Constraints on the inflationary vacuum and reheating era from NANOGrav

TL;DR

Using NANOGrav data, this paper constrains inflationary parameters and explores the effects of non-Bunch-Davies vacua on the gravitational wave spectrum, suggesting potential for future tests.

Contribution

It introduces the first constraints on inflationary parameters from NANOGrav assuming an inflationary origin of the SGWB and investigates non-Bunch-Davies vacuum effects on GW spectra.

Findings

Preference for an extremely blue-tilted tensor spectrum ($n_t=2.20^{+0.36}_{-1.2}$)

Identification of a specific non-Bunch-Davies vacuum (alpha-vacuum) favored by data

Proposal of frequency-dependent vacuum parameters to address the blue tilt issue

Abstract

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 $n_t=2.20^{+0.36}_{-1.2}$ and the radiation-like reheating scenario $\omega_{\text{re}}=0.33^{+0.14}_{-0.36}$. 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.