Cosmological Non-Gaussianity from Neutrino Seesaw Mechanism

TL;DR

This work builds a framework that connects the high-scale neutrino seesaw with cosmic inflation by letting the inflaton decay predominantly into right-handed neutrinos after inflation. Higgs fluctuations during inflation modulate the reheating process, generating a curvature perturbation whose local non-Gaussianity carries imprints of the seesaw scale. The analysis shows that the NG signal, especially of the local type, is sensitive to the heavy-neutrino mass scale $M$, the neutrino Yukawa coupling $y_\nu$, the Higgs self-coupling $\lambda$, and the inflationary Hubble scale $H_{\rm inf}$, offering a novel way to probe GUT/Planck-scale physics with cosmological data. The results also reveal a meaningful interplay with low-energy neutrino experiments and collider Higgs measurements, and highlight UV considerations through the cutoff $\Lambda$ in the derivative inflaton- neutrino coupling, motivating a holistic view of high-scale physics accessible via cosmological non-Gaussianity.

Abstract

The neutrino mass generation via conventional seesaw mechanism is realized at high scales around $O(10^{14})$GeV with natural Yukawa couplings of $O(1)$, making the test of neutrino seesaw a great challenge. It is intriguing to note that the neutrino seesaw scale is typically around the upper range of the cosmological inflation scale. In this work, we propose a new framework incorporating inflation and neutrino seesaw in which the inflaton primarily decays into right-handed neutrinos after inflation. This decay process is governed by the inflaton interaction with the right-handed neutrinos that respects the shift symmetry. With the neutrino seesaw mechanism, we construct a new realization of the Higgs modulated reheating, in which the fluctuations of Higgs field can modulate the inflaton decays and contribute to the primordial curvature perturbation. We investigate the induced non-Gaussian signatures and demonstrate, for the first time, that such signatures provide an important means to directly probe the high scale of natural neutrino seesaw. We further analyze the interplay of the non-Gaussianity signatures with the low-energy neutrino experiments, and their interplay with the Higgs self-coupling measurements at the LHC and future colliders.

Figures (8)

• Figure 1: Shape of the eigenfunction $\Psi_n^{}$ as a function of Higgs field $h\space$, where we choose the eigenvalue index $n=0,1,9$ for illustration. The SM Higgs self-coupling constant is set as $\lambda\space =\space 0.01\space$.
• Figure 2: $\!\!$Probability density distribution $\rho_{\rm{eq}}^{}$ as a function of the Higgs field $h$ at the end of inflation. The SM Higgs self-coupling constant is set as $\lambda\!=\space 0.01$.
• Figure 3: Evolution of background value of the Higgs field $|h(t)|$ after inflation, where we set an initial value $h_{\text{inf}}^{}\space=\! H_{\text{inf}}^{}\space$. In this plot, the red solid curve represents the numerical solution and the blue dashed curve denotes the analytic solution.
• Figure 4: Schematic plot showing how the comoving curvature perturbation $\zeta_h^{}$ sourced from the Higgs-modulated reheating is a function of the Higgs field $h_\text{inf}^{}$ during the inflation, $\zeta_h^{}\!=\space\zeta_h(h_\text{inf}^{})\space$.
• Figure 5: Three-point correlation function of Higgs fluctuation $\delta h$ from the Higgs self-interaction $\Delta\mathcal{L}\!=\!-\sqrt{-g\,}[(\lambda {\space}\bar{h})\delta h^3]\,$. The Higgs propagator is depicted by a blue solid line with a dot and a square at its endpoints, representing a bulk-to-boundary propagator, which includes one "plus type" and one "minus type". The square at one end of the propagator indicates its boundary point ($\tau_f^{}\!\rightarrow\! 0^-$). The shaded dot at the vertex means that contributions from both plus- and minus-type propagators must be summed.