Constraints on the Primordial Curvature Power Spectrum and Reheating Temperature from the NANOGrav 15-Year Dataset

The stochastic signal observed by collaborations such as NANOGrav, PPTA, EPTA +InPTA, and CPTA may originate from gravitational waves induced by primordial curvature perturbations during inflation. This study investigates small-scale properties of inflation and reheating, assuming a log-normal form for the power spectrum of the primordial curvature and a reheating phase equation of state w=1/9. Inflation and reheating scenarios are thoroughly examined using Bayesian methods applied to the NANOGrav 15-year dataset. The analysis establishes constraints on the reheating temperature, suggesting Trh≳0.1Gev, consistent with Big Bang nucleosynthesis constraints. Additionally, the NANOGrav 15-year dataset requires the amplitude (A∼0.1) and width (Δ≲0.001) of the primordial curvature power spectrum to be within specific ranges. A notable turning point in the energy density of scalar-induced gravitational waves occurs due to a change in the equation of state w. This turning point signifies a transition from the reheating epoch to radiation domination. Further observations of scalar-induced gravitational waves could provide insights into the precise timing of this transition, enhancing our understanding of early Universe dynamics.