Could PBHs and secondary GWs have originated from squeezed initial states?

[Abridged] Recently, the production of primordial black holes (PBHs) and secondary gravitational waves (GWs) due to enhanced scalar power on small scales have garnered considerable attention in literature. Often, mechanism considered arrive at such involves a modification standard slow roll inflationary dynamics, achieved with aid fine-tuned potentials. In this work, we investigate another well known method generate features spectrum wherein initial state perturbations is assumed be squeezed states. This approach technically straightforward implement since Bogoliubov coefficients characterizing states, can immediately determined from desired form spectrum. It that, for bispectrum strongly scale dependent consistency condition governing limit violated. fact, non-Gaussianity parameter $f_{_{\rm NL}}$ proves inversely proportional mode dependence enhances its amplitude large wave numbers making it highly sensitive even deviation Bunch-Davies vacuum. These aspects possibly leading formation PBHs generation GWs. However, find that: (i) states may challenging achieve dynamical mechanism, (ii) backreaction excited severely limits extent vacuum numbers. We argue unless issue circumvented, cannot lead substantial increase that required