Directly Probing Neutrino Interactions through CMB Phase Shift Measurements

Abstract

Perturbations in the cosmic neutrino background produce a characteristic phase shift in the acoustic oscillations imprinted in the anisotropies of the cosmic microwave background (CMB), providing a unique observational probe of neutrino physics. In this work, we explore how this phase shift signature is altered in the presence of neutrino interactions with temperature-dependent scattering rates, motivated by physical constructions for neutrino self-interactions and neutrino-dark matter couplings. A key finding is that the phase shift in these realistic models -- characterized by gradual rather than instantaneous decoupling -- maintains the same functional form as the free-streaming template, with only the asymptotic amplitude decreasing for stronger interactions that delay decoupling. This simple parametrization enables us to directly constrain neutrino interactions through phase shift measurements in the temperature and polarization power spectra from CMB observations. Analyzing the latest data from \textit{Planck}, the Atacama Cosmology Telescope, and the South Pole Telescope, we derive strong constraints on the neutrino decoupling redshift. Our global analysis indicates that neutrinos have been freely streaming since deep within the radiation-dominated epoch. We also explore flavor-dependent scenarios in which only one neutrino species interacts. Overall, our work establishes a signature-driven framework that exploits the clean phase shift signal in the acoustic oscillations of the CMB as a precise and robust probe of non-standard neutrino interactions in the early universe.

Figures (11)

• Figure 1: Illustration of the neutrino phase shift imprinted in the undamped polarization power spectrum $\mathcal{K}^{EE}_\ell$, Eq. \ref{['eq:K_ell']}, for interacting neutrinos with a scattering rate $\Gamma_\nu\propto T_\nu^5$. We show three distinct neutrino decoupling scenarios: (i) neutrinos effectively always free-streaming, corresponding to $z_{\nu,\rm dec}\gg10^{5}$; (ii) neutrinos decoupling close to recombination, specifically with $z_{\nu,\rm dec}\approx 5\times 10^{3}$; and (iii) fluid-like neutrinos throughout, corresponding to $z_{\nu,\rm dec}\ll10^{3}$. To clearly isolate the neutrino-induced phase shift parameterized by $N_\mathrm{eff}$, we fix $\omega_b$, $a_{\mathrm{eq}}$, $\theta_s$, $\theta_d$ (specifically to our fiducial $\Lambda \rm CDM$ parameter values shown in Table \ref{['tab:parameters']}), and the height of the fourth EE peak. The upper panels display the polarization power spectrum across the multipole range $\ell$ relevant for current CMB experiments, while the lower panels zoom in around the fourth EE peak, highlighting the sensitivity of the phase shift to the neutrino decoupling epoch. An equivalent phase shift signature is also present in the TT and TE power spectra.
• Figure 2: Spectrum-based templates $f_\ell$, as defined in Eqs. \ref{['eq:fell']} and \ref{['eq:fell_int']}, as a function of multipole $\ell$ for interacting neutrinos with scattering rates $\Gamma_\nu \propto T_\nu^3$ ( left) and $\Gamma_\nu \propto T_\nu^5$ ( right). Solid orange, red, and brown lines indicate the best-fit templates for three representative scenarios: fully free-streaming neutrinos ($z_{\nu,\rm dec} \gg 10^5$), delayed decoupling ($z_{\nu,\rm dec} \approx 5\times 10^3$), and fluid-like behavior ($z_{\nu,\rm dec} \ll 10^3$). The corresponding $2\sigma$ confidence intervals are shown as dashed lines. For these benchmark scenarios, we also display the numerically extracted phase shifts for the TT (squares), EE (circles), and TE (triangles) power spectra, obtained by sampling 100 cosmologies with $N_{\rm eff} \in [1, 6]$ and normalized as described in Appendix \ref{['sec:A2']}. The extracted phase shifts are color-coded to match the respective best-fit templates.
• Figure 3: The amplitude ratio $\mathcal{A}_\infty$, defined as the asymptotic amplitude of the neutrino-induced phase-shift template $\ell_\infty$ relative to that of SM free-streaming neutrinos $\ell^{\rm SM \nu}_\infty$, shown as a function of neutrino decoupling redshift $z_{\nu,\rm dec}$. Results are obtained from the spectrum-based template fits $f_\ell$ using the lensed TT, TE, and EE power spectra. Red and blue curves correspond to neutrino scattering rates scaling as $\Gamma_\nu \propto T_\nu^3$ and $\Gamma_\nu \propto T_\nu^5$, respectively. Solid lines indicate the corresponding best-fit values, while shaded regions depict their $2\sigma$ confidence intervals, further outlined by dashed lines. As expected, the template amplitude approaches the SM free-streaming limit, $\mathcal{A}_\infty = 1$, at high decoupling redshifts and the fluid-like limit, $\mathcal{A}_\infty \approx 0.3$, at low decoupling redshifts. The transition between these regimes is sharper in the $\Gamma_\nu \propto T_\nu^5$ scenario compared to the $\Gamma_\nu \propto T_\nu^3$ scenario, yet still spans 2-3 decades in redshift.
• Figure 4: Left: One dimensional posterior distributions of the phase-shift-amplitude ratio $A_\infty$ for Planck 2018 only (P18) in red, ACT and SPT data (ACT + SPT) in blue, and the combined P18 + ACT + SPT analysis in purple. Right: Corresponding posterior distributions for the neutrino decoupling redshift $z_{\nu,\rm dec}$ for interacting neutrinos with scattering rates $\Gamma_\nu\propto T_\nu^3$ (dashed) and $\Gamma_\nu\propto T_\nu^5$ (solid). These posteriors are obtained by mapping the $\mathcal{A}_\infty$ constraints through the numerically derived $\mathcal{A}_\infty - z_{\nu,\rm dec}$ relationships shown in Fig. \ref{['fig:3']}, with the shaded bands representing the propagated uncertainty in this mapping. The vertical green line marks the redshift of matter–radiation equality, $z_{\rm eq}$, in our fiducial $\Lambda$CDM model. All analyses strongly constrain neutrino interactions, requiring decoupling to occur deep within the radiation-dominated epoch.
• Figure 5: Same as the right panel of Fig. \ref{['fig:4']}, but for the flavor-dependent scenario, in which only one neutrino species is interacting, i.e. $\mathcal{F}_{\nu, \rm int}=1/3$. These posteriors are obtained by first rescaling the constraints on the universal amplitude ratio $\mathcal{A}_\infty$ to the flavor-dependent ratio $\mathcal{A}'_\infty$ via Eq. \ref{['eq:Aprime_infty']}, then converting to $z_{\nu,\rm dec}$ through the same numerically derived $A_\infty -z_{\nu,\rm dec}$ relationships shown in Fig. \ref{['fig:3']}. Restricting interactions to a single neutrino species significantly weakens the constraints: P18 data permit fluid-like behavior extending to low redshifts, while combined datasets constrain neutrino decoupling to occur in the radiation-dominated era.