Investigating the accelerated expansion of the Universe through updated constraints on viable $f(R)$ models within the Palatini formalism

The observed accelerated expansion of the Universe at present epoch can be explained by some of the $f(R)$ models without invoking the existence of dark energy or any other such exotic component in cosmic fluid. The $f(R)$ models in Palatini formalism is relatively less explored in recent times with respect to their counterpart in metric formalism. We study seven $f(R)$ models in Palatini formalism: Hu-Sawicki (two cases), Starobinsky, exponential, Tsujikawa, f(R) = R -β /R^ n, and f(R)= R + α ln(R) - β. Following standard statistical procedure and utilizing data sets: type Ia supernovae data, cosmic chronometer observations, baryonic acoustic oscillations data, data from H {ii} starburst galaxies, local measurements of the Hubble parameter (H₀), and distance priors of cosmic microwave background radiation data, we obtain constraints on the model parameters. When compared with the standard `lambda-cold dark matter model', for many data set combinations, the support for $f(R)$ models is significant. We obtain the relevant quantities for characterizing the accelerated expansion of the Universe, and these quantities are consistent with those obtained in a model-independent way by others. The curve of effective/total equation-of-state parameter, obtained from parameter constraints, clearly shows correct phases of the expansion history: the radiation-dominated epochs and the matter-dominated epochs, of the past, and the current accelerated expansion epoch eventually evolving to de-Sitter phase in the distant future. Overall, our results advocate in favour of pursuing $f(R)$ models in Palatini formalism as a potential alternative for explaining accelerated expansion of the Universe.