Broken blue-tilted inflationary gravitational waves: a joint analysis of NANOGrav 15-year and BICEP/Keck 2018 data

Recently, the pulsar timing array (PTA) collaborations have reported the evidence for a stochastic gravitational wave background (SGWB) at nano-Hertz band. The spectrum of inflationary gravitational wave (IGW) is unknown, which might exhibit different power law at different frequency-bands, thus if the PTA signal is primordial, it will be significant to explore the underlying implications of current PTA and CMB data on IGW. In this paper, we perform a joint Markov Chain Monte Carlo analysis for a broken power-law spectrum of IGW with the NANOGrav 15-year and BICEP/Keck 2018 data. It is found that though the bestfit spectral tilt of IGW at PTA band is $n_{\text{T}}^{\text{PTA}}=2.42_{-0.91}^{+0.32}$, at CMB band the bestfit is $n_{\text{T}}^{\text{CMB}}=0.55_{-0.10}^{+0.37}$ while a detectable amplitude of $r$ with $n_{\text{T}}^{\text{CMB}}\simeq 0$ is still compatible. The implication of our results for inflation is also discussed.