Investigation of Super-Poissonian Nonclassical Nature of Inflaton Field in Flat FRW Universe through Cosmological Mandels $Q$ Parameter

This study investigates the nonclassical properties of the inflaton field within the framework of semiclassical gravity by analyzing Cosmological Mandels $Q$ parameter for Squeezed Number States (SNS) and Coherent Squeezed Number States (CSNS). Mandels $Q$ parameter serves as a critical tool for identifying nonclassical states by differentiating between sub-Poissonian and super-Poissonian statistics. The values of Cosmological Mandels $Q$ are positive shows the super-Poissonian non-classical nature of inflaton for Squeezed Number States (SNS) and Coherent Squeezed Number States (CSNS). These results provide deeper insights into the statistical properties of quantum states in early-universe cosmology and emphasize the relevance of SNS and CSNS in understanding quantum effects on cosmic inflation and particle production.