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Semiclassical Einstein equations are used to describe the interaction of the back-reaction of the classical gravitational field with quantum matter fields in semiclassical gravity. We in our previous studies have made use of the semiclassical approximation to demonstrate the phenomenon of particle production, commonly called as preheating/reheating of the universe, which occurs after the inflationary epoch during the oscillatory phase of two-mode quantised massive scalar field of the chaotic inflationary model. We have previously used the language of two-mode coherent and squeezed quantum optical states formalisms to represent the massive scalar field; therefore, it would be useful to examine whether the field states exhibits classical or nonclassical nature in the cosmological context. In the present article, we will examine the nonclassical nature of two-mode quantum optical states in the cosmological context. We have made use of the criterion suggested by Lee in quantum optics, for the existence of nonclassical effects in two-mode states and calculated the equivalent Lee's D 12 (2) parameter with the associated cosmological parameters, to examine the nonclassical nature of the states after inflation during the oscillatory phase of the scalar field. [ABSTRACT FROM AUTHOR]

By the use of coherent and squeezed thermal states formalism, we analyzed the phenomena of particle creation when coherently oscillating a homogeneous scalar field (Inflaton) in semi-classical gravity. We also obtained an estimated solution for the semi-classical Einstein equation in non-classical thermal states formalism perturbatively, which is similar to the power-law expansion of classical Einstein equation. This solution, apart from a particular condition, shows oscillatory behavior in nature. We also analyzed a coherently oscillating homogeneous scalar field, in a thermal vacuum, coherent thermal, squeezed thermal vacuum and coherent squeezed thermal states, suffering from particle creation, and created particles are showing oscillatory behavior. Particle production can be raised due to thermal and quantum effects. We also studied quantum fluctuations of a homogeneous scalar field in the above-mentioned non-classical thermal states. [ABSTRACT FROM AUTHOR]

We study the two-mode thermal squeezed states formalism to examine the particle creation by black holes.We also study the entropy generation and derive an equation for Hawking temperature in terms of squeezed parameter and an associated temperature dependent parameters. [ABSTRACT FROM AUTHOR]