Exploring cosmic acceleration using dynamical system analysis in gravity-modified models.

The acceleration of cosmic expansion is a challenging problem in contemporary cosmology, drawing the attention of cosmologists. In relation to the subtle nature of the phenomenon in question, theories beyond general relativity abound to accommodate it in their purviews. f(R) models of gravity still offer a promising choice both at local and global horizons. In this study, we conduct a study of the accelerated cosmic expansion observed since the late-time era of the universe's evolution, specifically within the context of f(R) gravity, which modifies the geometry of cosmic spacetime. By considering an f(R) model, we investigate first its viability conditions concerning radiation and matter eras and then follow a dynamical system approach to the analysis of the model. The dynamical system, under various conditions arising from the model using the variables m and r, is solved for fixed points, over which studying the stability properties of the system leads to the desired results. The parameters describing the densities of radiation, matter, and geometric curvature are calculated in each corresponding case. Through eigenvalues corresponding to the fixed points, we infer whether the system is stable or unstable. Apart from this, we consider all possible cosmic factors to assess the impact of their presence, as well as their individual and interactive effects. We observe that within the model, the critical points, corresponding eigenvalues, and the state parameter collectively justify the accelerating expansion, regardless of the dark energy considered. We also study the Lyapunov stability by linearising nonlinear systems and investigating how phase space analysis retains stability against small perturbations. [ABSTRACT FROM AUTHOR]