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

Abstract

Recently, the production of primordial black holes (PBHs) andsecondary gravitational waves (GWs) due to enhanced scalar power on smallscales have garnered considerable attention in the literature.Often, the mechanism considered to arrive at such increased power involvesa modification of the standard slow roll inflationary dynamics, achievedwith the aid of fine-tuned potentials.In this work, we investigate another well known method to generate featuresin the power spectrum wherein the initial state of the perturbations isassumed to be squeezed states.The approach allows one to generate features even in slowroll inflation with a specific choice for the Bogoliubov coefficientscharacterizing the squeezed initial states.Also, the method is technically straightforward to implement since theBogoliubov coefficients can be immediately determined from the formof the desired spectrum with increased scalar power at small scales.It is known that, for squeezed initial states, the scalar bispectrum isstrongly scale dependent and the consistency condition governing the scalarbispectrum in the squeezed limit is violated.In fact, the non-Gaussianity parameter characterizing the scalarbispectrum proves to be inversely proportional to the squeezed mode andthis dependence enhances its amplitude at large wave numbers making ithighly sensitive to even a small deviation from the standard Bunch-Daviesvacuum.These aspects can possibly aid in leading to enhanced formation of PBHsand generation of secondary GWs.However, we find that: (i) the desired form of thesqueezed initial states may be challenging to achieve from a dynamicalmechanism, and (ii) the backreaction due to the excited states severelylimits the extent of deviation from the Bunch-Davies vacuum at large wavenumbers.We argue that, unless the issue of backreaction is circumvented,squeezed initial states cannot lead to a substantial increase in poweron small scales that is required for enhanced formation of PBHs and generationof secondary GWs.