  In this paper, we review in detail different mechanisms of generation of
large primordial fluctuations and their implications for the production of
primordial black holes (PBHs) and scalar-induced secondary gravity waves
(SIGW), with the ultimate aim of understanding the impact of loop correction on
quantum correlations and the power spectrum. To accomplish the goal, we provide
a concise, comprehensive, but in depth review of conceptual and technical
details of the standard model of the universe, namely, causal structure and
inflation, quantization of primordial perturbations and field theoretic
techniques such as "in-in" formalism needed for the estimation of loop
correction to the power spectrum. We discuss at length the severe constraints
(no-go) on PBH production in single-field inflation imposed by appropriately
renormalized quantum loop corrections, computed while maintaining the validity
of the perturbation framework and assuming sufficient inflation to address the
causality problem. Thereafter, we discuss in detail the efforts to circumvent
the no-go result in Galileon inflation, multiple sharp transition (MST)-induced
inflation, and stochastic single field inflation using an effective field
theoretic (EFT) framework applicable to a variety of models. We provide a
thorough analysis of the Dynamical Renormalization Group (DRG) resummation
approach, adiabatic and late-time renormalization schemes, and their use in
producing solar and sub-solar mass PBHs. Additionally, we give a summary of how
scalar-induced gravitational waves (SIGWs) are produced in MST setups and
Galileon inflation.Finally, the PBH overproduction issue is thoroughly
discussed.
