Constraints on the inflationary vacuum and reheating era from NANOGrav

NANOGrav and various pulsar timing array experiments recently reported evidence for a common red noise signal across millisecond pulsars. This signal exhibits Hellings-Downs inter-pulsar correlation patterns, providing compelling evidence for a stochastic gravitational wave background (SGWB) signal. In general, such a background can come from several astrophysical and cosmological phenomena. Assuming such SGWB has an inflationary origin, we use latest NANOGrav 15-year dataset to constrain the inflationary parameters e.g., tensor spectral index ($n_t$), tensor-to-scalar ratio ($r$), and explore the implications for the reheating phase through constraints on the reheating equation of state (${\omega }_{\text{re}}$) and reheating temperature ($T_{\text{re}})$. We find the preference for an extremely blue-tilted tensor spectrum $n_t=2.20_{-1.2}^{+0.36}$ and the radiation-like reheating scenario ${\omega }_{\text{re}}=0.33_{-0.36}^{+0.14}$. Despite having no concrete evidence for the nature of the primordial vacua, the computation of gravitational wave (GW) sourced by tensor perturbations assumes the inflationary vacuum to be a Bunch-Davies vacuum. In this work, we examine modifications to the GW spectrum originating from the non-Bunch-Davies primordial vacuum. We find that NANOGrav observations favour a specific type of non-Bunch-Davies vacuum, known as the alpha-vacuum. Furthermore, our analysis demonstrates that the observations strikingly narrow down the range of the parameter $\alpha$ characterizing the vacua. On top of that, we find that a frequency-dependent parametrization of the vacuum parameter $\alpha$ beyond a threshold frequency can yield a minimal solution to alleviate the blue-titled issue. Finally, we highlight the possibility of testing such frequency dependence of $\alpha$ by probing the GW spectrum through future GW experiments.