacting particles are Boltzmann-suppressed and, therefore, do not contribute a cosmologically interesting density. Dark radiation separates into free-streaming and non-free-streaming particles. Note that axions, and other non-thermal relics, escape the simple characterization of this figure.
• Figure 2: Illustration of the coupled perturbations in the primordial plasma.
• Figure 3: Phase shift $\theta$ for varying speed of sound ($c_s$) and equation of state ($w$). The dashed line denotes $\theta=0$. Below this line, the phase shift is negative, while above it is positive.
• Figure 4: Phase shift $\theta$ for varying $c_s^2=w$ (left) and for varying $c_s^2$ and fixed $w=\frac{1}{3}$ (right).
• Figure 5: Numerical value of $B^{\rm iso} \, c_\gamma k \tau_{\rm eq}$ as a function of $y_{\rm dec}$. The blue and red solid lines show the effect from $c_1$ and $c_2$, respectively. The dashed lines are the asymptotic values calculated in (\ref{['eq:Bisofinal']}).