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 \({{\mathcal {D}}}_{12}^{(2)}\) parameter with the associated cosmological parameters, to examine the nonclassical nature of the states after inflation during the oscillatory phase of the scalar field.

半经典爱因斯坦方程用于描述经典引力场的反向反应与半经典引力中的量子物质场的相互作用。在我们之前的研究中，我们利用半经典近似来证明粒子产生现象，通常称为宇宙的预热/再加热，这种现象发生在暴胀时期之后，在宇宙的双模量化大质量标量场的振荡阶段。混沌膨胀模型。我们之前使用双模相干和压缩量子光学状态形式的语言来表示大规模标量场；因此，检查场态在宇宙学背景下是否表现出经典或非经典性质将是有用的。在本文中，我们将在宇宙学背景下研究双模量子光学态的非经典性质。我们利用了 Lee 在量子光学中提出的准则来判断双模态中非经典效应的存在，并计算了等效的 Lee's\({{\mathcal {D}}}_{12}^{(2)}\)参数和相关的宇宙学参数，以检查标量场振荡阶段暴胀后状态的非经典性质。