Largest temperature of the radiation era and its cosmological implications

TL;DR

The paper analyzes the consequences of a non-instantaneous reheating phase with a low reheat temperature $T_{ m RH}$, showing that the maximum reheating temperature $T_{ m MAX}$ can exceed $T_{ m RH}$ and that relic abundances of dark matter, neutrinos, and axions, as well as baryogenesis scenarios, can differ markedly from standard Big Bang cosmology. By deriving and solving the Boltzmann equations for the decaying scalar field, radiation, and dark-matter species during reheating, the authors demonstrate that the final relic densities depend sensitively on $T_{ m RH}$ and the dynamics before reheating completes, rather than solely on equilibrium freeze-out in a radiation-dominated universe. They apply this framework to supersymmetric dark matter candidates, massive neutrinos, and axions, finding that traditional bounds (e.g., unitarity limits on WIMP masses, CMLW neutrino bounds, and PQ-scale constraints) can be substantially relaxed, and that efficient leptogenesis and GUT baryogenesis can proceed even when $T_{ m RH}$ is well below the decaying particle masses. Overall, the work broadens the viable parameter space for beyond-Standard-Model physics by highlighting the critical role of reheating history in shaping cosmological constraints and early-universe processes.

Abstract

The thermal history of the universe before the epoch of nucleosynthesis is unknown. The maximum temperature in the radiation-dominated era, which we will refer to as the reheat temperature, may have been as low as 0.7 MeV. In this paper we show that a low reheat temperature has important implications for many topics in cosmology. We show that weakly interacting massive particles (WIMPs) may be produced even if the reheat temperature is much smaller than the freeze-out temperature of the WIMP, and that the dependence of the present abundance on the mass and the annihilation cross section of the WIMP differs drastically from familiar results. We revisit predictions of the relic abundance and resulting model constraints of supersymmetric dark matter, axions, massive neutrinos, and other dark matter candidates, nucleosynthesis constraints on decaying particles, and leptogenesis by decay of superheavy particles. We find that the allowed parameter space of supersymmetric models is altered, removing the usual bounds on the mass spectrum; the cosmological bound on massive neutrinos is drastically changed, ruling out Dirac (Majorana) neutrino masses $m_ν$ only in the range 33 keV $\simlt m_ν\simlt$ 6 (5) MeV, which is significantly smaller from the the standard disallowed range 94 eV $\simlt m_ν\simlt$ 2 GeV (this implies that massive neutrinos may still play the role of either warm or cold dark matter); the cosmological upper bound on the Peccei-Quinn scale may be significantly increased to $ 10^{16}$GeV from the usually cited limit of about $10^{12}$GeV; and that efficient out-of-equilibrium GUT baryogenesis and/or leptogenesis can take place even if the reheat temperature is much smaller than the mass of the decaying superheavy particle.

Figures (8)

• Figure 1: Shown in the upper graph is the evolution of the $X$ density in the case that the cross section is sufficiently large to establish chemical equilibrium prior to freeze out. The lower graph illustrates the case where the cross section is too small to establish chemical equilibrium. The two cross sections were chosen to result in the same final $X$ abundances necessary to give a critical density of $X$ particles today. In the calculations $g_*$ was kept constant at $g_*=30$.
• Figure 2: The shaded areas show the cosmologically excluded regions for a particle of mass $M_X$ with 2 degrees of freedom which annihilates in $s$-wave with a thermal-averaged nonrelativistic cross section $\langle \sigma v \rangle$. The upper-left figure is the usual case where particle freeze out occurs when the universe is radiation dominated. In the other frames, we have chosen $M_X/T_{RH}=50$, 100, and 200. The interesting region for cold dark matter ($0.025<\Omega_X h^2<1$) is between the dashed line and the shaded area. The upper right-hand corner of the $M_X- \langle \sigma v \rangle$ plane is excluded by unitarity arguments.
• Figure 3: The shaded region shows the cosmologically excluded region, as a function of the reheat temperature $T_{RH}$, for a particle of mass $M_X=100$ GeV with 2 degrees of freedom which annihilates with a thermal-averaged nonrelativistic $s$-wave cross section $\langle \sigma v \rangle$. The region interesting for cold dark matter ($0.025<\Omega_X h^2<1$) is delimited between the dashed line and the shaded area.
• Figure 4: The relic abundance $\Omega_X h^2$ as a function of the reheat temperature $T_{RH}$ for a particle with 2 degrees of freedom, mass $M_X$ and a nonrelativistic annihilation cross section in $s$-wave saturating the unitarity bound.
• Figure 5: Comparison of numerical vs. analytic results. The nonequilibrium calculation is relevant for $\alpha<\bar{\alpha}$, shown in the figure. The equilibrium calculation assumes decoupling while nonrelativistic, or $x_F>1$.