The post-inflationary cosmology of the VISH$ν$ axion-majoron model

TL;DR

The paper develops a complete cosmological history for the VISHν axion-majoron model, tying inflation to a lattice-informed reheating phase where non-perturbative dynamics in the hidden sector largely govern energy transfer to the SM bath. It identifies three natural, radiatively stable reheating/leptogenesis pathways in which long-lived right-handed neutrinos reheat the universe while curbing dark radiation, thereby enabling viable leptogenesis and consistent dark radiation bounds. The study makes concrete predictions for the scalar spectral index via the non-standard expansion history, and for the stochastic gravitational-wave background shaped by preheating, turbulence, and axion-string dynamics, offering potential tests with future CMB and GW experiments. It also reinforces the role of post-inflationary axion dark matter with $f_a\sim 10^{11}$ GeV and highlights how upcoming neutrino mass measurements and GW observatories could falsify or support the VISHν framework.

Abstract

It was previously shown how several explanatory deficiencies of the Standard Model (including the origin of dark matter, matter-antimatter asymmetry, small active neutrino mass, strong CP-conservation and the seeds for large-scale structure formation) may be economically resolved when an experimentally-accessible QCD axion also plays the role of the majoron, and the scalar partner of the axion is dynamical during inflation. In this paper, we complete this general study of the cosmological history for a unit domain-wall number option of the DFSZ-type, dubbed VISH$ν$, by performing a detailed lattice-informed analysis of the reheating era. In doing so, we make inflationary and leptogenesis predictions more precise through estimates of the reheating temperature and the expansion history. The viable reheating scenarios, which at the same time satisfy strict conditions for naturalness (radiative stability), are also shown to respect dark radiation bounds. We also characterise the high-frequency spectrum of gravitational waves, and mention other phenomenological implications that distinguish VISH$ν$ from alternative proposals.

Figures (19)

• Figure 1: We plot the numerical relationship between the $S^\dagger S$ non-minimal gravitational coupling ($\xi_S$) and the $S$ self-coupling ($\lambda_S$). The latter must be highly suppressed for the consistency of the inflation model (the fitting of the scalar spectral amplitude $A_s$Planck:2018jri). The allowed domain of $\xi_S$ values is further explained in Section \ref{['sec:efolds']}, alongside the dependence on e-folds of inflation ($N$). The starred point represents our benchmark value in what follows.
• Figure 2: In the left panel we plot the fermionic occupation number spectrum after 16 oscillation periods of the background field ($\tau < 100$), choosing $y_{N_i} = 10^{-2}$ and $\lambda_S = 2.5\times10^{-10}$ (see Section \ref{['sec:neutrinos']} for details). The apparent Pauli blocking effect, restricting $n_k \leq 1$, results in the almost immediate saturation of the neutrino energy density fraction, as seen in the right panel. Colours are used in each plot to correlate the time point (energy fraction) with the spectral contours. Note that, in this regime, perturbative production of neutrinos from the inflaton is otherwise kinematically blocked, and the neutrinos are produced with low momentum ($\kappa < y_N/\sqrt{\lambda_S}$).
• Figure 3: We plot the power spectra for the field fluctuations at the end of inflation used in the initialisation scheme for the lattice simulation. It may be seen that all scalar fluctuations remain in vacuum on sub-horizon scales; the Higgs fluctuations are suppressed on super-horizon scales; the axion modes are excited into an initial, subdominant, isocurvature spectrum; while the radial modes may be identified with the inflaton. (This recapitulates the main points of the "effectively single-field" discussion in Section \ref{['sec:vishnu']}).
• Figure 4: We compare, for (\ref{['eq:sim1']}), the preheating of the inflaton ($\delta\sigma_R$, left) and axion ($\delta\sigma_I$, right) fluctuations. In the first row, we plot the occupation number spectrum, excited through parametric resonance from the initial inflationary spectrum, with a peak efficiency at the wavenumbers indicated by the dotted grey line (see text for details). In the second, we plot the corresponding energy density per wavenumber decade. In the third row, the growth in fluctuation energy is depicted, which becomes comparable to the background energy source at the end of preheating. As in Figure \ref{['fig:fermionicpreheating1']}, colours are used to correlate spectral contours at the indicated times, while the dashed line in first two rows indicates a much later time point after preheating.
• Figure 5: We depict the time evolution of the following quantities during preheating using (\ref{['eq:sim1']}): (top) the inflaton zero mode, $|\langle \sigma_R\rangle|$, along side root-mean squared fluctuations of inflatons, $\sqrt{\delta\sigma^2_R}$, and axions, $\sqrt{\delta\sigma^2_I}$; (middle) the energy fractions in potential, gradient and kinetic energy for the PQ sector, as well as the Higgs and radiation baths (into which the Higgs are quickly depleted); and (bottom) the time-smoothed equation of state (solid), alongside the oscillating lattice output (semi-transparent), compared to radiation $w=\frac{1}{3}$ (dashed black).