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

Multiple pulsar timing array (PTA) collaborations, including the European PTA in partnership with the Indian PTA, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the Parkes PTA, and the Chinese PTA have 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 \(\Omega _\textrm{gw}^{s}\) 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 \(f_s = 1.2^{+0.6}_{-\,0.6}\times 10^{-8} \textrm{Hz}\) and \(\Omega _\textrm{gw}^{s} = 2.9^{+5.4}_{-2.3}\times 10^{-8}\), 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. Future pulsar timing array observations with improved sensitivity and extended frequency coverage will enable tighter constraints on string cosmology parameters.