NANOGrav Spectral Index =3 from Melting Domain Walls

We discuss cosmic domain walls described by a tension redshifting with the expansion of the Universe. These melting domain walls emit gravitational waves with the low-frequency spectral shape Slgw << f2 corresponding to the spectral index gamma 1/4 3 favored by the recent NANOGrav 15 yrs data. We discuss a concrete high-energy physics scenario leading to such a melting domain wall network in the early Universe. This scenario involves a feebly coupled scalar field, which can serve as a promising dark matter candidate. We identify parameters of the model matching the gravitational wave characteristics observed in the NANOGrav data. The dark matter mass is pushed to the ultralight range below 10-11 - 10-12 eV which is accessible through planned observations thanks to the effects of superradiance of rotating black holes.