NANOGrav and PPTA Tension: Gravity Waves, Cosmic Strings, and Inflation

The NANOGrav collaboration has recently presented its pulsar timing array data which seem compatible with the presence of a stochastic gravity wave background emitted by cosmic strings with a dimensionless string tension $Gmusimeq 2times 10^{-11}-3times 10^{-10}$ at $95%$ confidence level ($G$ is Newtons constant and $mu$ denotes the string tension). However, there is some tension between these results and the previous pulsar timing array bound $Gmulesssim 4times 10^{-11}$ from the PPTA experiment. We propose a relaxation of this tension by invoking primordial inflation which partially inflates the string network. The latter re-enters the horizon at later times after the end of inflation, and thus the short string loops are not produced. This leads to a reduction of the gravity wave spectrum which is more pronounced at higher frequencies. The reconciliation of the NANOGrav results with the PPTA bound is possible provided that the strings re-enter the horizon at adequately late times. We consider an example of a realistic $SO(10)$ model incorporating successful inflation driven by a gauge singlet real scalar field with a Coleman-Weinberg potential. This model leads to the production of intermediate scale topologically stable cosmic strings that survive inflation. We show regions of the parameter space where the tension between NANOGrav and PPTA is alleviated. Finally, we present an example in which both monopoles and strings survive inflation with the above tension resolved.