On initial conditions for the Hot Big Bang

TL;DR

This work analyzes initial conditions for the Hot Big Bang in a framework where the SM Higgs plays the inflaton with a large non-minimal gravity coupling. It develops the Higgs-driven inflation scenario, derives the Einstein-frame dynamics, and provides a detailed reheating analysis that yields a radiation-dominated start at $T_r \sim (3-15) \times 10^{13}$ GeV, with the post-inflation evolution transitioning from a Higgs-oscillation–driven matter era to thermal SM radiation. It shows that sterile-neutrino abundances are negligible at $T_r$ in the minimal nuMSM, and explores addition of Planck-suppressed higher-dimensional operators, finding they do not drive inflation nor baryogenesis but can induce DM production during preheating for certain sterile-neutrino masses. The results constrain DM sterile-neutrino masses (heavier than a few MeV risk overclosure) and indicate that WDM production must occur at low temperatures, reinforcing a low-energy origin for baryogenesis and DM in this setup. Overall, the paper provides a coherent link between inflationary physics and later cosmological processes, clarifying the role of higher-dimensional operators and establishing concrete initial conditions for the Hot Big Bang in Higgs-driven inflation scenarios.

Abstract

We analyse the process of reheating the Universe in the electroweak theory where the Higgs field plays a role of the inflaton. We estimate the maximal temperature of the Universe and fix the initial conditions for radiation-dominated phase of the Universe expansion in the framework of the Standard Model (SM) and of the nuMSM -- the minimal extension of the SM by three right-handed singlet fermions. We show that the inflationary epoch is followed by a matter dominated stage related to the Higgs field oscillations. We investigate the energy transfer from Higgs-inflaton to the SM particles and show that the radiation dominated phase of the Universe expansion starts at temperature T_r~(3-15)*10^{13} GeV, where the upper bound depends on the Higgs boson mass. We estimate the production rate of singlet fermions at preheating and find that their concentrations at T_r are negligibly small. This suggests that the sterile neutrino Dark Matter (DM) production and baryogenesis in the nuMSM with Higgs-driven inflation are low energy phenomena, having nothing to do with inflation. We study then a modification of the nuMSM, adding to its Lagrangian higher dimensional operators suppressed by the Planck scale. The role of these operators in Higgs-driven inflation is clarified. We find that these operators do not contribute to the production of Warm Dark Matter (WDM) and to baryogenesis. We also demonstrate that the sterile neutrino with mass exceeding 100 keV (a Cold Dark Matter (CDM) candidate) can be created during the reheating stage of the Universe in necessary amounts. We argue that the mass of DM sterile neutrino should not exceed few MeV in order not to overclose the Universe.