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We demonstrate that the leptogenesis mechanisms, which are associated withB-L symmetry breaking mechanism has notable effects on the production ofgravitational waves. These gravitational waves align well with the recentobservations of a stochastic gravitational wave background by NANOGrav andpulsar-timing arrays (PTAs). For these gravitational waves to match the recentmeasurements, the critical value of the B-L breaking should be around the GUTscale. Moreover, we consider the generation of primordial gravitational wavesfrom binary systems of Primordial Black Holes (PBHs) which could be predictedby the recent detection of gravitational waves. PBHs with specific masses canbe responsible for massive galaxy formation observed at high redshifts reportedby the James Webb Space Telescope (JWST). We contemplate the potential for ashared source between the NANOGrav and JWST observations, namely primordialblack holes. These black holes could serve as seeds of rapid galaxy formation,offering an explanation for the galaxies observed by JWST.

Leptogenesis Effects on the Gravitational Waves Background: Interpreting the NANOGrav Measurements and JWST Constraints on Primordial Black Holes