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.

In this paper, we study the semiclassical evolution of a “coherently oscillating massive scalar field”. This field is nominally linked to the spatially levelled Friedmann–Robertson–Walker (FRW) metric. By use of two-mode quantum optical states formalism, we evaluated the power-law cosmology with scale factor as a power function of cosmic time. In the oscillatory phase of scalar field, it was found that, in all the four different combinations of quantum states, quantum scalar field obeying the time-dependent Schrödinger equation leads to the power-law expansion, in good agreement with that of the matter-dominated era. However, in the semiclassical theory of gravity in contrary to the classical description of gravity, we obtained two behavioral solutions corresponding to two different pattern evolution of the scale factor. This behavioral pattern evolution of scale factor of the universe has an important quantum implication associated with it.

In this paper, by the use of entangled and nonentangled coherent and squeezed state formalism of two-mode nonclassical states, we studied the chaotic inflationary model of a massive scalar field with quadratic potential in the semiclassical gravity, derived from canonical quantum gravity. It was found that the semiclassical quantum gravity leads to the same power-law expansion of the universe as that of the matter-dominated era [Formula: see text] in an oscillatory phase of the scalar field in all the nonclassical quantum states considered. The coherently oscillating scalar field in the expanding universe suffers from the phenomenon of particle creation which restricts the duration of stable coherent oscillations of the scalar field dependent on the parameters of the states considered and affect in a certain way the abundant particle production owing to the parametric resonance of bosonic fields coupled to this coherently oscillating scalar field.

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