Reheating with Thermal Dissipation and Primordial Gravitational Waves

TL;DR

This work investigates reheating after inflation via thermal dissipation, showing that a temperature-dependent decay rate $\Gamma(T)$ can imprint characteristic bends in the primordial gravitational wave spectrum. Using a Schwinger–Keldysh open EFT framework, it derives the inflaton's equation of motion with $\Gamma$ and a thermally corrected potential $V_{\rm eff}$ and establishes a fluctuation–dissipation relation via bath correlators. It provides concrete examples for scalar trilinear and Yukawa couplings to illustrate how $\Gamma(T)$ scales with temperature and inflaton amplitude across regimes. Forecasts indicate that future missions like ultimate-DECIGO could distinguish different dissipation exponents $n$, thereby probing the microphysics of reheating and inflaton interactions.

Abstract

In order for an inflationary universe to evolve into a hot universe, a process known as reheating is required. However, the precise mechanism of reheating remains unknown. We show that if the reheating is triggered by thermal dissipation effects, distinctive features appear in the spectrum of primordial gravitational waves. This suggests a possible way to observationally probe the physics of reheating.

Figures (6)

• Figure 1: The Schwinger--Keldysh contour $\mathcal{C}_{1 + 2 + \beta}$ in the complex time plane is shown. The contour consists of three segments: $\mathcal{C}_1$ (from $t_\mathrm{i}$ to $t_\mathrm{f}$), $\mathcal{C}_2$ (from $t_\mathrm{f}$ to $t_\mathrm{i}$), and $\mathcal{C}_\beta$ (from $t_\mathrm{i}$ to $t_\mathrm{i} - i \beta$). $\phi_1$ and $\phi_2$ are defined on $\mathcal{C}_1$ and $\mathcal{C}_2$, respectively. If a non-vanishing field value of $\phi$ changes the property of the thermal plasma, $\phi_\mathrm{i}$ resides on the imaginary-time segment $\mathcal{C}_\beta$. $\phi_\mathrm{i}$ also lives both on $\mathcal{C}_{1 + 2}$ but these contributions are cancelled out due to the unitarity, and therefore one may only consider $\Delta \phi_{1/2} = \phi_{1/2} - \phi_\mathrm{i}$.
• Figure 2: (Left) Time evolution of the inflaton energy density $\rho_\phi$ for different thermal dissipation model $n=1, 0, -1$ and $-10$ in (\ref{['GammaT']}). For comparison, $\rho_r$ for $n=0$ is also plotted. (Right) Time evolution of the equation of state parameter $w$ for $n=1, 0, -1$ and $-10$.
• Figure 3: (Left) GW spectrum with reheating under thermal dissipation (\ref{['GammaT']}). The case of $n=1,0,-1$ and $-10$ are shown. They are normalized so that the leftmost part becomes equal to unity. (Right) Enlarged view of the left figure.
• Figure 4: GW spectrum for $H_{\rm inf}=7\times 10^{13}\,{\rm GeV}$ and $T_{\rm R} = 6\times 10^6\,{\rm GeV}$ for $n=1$ (left) and $n=-10$ (right). For comparison, the case of $n=0$ is also shown. Error bars are based on the noise spectrum of FP-DECIGO with 10 years observation.
• Figure 5: GW spectrum for $H_{\rm inf}=7\times 10^{13}\,{\rm GeV}$ and $T_{\rm R} = 6\times 10^6\,{\rm GeV}$ for $n=1$ (left) and $n=-10$ (right). For comparison, the case of $n=0$ is also shown. Error bars are based on the noise spectrum of ultimate-DECIGO with 10 years observation.