Cosmic evolution beyond the singularity: a study of viscous bounce dynamics in F(R) theory

This paper studies the impact of bulk viscosity on the feasibility of the cosmological bounce solutions in the framework of F(R) theory. In this perspective, the behavior of an isotropic homogeneous universe with a perfect matter configuration and new formulation of the bulk viscosity coefficient is explored. We select a specific mathematical form of the modified gravity model to see how it affects the dynamics of cosmic evolution. In addition, we analyze various cosmological parameters, exploring the presence of feasible cosmological bounce solutions. A physically acceptable bouncing scenario occurs when the energy density stays positive, pressure becomes negative, and the violation of null and strong energy conditions highlight the important role of bulk viscosity. We also study the cosmographic parameters and their paths in the r-s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r-s$$\end{document} diagnostic framework. Finally, a thermodynamic investigation is carried out to test the generalized second law of thermodynamics and the overall stability of the cosmological model. The results show that F(R) gravity is a realistic and promising alternative to the standard cosmological model, giving deeper understanding of gravitational dynamics and the early evolution of cosmos.