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Thermal gravitons from warm inflation

Gabriele Montefalcone1,*, Barmak Shams Es Haghi1,†, Tao Xu2,‡, and Katherine Freese1,3,4,§

  • *Contact author: montefalcone@utexas.edu
  • †Contact author: shams@austin.utexas.edu
  • ‡Contact author: tao.xu@ou.edu
  • §Contact author: ktfreese@utexas.edu
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Phys. Rev. D 112, 063556 – Published 26 September, 2025

DOI: https://doi.org/10.1103/rnvb-t4lx

Abstract

In warm inflation (WI), the persistent thermal bath that is sustained by dissipative interactions with the inflaton field produces a stochastic background of gravitational waves (GWs). In this paper we study the production and evolution of these GWs. Specifically, we investigate the emission of thermal gravitons (gravitons emitted by a thermal bath) from scattering with particles in the bath and then the evolution of the corresponding high-frequency GWs. We find that the bulk of thermal graviton production in WI occurs during the transition to radiation domination after inflation. Further, the energy density of thermal gravitons is enhanced by roughly 1 to 2 orders of magnitude compared to that in a radiation-dominated scenario with the same reheating temperature. We also calculate the spectrum of the resulting stochastic GW background and find that it has a distinctive shape, consisting of a peak at high frequencies (∼100  GHz) and an almost flat spectrum extending to low frequencies. The peak arises from emission of subhorizon modes that follow the temperature of the bath. The flat part of the spectrum corresponds to the modes that exit the horizon during WI and reenter during radiation domination and reflects the approximately constant temperature of the thermal bath during WI. We show that the detection prospects for the high-frequency peak of the GW spectrum, while improved slightly compared to the radiation-dominated case, still remain challenging. The thermal spectrum’s low-frequency plateau is typically subdominant to the amplitude of the standard vacuum tensor modes from inflation, although WI models can exist where the thermal graviton plateau surpasses the vacuum contribution without exceeding current observational limits on the tensor-to-scalar ratio. Furthermore, we calculate the thermal graviton contribution from WI to dark radiation and show that WI models are generally expected to satisfy current observational bounds including those from the cosmic microwave background.

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Phys. Rev. D 112, 063556– Published 26 September, 2025
  • Received 5 August 2025
  • Accepted 11 September 2025
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