Inflaton mass in the nuMSM inflation

TL;DR

The paper investigates reheating in a nuMSM-inspired inflation scenario where the inflaton decays generate Dark Matter sterile neutrinos, arguing that energy transfer to the Standard Model sector is inefficient and yields a low reheating temperature. By combining parametric-resonance analysis, perturbative decay channels, and the possibility of a non-minimal coupling to gravity, it derives conditioned inflaton-mass bounds in two regimes: a light inflaton with $m_I \sim 0.1$–$10\,\mathrm{GeV}$ and a heavy inflaton with $m_I \sim 300$–$1000\,\mathrm{GeV}$ (for small $α$). These bounds hinge on COBE normalization $β \simeq 1.3\times 10^{-13}$ and radiative-correction limits $α \le 3\times 10^{-7}$, as well as the requirement $T_R > 150\,\mathrm{GeV}$ for successful baryogenesis. The results constrain the inflaton’s properties in the nuMSM framework and have implications for Dark Matter production, baryogenesis, and potential experimental signatures, while leaving room for higher $ξ$ scenarios to modify the preheating dynamics to be explored further.

Abstract

We analyse the reheating in the modification of \nuMSM (Standard Model with three right handed neutrinos with masses below the electroweak scale) where the sterile neutrino providing the Dark Matter is generated in decays of the additional inflaton field. We deduce that due to rather inefficient transfer of energy from the inflaton to the Standard Model sector reheating tends to happen at very low temperature, thus providing strict bounds on the coupling between the inflaton and the Higgs particles. This in turn translates to the bound on the inflaton mass, which appears to be very light 0.1 GeV <~ m_I <~ 10 GeV, or slightly heavier then two Higgs masses 300 GeV <~ m_I <~ 1000 GeV.

Figures (5)

• Figure 1: Number densities of the Higgs boson and the inflaton are shown for different values inflaton-Higgs coupling $\alpha$. Higgs self-coupling is taken as $\lambda=10^{-2}$. Time is given in program units, see Felder:2000hq. Preheating ends earlier for Higgs field ($t_{pr}\lesssim 100$) than for inflaton ($t_{pr}\lesssim 500$). For $\alpha=10^{-9}$ one has the border case when the average momenta of the fields are less then the lattice ultraviolet cutoff.
• Figure 2: Energy transfer dependence on $\lambda$ (here $\alpha=\beta=2.6\times10^{-13}$). Values are taken at late time $t_{pr}=10^3$. LatticeEasy parameters are as in Fig. \ref{['fig1']}.
• Figure 3: Energy transfer dependence on inflaton--Higgs coupling $\alpha$. Values are taken at late time $t_{pr}=10^3$. Dashed and dotted lines show respectively the dependence of $\frac{\rho_{\phi}}{\rho_{\chi}}$ and $\frac{n_{\phi}}{n_{\chi}}$ on $\alpha$. Extrapolation gives $\rho_{\phi} \simeq \rho_{\chi}$ at $\alpha \simeq 3\times 10^{-8}$. LatticeEasy parameters are as in Fig. (\ref{['fig1']}). For a physical value of the Higgs self-coupling $(\lambda\simeq 0.1$ the energies become comparable even closer to $\alpha=10^{-7}$.
• Figure 4: The dependence of the quartic coupling $\beta$ on the non-minimal coupling parameter $\xi$.
• Figure 5: Bounds on the inflation mass for successful reheating. Allowed regions for the case of $II\to HH$ scattering (lower region, light inflaton) and inflaton decay (upper region, heavy inflaton). Higgs mass is chosen $m_H=\unit[150]{GeV}$ and $T_R\geq \unit[150]{GeV}$. Bounds are: I (inflaton decay), II ($m_I\geq2 m_H$), III (2-2 scattering, non-thermal $I$ distribution), IV (2-2 scattering, thermal $I$ distribution), V ($\alpha\le 3\times 10^{-7}$, smallness of radiative corrections).