Constraints on the inflationary vacuum and reheating era from NANOGrav

Abstract

Abstract NANOGrav and various pulsar timing array experiments recently reported 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 ( ω re ) and reheating temperature ( T re ). We find a preference for an extremely blue-tilted tensor spectrum and a non-instantaneous reheating epoch. 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 a two-parameter Bogoliubov family of non-Bunch-Davies vacuum. 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 α 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 adopted non-Bunch-Davies vacuum framework, a non-matter-like scenario is preferred, as matter-like reheating requires relatively large values of α , which violate both the upper bound set by NANOGrav observations and the backreaction constraint. Furthermore, we find that a frequency-dependent parametrization of the vacuum parameter α 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 α by probing the GW spectrum through future GW experiments.