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

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