Abstract
The stochastic signal detected by the NANOGrav, PPTA, EPTA, and CPTA collaborations can be attributed to gravitational waves induced by the primordial curvature perturbations generated during inflation. These scalar-induced gravitational waves provide valuable insights into the small-scale inflation and reheating epochs. In this paper, we assume an equation of state of w=1 during reheating and adopt a log-normal form for the primordial curvature power spectrum to elucidate the observed stochastic signal. The inflation and reheating scenarios are rigorously constrained utilizing Bayesian methods applied to the NANOGrav 15-year data set. The analysis yields constraints on the reheating temperature, indicating Trh≳0.01Gev, a result consistent with constraints derived from Big Bang nucleosynthesis. Furthermore, the NANOGrav 15-year data set necessitates the primordial curvature power spectrum's amplitude and width to satisfy A∼0.01 and Δ≲0.1, respectively. Due to the change in the equation of state w, there exists a turning point in the energy density spectrum of scalar-induced gravitational waves. This suggests that if more data about the scalar-induced gravitational waves is observed, it could potentially provide constraints on the time when the reheating epoch transitions to radiation domination.
Published Version
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