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arXiv · 2610.18460

Constraints on the cosmic reheating history from PTA data

Qi-Lin Yang·Shi-Jie Wang·Nan Li
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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 $f_{\mathrm{reh}}$ 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 $f_{\mathrm{reh}}$ 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 $f_{\rm p}\sim 10^{-7.6}$--$10^{-7.0}$ Hz, along with $f_{\rm reh}\sim 10^{-9.0}$--$10^{-8.3}$ Hz and $w\sim 0.19$--$0.79$ (the $68\%$ confidence level), when the power spectrum has a relatively narrow width $Δ\lesssim 1$. 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 $10^{-6}$--$10^{-4} M_{\odot}$. 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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Qi-Lin Yang, Shi-Jie Wang, Nan Li. 2026-10-13. Constraints on the cosmic reheating history from PTA data. https://doi.org/10.1103/zpvp-rmd8

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