Evading no-go for PBH formation and production of SIGWs using Multiple Sharp Transitions in EFT of single field inflation

Deploying multiple sharp transitions (MSTs) under a unified framework, we investigate the formation of Primordial Black Holes (PBHs) and the production of Scalar Induced Gravitational Waves (SIGWs) by incorporating one-loop corrected renormalized-resummed scalar power spectrum. With effective sound speed parameter, $1⩽c_s⩽1.17$, the direct consequence is the generation of PBH masses spanning $M_{\mathrm{PBH}}\sim O(10^{-31}{M}_{\odot }-10^4{M}_{\odot })$, thus evading well known No-go theorem on PBH mass. Our results align coherently with the extensive NANOGrav 15-year data and the sensitivities outlined by other terrestrial and space-based experiments (e.g.: LISA, HLVK, BBO, HLV(O3), etc.).