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We study non-classical inflaton, which is minimally coupled to the semiclassical gravity in FRW universe in Coherent Squeezed Vacuum State (CSVS). We determined Oscillatory phase of inflaton, power-law expansion, scale factor, density fluctuations, quantum fluctuations and particle production for CSVS. We obtained an estimated leading solution of scale factor in CSVS proportional to $t^{2/3}$ follow similar diversification as demonstrated by Semiclassical Einstein Equation (SCEE) of gravity in matter dominated universe. We also studied the validity of SCEE in CSVS. By determining the quantum fluctuation for CSVS validity of uncertainty relation for FRW Universe also computed. The results shows that Quantum fluctuations doesn't depend on coherent parameter $\Upsilon$ as uncertainty relation doesn't effected by the displacement of $\Upsilon$ in phase space. We study the production of particles in CSVS for oscillating massive inflaton in flat FRW universe.

We study the density fluctuations for Coherent Squeezed Number State (CSNS) and Squeezed Number States (SNS) formalism in Semiclassical theory of grav ity in flat FRW universe. We used Number state evolution of oscillatory phase of inflaton for coherent squeezed number state and squeezed number states for malisms. We analyzed that density fluctuations for SNS depends upon squeezing parameter and number state while for CSNS density fluctuations depends upon squeezing parameter, number state and coherent state parameter. These param eters plays an important role for quantum consideration of SNS and CSNS. The results of the analysis shows that increase in density fluctuations for both SNS and CSNS, demonstrate quantum behavior of SCEE as well as production of various kind of particles in these states.

The Reheating era of inflationary universe can be parameterized by various parameters like reheating temperature \(T_{\text{re}}\), reheating duration \(N_{\text{re}}\) and average equation of state parameter \(\overline{\omega }_{\text{re}}\), which can be constrained by observationally feasible values of scalar power spectral amplitude \(A_{\text{s}}\) and spectral index \(n_{\text{s}}\). In this work, by considering the quadratic chaotic inflationary potential with logarithmic-correction in mass, we examine the reheating era in order to place some limits on model's parameter space. By investigating the reheating epoch using Planck 2018+BK18+BAO data, we show that even a small correction can make the quadratic chaotic model consistent with latest cosmological observations. We also find that the study of reheating era helps to put much tighter constraints on model and effectively improves accuracy of model.

Using coherent and squeezed state formalisms of quantum optics for a minimally coupled non-classical inflaton in the FRW mertic is studied, in semiclassical theory of gravity. The leading order solution for the semiclassical Einstein equations in the coherent, squeezed and squeezed vacuum states are obtained perturbatively and are exhibit powerlaw expansion behaviour. The validity of the semiclassical theory is examined in the squeezed vacuum state in the oscillatory phase of the inflaton. The semiclassical theory in the oscillatory phase of the non-classical inflaton holds only if the associated squeezing parameter is much less compared to unity. Quantum fluctuations of the inflaton is also examined in coherent and squeezed state formalisms., Comment: 14 pages, 2 figures, To appear in Int.J.Mod.Phys.D

We study particle production of coherently oscillating inflaton in the semiclassical theory of gravity by representing inflaton in coherent and squeezed state formalisms. A comparative study of the inflaton in classical gravity with coherent state inflaton in semiclassical gravity is also presented., Comment: 15 pages, 1 figure, to appear in IJMPD