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

Recently, the NANOGrav Collaboration has reported 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 the NANOGrav observation can be explained by first-order GWs in the nonstandard thermal history with an early matter-dominated era, whereas the parameter space required to explain the NANOGrav observation in the standard cosmology or in the nonstandard epoch of kination domination is ruled out by the big bang nucleosynthesis and cosmic microwave background observations. For the second-order GWs arising from the large primordial scalar fluctuations, we study the standard radiation domination and two specific nonstandard cases with a few forms of the primordial power spectrum Pζ(k) to achieve abundant primordial black hole (PBH) production. We find that the NANOGrav observation can be explained with standard radiation domination for all of these Pζ(k). Furthermore, a dustlike epoch leads to abundant PBH formation for a lower amplitude of Pζ(k) than the radiation-dominated case and complies with the NANOGrav observation only for a few of the Pζ(k) forms considered here, where the peak wave number is larger than the wave number range probed by NANOGrav. In this nonstandard epoch, for a broad power spectrum, PBHs are produced in a wide mass range in the planetary mass regime. A nonstandard epoch of kination domination cannot produce enough PBHs for any of the Pζ(k) if the NANOGrav result is to be satisfied.