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 the 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 BBN and CMB 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 $P_{\zeta}(k)$ 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 $P_{\zeta}(k)$. Furthermore, a dustlike epoch leads to abundant PBH formation for a lower amplitude of $P_{\zeta}(k)$ than the radiation dominated case and complies with the NANOGrav observation only for a few of the all $P_{\zeta}(k)$ forms considered here, where the peak wavenumber is larger than the wavenumber range probed by the 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 PBH for any of the $P_{\zeta}(k)$ if the NANOGrav result is to be satisfied.