“…Recently, several pulsar timing array (PTA) collaborations, including NANOGrav [16,17], PPTA [18,19], EPTA [20,21], and CPTA [22], have independently announced compelling evidence for a stochastic signal in their latest data sets, displaying the Hellings-Downs [23] spatial correlations consistent with an SGWB as predicted by general relativity. While the PTA window encompasses a wide range of potential sources [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], the nature of the observed signal, whether it originates from astrophysical phenomena or cosmological processes, remains the subject of ongoing investigation [39][40][41][42][43][44][45][46][47]. The PTA signal can potentially be attributed to various sources [48][49][50][51], such as the SGWB produced by supermassive black hole binaries [52][53][54][55][56], scalar-induced GWs associated with the formation of primordial black holes [81][82]…”