  The phenomena of Squeezing and chaos have recently been studied in the
context of inflation. We apply this formalism in the post-inflationary
preheating phase. During this phase, inflaton field undergoes quasi-periodic
oscillation, which acts as a driving force for the resonant growth of quantum
fluctuation or particle production. Furthermore, the quantum state of the
fluctuations is known to have evolved into a squeezed state. In this
submission, we explore the underlying connection between the resonant growth,
squeezing, and chaos by computing the Out of Time Order Correlator (OTOC) of
phase space variables and establishing a relation among the Lyapunov, Floquet
exponents, and squeezing parameters. For our study, we consider observationally
favored $\alpha$-attractor E-model of inflaton which is coupled with the
bosonic field. After the production, the system of produced bosonic
fluctuations/particles from the inflaton is supposed to thermalize, and that is
believed to have an intriguing connection to the nature of chaos of the system
under perturbation. %By using this we calculated approximate lower bound of
temperature ${\bar T}_{\rm MSS}$. We conjecture a relation between the
thermalization temperature $({\bar T}_{\rm SS})$ of the system and quantum
squeezing, which is further shown to be consistent with the well-known
Rayleigh-Jeans formula for the temperature symbolized as ${\bar T}_{\rm RJ}$,
and that is ${\bar T}_{\rm SS} \simeq {\bar T}_{\rm RJ}$. Finally, we show that
the system temperature is in accord with the well-known lower bound on the
temperature of a chaotic system proposed by Maldacena-Shenker-Stanford (MSS).
