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

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 ${\mathrm{\Omega }}_{\mathrm{g}\mathrm{w}}^s$ 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 $f_s=1.2_{-0.6}^{+0.6}\times {10}^{-8}\mathrm{H}\mathrm{z}$ and ${\mathrm{\Omega }}_{\mathrm{g}\mathrm{w}}^s=2.9_{-2.3}^{+5.4}\times {10}^{-8}$, 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.