Constraints on the inflationary vacuum and reheating era from NANOGrav

Abstract

NANOGrav and various pulsar timing array experiments recently reported compelling evidence for a stochastic gravitational wave background (SGWB). Such a background may originate from several astrophysical or cosmological sources. Assuming an inflationary origin, we use the latest NANOGrav 15-year dataset to constrain inflationary parameters, including the tensor spectral index ($n_t$), tensor-to-scalar ratio ($r$), and explore the implications for reheating through constraints on the reheating equation of state ($\omega_{\text{re}}$) and reheating temperature ($T_{\text{re}}$). We find a preference for an extremely blue-tilted tensor spectrum and a non-instantaneous reheating epoch. Despite no concrete evidence on primordial vacua, inflationary vacuum is commonly assumed to be the Bunch-Davies vacuum. In this work, we study modifications to the GW spectrum arising from a two-parameter Bogoliubov family of non-Bunch-Davies vacua. Within this framework, we find that NANOGrav observations favour a subclass of non-Bunch-Davies vacuum, known as the alpha-vacuum. In addition, our analysis demonstrates that the observations strikingly narrow the range of the parameter $\alpha$ that characterizes the vacua. Our analysis indicates that the NANOGrav data can accommodate both matter- and radiation-like reheating scenarios for the standard Bunch-Davies vacuum case. However, within the non-Bunch-Davies framework considered here, a non-matter-like reheating is preferred because matter-like reheating requires relatively large $\alpha$, violating both the NANOGrav upper bound and the backreaction constraint. We further show that a frequency-dependent parametrization of $\alpha$ beyond a threshold frequency can yield a minimal solution that alleviates the blue-tilted issue. Finally, we highlight the possibility of testing such frequency dependence of $\alpha$ through future GW experiments.