Constraining f(R) Gravity Models with The Late-Time Cosmological Evolution

The f(R) Modified Gravity is a modification of Einstein’s general theory of relativity, which aims to explain issues beyond The Standard Model of Cosmology, such as dark energy and dark matter, which make up 68% and 27% of the energy density of the universe today, respectively. As a theory of gravitation that govern major dynamics on the large scale of the universe, an f(R) The model should be able to explain the transition from a matter-dominated universe to a dark-energy-dominated universe to explain the recent accelerated expansion of the universe. Assuming that the density parameter of the radiation can be neglected during the transition from a matter-dominated universe to a dark-energy-dominated universe, we find some fixed points regarding the dynamical stability of the density parameters of the model. The phase transition can be achieved if the f(R) Model can connect the fixed point P5 (representing the matter-dominated era) to the fixed point P1 (representing the dark energy-dominated era). In this study, we analyze the viability of f(R) Models proposed by Starobinsky, Hu-Sawicki, and Gogoi-Goswami regarding the phase transition from a matter-dominated universe to a dark-energy-dominated universe. It is shown that those models are viable by choosing some appropriate parameters. For example, in the Starobinsky and Hu-Sawicki models, the parameter μ can be chosen to correspond to the lower bound of xd = RR1c, where R1 represents the de-Sitter point. Meanwhile, for the Gogoi-Guswami model, the same results can be achieved by taking α and β parameters satisfying the existence and stability conditions for the de-Sitter point. From these results, it can be concluded that those f(R) Models allow such phase transitions of the universe to realize late-time accelerated expansion.