Constraining string cosmology with the gravitational-wave background using the NANOGrav 15-year data set

Abstract: The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration has recently reported strong evidence for a signal at nanohertz, potentially the first detection of the stochastic gravitational-wave background (SGWB). We investigate whether the NANOGrav signal is consistent with the SGWB predicted by string cosmology models. By performing Bayesian parameter estimation on the NANOGrav 15-year data set, we constrain the key parameters of a string cosmology model: the frequency $f_s$ and the fractional energy density $\Omega_\mathrm{gw}^{s}$ of gravitational waves at the end of the dilaton-driven stage, and the Hubble parameter $H_r$ at the end of the string phase. Our analysis yields constraints of $f_s = 1.2^{+0.6}_{-0.6}\times 10^{-8} \mathrm{Hz}$ and $\Omega_\mathrm{gw}^{s} = 2.9^{+5.4}_{-2.3}\times 10^{-8}$, consistent with theoretical predictions from string cosmology. However, the current NANOGrav data is not sensitive to the $H_r$ parameter. We also compare the string cosmology model to a simple power-law model using Bayesian model selection, finding a Bayes factor of $2.2$ in favor of the string cosmology model. Our results demonstrate the potential of pulsar timing arrays to constrain cosmological models and study the early Universe.