Limits of self-interacting neutrinos from the BAO and CMB phase shift

TL;DR

This work develops phase-shift templates for both Standard Model and non-standard (self-interacting) neutrinos to quantify how ($G_{\rm eff}$) alters free-streaming and the resulting phase in BAO and CMB observables. By constructing scale- and amplitude-sensitive templates $A(G_{\rm eff})$ and $B(G_{\rm eff})$, the authors forecast constraints from BAO and CMB data using CLASS-PT, Fisher analyses, and profile-χ² approaches. They find BAO alone yields limited sensitivity to $G_{\rm eff}$ except for very strong interactions, while CMB phase information provides strong constraints, with combined BAO+CMB analyses offering the best prospects, especially for weaker interactions. The results imply that phase-shift measurements can robustly probe self-interacting neutrinos and, when combined with external priors on $N_{\rm eff}$, can help disfavor or detect non-standard neutrino couplings, motivating extensions to non-universal interaction scenarios and additional cosmological probes.

Abstract

Neutrinos with Standard Model interactions free-stream in the early Universe, leaving a distinct phase shift in the pattern of baryon acoustic oscillations (BAO). When isolated, this phase shift allows one to robustly infer the presence of the cosmic neutrino background in BAO and cosmic microwave background (CMB) data independently of other cosmological parameters. While in the context of the Standard Model, this phase shift follows a known scale-dependent relation, new physics in the cosmic neutrino background could alter the overall shape of this feature. In this paper, we discuss how changes in the neutrino phase shift could be used to constrain self-interactions among neutrinos. We produce simple models for this phase-shift assuming universal self-interactions, and use these in order to understand what constraining power is available for the strength of such interactions in BAO and CMB data. We find that, although challenging, it may be possible to use a detection of the phase to put a more robust limit on the strength of the self-interaction, $G_{\mathrm{eff}}$, which at present suffers from bimodality in cosmological constraints. Our forecast analysis reveals that BAO data alone will not provide the precision needed to tightly constrain self-interactions; however, the combined analysis of the phase shift signature in both CMB and BAO can potentially provide a way to detect the impact of new neutrino interactions. Our results could be extended upon for models with non-universal interactions.

Figures (12)

• Figure 1: The impact of $G_{\mathrm{eff}}$ (the interaction strength of neutrinos) on the matter power spectrum. This is directly shown in the first panel, with the relative change to a power spectrum with $\log_{10}{(G_{\mathrm{eff}})} = -6$ (effectively indistinguishable to $\Lambda$CDM) shown in the next panel. In the third panel, we show the BAO oscillations computed by dividing out the smoothed broadband power spectrum. We also alter $A_s$ and $n_s$ before implementing the smoothing procedure, which is explained in further detail in the main text. The shift in the phase $\Delta \phi = \Delta k r_s$ as a function of $k$ is computed as the shifts in the peaks and troughs of the power spectrum oscillations relative to a power spectrum with $\log_{10}{(G_{\mathrm{eff}})} = -6$; this is shown in the fourth panel. It is possible to also see this signal as a function of $\ell$ in the CMB power spectrum, by plotting $\Delta \ell$ (or $\theta_s \Delta \ell$); see Figure \ref{['fig:phaseshiftdemo_CMB']}.
• Figure 2: The effect of neutrino self-interactions and thus delayed free-streaming on the CMB temperature-temperature (TT) power spectrum; this is directly shown by plotting power spectra with various $G_{\mathrm{eff}}$ in the top panel, with the relative difference shown in the second panel. The final panel shows the shift in the peaks and troughs of the CMB oscillations, $\Delta \ell$, which is the phase shift caused by neutrino self-interactions.
• Figure 3: The phase shift function $f(k)$ extracted from the BAO signal. $f(k)$ has been extracted for 120 spectra by computing $\Delta k/ r_s$ relative to a spectrum with $N_{\mathrm{eff}} = 3.044$, for a range of values of $N_{\mathrm{eff}}$ indicated by the colour bar, with each normalized by $\beta_{\phi}(N_{\mathrm{eff}})$. The dotted line shows the fitting function given in baumann2018searchingbaumann2019first, and the black points show the average value of $f(k)$ from the 120 spectra. The power spectra were computed using CLASSblas2011cosmic.
• Figure 4: The scale dependent function $f_{\nu}(\ell)$ that captures the phase shift in the CMB power spectra, calculated by averaging the phase from 100 power spectra with varying $N_{\mathrm{eff}}$ after dividing by the amplitude $A_{\nu}$, defined in Equation \ref{['eq:montefalconetemplate']}. The red line shows the template of montefalcone2025free, and the data points show the phase shift extracted from each of the spectra, with the shaded regions showing the spread in the averaged data points.
• Figure 5: The phase shift signal for different fixed values of $G_{\mathrm{eff}}$. The red line shows a fit through the extracted phase shift and the blue line shows the template for Standard Model neutrinos baumann2018searchingwallisch2019cosmological. The dashed black lines correspond to the standard model theoretical prediction derived by bashinsky2004neutrino. The numerical calculations are noisy for $-2 < \log_{10}{(G_{\mathrm{eff}})} < -1$, likely because there is more power on scales close to the BAO scale for these interaction strengths which introduces noise into the dewiggling process. Additionally, for all plots on scales $> 0.4 h\, \mathrm{Mpc}^{-1}$ the BAO oscillations are very small, leading to a noisier signal. As such we fit only for $k \leq 0.4 h\, \mathrm{Mpc}^{-1}$. The power spectra were generated using CLASS-PT.