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 (nt), tensor-to-scalar ratio (r), and explore the implications for reheating through constraints on the reheating equation of state (ωre) and reheating temperature (Tre). 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 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 non-Bunch-Davies framework considered here, a non-matter-like reheating is preferred because matter-like reheating requires relatively large α, violating both the NANOGrav upper bound and the backreaction constraint. We further show that a frequency-dependent parametrization of 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 through future GW experiments.
Versions
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BibTeX
@misc{chowdhury2026constraints,
title = {{Constraints on the inflationary vacuum and reheating era from NANOGrav}},
author = {Debtosh Chowdhury and Rounak Nath and Sudipta Show},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.05310},
eprint = {2605.05310},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.05310},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constraints on the inflationary vacuum and reheating era from NANOGrav
AU - Debtosh Chowdhury
AU - Rounak Nath
AU - Sudipta Show
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2605.05310
UR - https://arxiv.org/abs/2605.05310
AB - 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 (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 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 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 non-Bunch-Davies framework considered here, a non-matter-like reheating is preferred because matter-like reheating requires relatively large α, violating both the NANOGrav upper bound and the backreaction constraint. We further show that a frequency-dependent parametrization of 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 through future GW experiments.
ER -