Abstract
Recently, the pulsar timing array (PTA) collaborations havereported the evidence for a stochastic gravitational wavebackground (SGWB) at nano-Hertz band. The spectrum of inflationarygravitational wave (IGW) is unknown, which might exhibit differentpower law at different frequency-bands, thus if the PTA signal isprimordial, it will be significant to explore the underlyingimplications of current PTA and CMB data on IGW. In this Letter,we perform a joint Markov Chain Monte Carlo analysis for a brokenpower-law spectrum of IGW with the NANOGrav 15-year and BICEP/Keck2018 data. It is found that though the bestfit spectral tilt ofIGW at PTA band is n PTA T = 2.42+0.32 -0.91,at CMB band the bestfit is n CMB T = 0.55+0.37 -0.10 while a detectable amplitude of r with n CMB T ≃ 0 is still compatible. Theimplication of our results for inflation is also discussed.
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