Evolutionary phases of the accelerating universe in modified gravity and its solar system test

Einstein's gravity is modified to explain an accelerating universe's present and past scenarios by numerically exploring different cosmological parameters. A new f (R) gravity model constrained with coupling constants is introduced in the Einstein- Hilbert action to explain current issues and open up new possibilities in gravity physics by fitting the model with newly collected data from observations. It is proposed that the current universe is undergoing an accelerating expansion that behaves as Chaplygin Gas-type dark energy. The values of the coupling constants involved in f(R) gravity are chosen so that the current value of the effective equation of state (weff0) is shown within the observational approximation, that is, between -0.8 and -1.0. Cosmological parameters such as deceleration, cosmic jerk, and snap are consistent with the fundamental observational constraint, and their relevance in terms of coupling constant is also emphasized. The viability of the model as well as the existence and origin of scalaron mass are also investigated.