Implications of the NANOGrav result on primordial gravitational waves in nonstandard cosmologies

Recently, the NANOGrav collaboration has reported the evidence for a common-spectrum stochastic process, which might be interpreted as the first ever detection of stochastic gravitational wave (GW) background. We discuss the possibility of the signal arising from the first and second order GWs in nonstandard cosmological history. We show that NANOGrav observation can be explained by the first order GWs in the nonstandard thermal history with an early matter dominated era, whereas the parameter space required to explain NANOGrav observation in the standard cosmology or in the nonstandard epoch of kination domination is ruled out by the BBN and CMB observations. For the second order GWs arising from the large primordial scalar fluctuations with a broad Gaussian power spectrum, we study two specific cases to achieve abundant primordial black hole (PBH) production. We find that the NANOGrav observation can be explained with standard radiation domination, or with a dust-like epoch where the gain in the latter case is the lower requirement of primordial amplitude. In this nonstandard epoch, for a broad power spectrum, PBH are produced in a wide mass range in the planetary mass regime. A nonstandard epoch of kination domination cannot produce enough PBH if NANOGrav result is to be satisfied.