Gravitational scalar production with a generic reheating scenario

TL;DR

This work analyzes gravitational production of a decoupled scalar $s$ during inflation and a generic reheating history, including instantaneous, matter-dominated, power-law, and multi-stage reheating. By tracking the post-inflationary evolution of the inflationary condensate and by evaluating production via Planck-suppressed operators during reheating, the authors derive how the final relic abundance depends on the reheating dynamics and the inflaton potential power $k$. They obtain explicit constraints on the scalar self-coupling $\λ_s$, mass $m_s$, and on Wilson coefficients $|C_1|$ and $|C_2|$, highlighting that $k<4$ can dilute the relic while $k>4$ enhances it, and that multi-stage reheating yields a factorised, stage-by-stage modification of the abundance. The results have direct implications for the viability and detectability of non-thermal dark matter in the presence of unavoidable gravitational effects, especially at low reheating temperatures where dilution can restore consistency for certain parameter ranges.

Abstract

Gravitational production of decoupled scalars during inflationary and post-inflationary phases is efficient and can lead to over-production. We study this production with various reheating scenarios such as a generic power-law inflaton potential $V_{\rm inf}\propto φ^k$ as well as a multi-stage reheating scenario. We derive constraints on the scalar self-interaction coupling $λ_s$, the mass $m_s$, and coefficients of quantum gravity-induced operators. We find that the constraints depend sensitively on the reheating dynamics. Our analysis demonstrates that universal gravity effects do not necessarily spoil the predictivity of non-thermal dark matter scenarios with $k < 4$ and low reheating temperatures, as an extended reheating phase dilutes gravitationally-produced relics. For $k > 4$, on the other hand, the relic abundance is enhanced during the reheating phase, leading to stringent constraints on the scalar. In multi-stage reheating, we show that the enhancement/dilution effect of subsequent reheating phases factorises.

Figures (11)

• Figure 1: Schematic diagram for the evolution of the dominant energy component and a decoupled scalar. The instantaneous reheating scenario, where the energy of the inflaton gets immediately transferred to radiation at the end of inflation, is assumed here.
• Figure 2: Constraints on the scalar self-interaction coupling $\lambda_s$ in terms of the scalar mass $m_s$ in the instantaneous reheating scenario. Together with the choice of $g_* = g_{*s} = 100$, three reheating temperatures are considered, namely $T_{\rm reh} = 10^{15}$ GeV (solid), $10^{14}$ GeV (dashed), and $10^{13}$ GeV (dot-dashed). In terms of the Hubble parameter at the end of inflation, these values of the reheating temperature correspond to $H_{\rm end} = 1.3 \times 10^{12}$ GeV, $1.3 \times 10^{10}$ GeV, and $1.3 \times 10^{8}$ GeV, respectively. The self-thermalisation bound (green region) is adopted from Refs. Arcadi:2019oxhLebedev:2022cic.
• Figure 3: Schematic diagram for the evolution of the dominant energy component and the decoupled scalar $s$ across inflation, reheating, and radiation domination. Here, reheating is assumed to be completed before the onset of the dust regime of the scalar condensate.
• Figure 4: Constraints on the scalar self-interaction coupling $\lambda_s$ in terms of the scalar mass $m_s$ for the $k = 2$ (blue), $k = 4$ (red), and $k = 6$ (olive) cases, with the choice of $g_* = g_{*s} = 100$. With the Hubble parameter at the end of inflation being fixed to be $H_{\rm end} = 10^{12}$ GeV, three values of the reheating temperatures are considered, namely $10^{13}$ GeV (solid), $10^{10}$ GeV (dashed), and $10^7$ GeV (dot-dashed). The self-thermalisation bound (green region) is adopted from Refs. Arcadi:2019oxhLebedev:2022cic.
• Figure 5: Constraints on the scalar self-interaction coupling $\lambda_s$ in terms of the scalar mass $m_s$ for the two-stage reheating scenario. Three cases of $\{k_1, k_2\}$ are considered: $\{4, 2\}$ (blue), $\{4, 6\}$ (red), and $\{2, 4\}$ (olive). As in Fig. \ref{['fig:inflation_power-law']}, the Hubble parameter at the end of inflation is chosen to be $H_{\rm end} = 10^{12}$ GeV, and $g_* = g_{*s} = 100$ is taken. The reheating temperature $T_{\rm reh}$ is varied, while fixing the Hubble parameter at the end of the first stage to $H_1 = 10^8$ GeV. The green region represents the self-thermalisation bound Arcadi:2019oxhLebedev:2022cic.