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High-Frequency Thermal Graviton Remnant from the End of Inflation

Chen-Hao Wu, Xiao Liang, Ya-Peng Hu

TL;DR

This work proposes that sub-horizon gravitons, kept in local thermal equilibrium by a Gibbons-Hawking bath during inflation, survive as a decoupled, relativistic relic once inflation ends. Using an open quantum system framework, it shows the Gibbons-Hawking radiation has a Planckian spectrum with temperature $T_{\text{dS}} = H_\Lambda/(2\pi)$ and yields a HF gravitational-wave background whose energy density scales as $\rho_G = a_H T_H^4$ and peaks at a frequency set by the reheating temperature. Through cosmological redshift and entropy considerations, the authors derive the present-day spectrum $\Omega_G(f_0)$, mapping the peak properties to $H_\Lambda$ and $T_{\rm reh}$; they provide concrete forecasts for realistic inflationary scales and reheating scenarios, showing MHz-band signals with amplitudes that could be tested by future HF GW detectors. The Planck-like HF remnant is distinct from vacuum-fluctuation GWs, offering a unique probe of the end of inflation and the thermal history of the early universe. If detected, this signal would serve as a thermometer for reheating and a window into the microphysics of the inflation-to-reheating transition.

Abstract

The standard inflationary theory focuses on the freezing of super-horizon fluctuations, which generate a scale-invariant spectrum, while the sub-horizon modes are expected to remain in thermal equilibrium. Building upon recent development of quantum thermodynamics of the de Sitter universe, we investigate the graviton remnant originating from this thermal horizon radiation released at the end of inflation. Unlike the stochastic background from super-horizon fluctuations, this signal represents a snapshot of the thermal dS state, which subsequently decouples and undergoes cosmological redshift. We present a semi-analytical approximation prediction for this relic background, typically peaking in near MHz band, with characteristic energy density of $\log_{10}(Ω_{\rm G} h^2) \sim \mathcal{O}(-18)$. These signals occupy a High-Frequency band, offering a potential novel probe of the reheating temperature and the thermal history of the early universe.

High-Frequency Thermal Graviton Remnant from the End of Inflation

TL;DR

This work proposes that sub-horizon gravitons, kept in local thermal equilibrium by a Gibbons-Hawking bath during inflation, survive as a decoupled, relativistic relic once inflation ends. Using an open quantum system framework, it shows the Gibbons-Hawking radiation has a Planckian spectrum with temperature and yields a HF gravitational-wave background whose energy density scales as and peaks at a frequency set by the reheating temperature. Through cosmological redshift and entropy considerations, the authors derive the present-day spectrum , mapping the peak properties to and ; they provide concrete forecasts for realistic inflationary scales and reheating scenarios, showing MHz-band signals with amplitudes that could be tested by future HF GW detectors. The Planck-like HF remnant is distinct from vacuum-fluctuation GWs, offering a unique probe of the end of inflation and the thermal history of the early universe. If detected, this signal would serve as a thermometer for reheating and a window into the microphysics of the inflation-to-reheating transition.

Abstract

The standard inflationary theory focuses on the freezing of super-horizon fluctuations, which generate a scale-invariant spectrum, while the sub-horizon modes are expected to remain in thermal equilibrium. Building upon recent development of quantum thermodynamics of the de Sitter universe, we investigate the graviton remnant originating from this thermal horizon radiation released at the end of inflation. Unlike the stochastic background from super-horizon fluctuations, this signal represents a snapshot of the thermal dS state, which subsequently decouples and undergoes cosmological redshift. We present a semi-analytical approximation prediction for this relic background, typically peaking in near MHz band, with characteristic energy density of . These signals occupy a High-Frequency band, offering a potential novel probe of the reheating temperature and the thermal history of the early universe.

Paper Structure

This paper contains 5 sections, 25 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Gibbons-Hawking radiation spectrum: An Open System Perspective from Quantum Thermodynamics
  3. Standard cosmological evolution
  4. Concrete examples and observational prospects
  5. Discussion and Outlook

Figures (2)

  • Figure 1: The plot of energy density spectra versus the frequency at the instant of reheating, shown for $\gamma = 1$. We select three sets of traditional inflationary Hubble values $H_\Lambda \sim 10^{12}$ (blue), $10^{13}$ (green), and $10^{14}\, \text{GeV}$ (orange), respectively.
  • Figure 2: The dimensionless density parameter spectrum today versus frequency. We choose $H_\Lambda \sim 10^{12}$ (blue), $10^{13}$ (green), and $10^{14}\, \text{GeV}$ (orange), respectively, as the typical Hubble rate. We also set two popular reheating energy scales as $T_{\rm reh,h} \sim 10^{13}\, \text{GeV}$ (solid) and $T_{\rm reh,l} \, \sim 10^{9}\,\text{GeV}$ (dashed). This graph has been processed by log-log coordinates.