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Modified theories of gravity encompass a class of $f(R)$-models that seek toelucidate the observed late time accelerated expansion of the universe. In thisstudy, we examine a set of viable $f(R)$ models (Hu-Sawicki: two cases,Satrobinsky, Tsujikawa, exponential and arcTanh models) in metric formalism,using recent cosmological data sets: type Ia supernovae data, cosmicchronometer observations, baryonic acoustic oscillations data, data fromH\textsc{ii} starburst galaxies, and local measurements of the Hubble parameter$H_0$. The model parameters are constrained using a Bayesian analysis with theMonte Carlo Markov Chain method. We employ statistical tools such as the AkaikeInformation Criterion, Bayesian Information Criterion, and reduced chi-squarestatistics to conduct a comparative investigation of these models. We determinethe transition redshift, the evolution of total equation-of-state (EoS)parameter, and the EoS for the component responsible for current acceleratedexpansion to characterize the expansion's evolution. Taking into account the``Hubble tension," we perform the study with and without a Gaussian prior for$H_0$ from local measurements. Our findings are as follows: (i) in many casesthe $f(R)$ models are strongly favored over the standard $\Lambda$CDM model,(ii) the deviation parameter ($b$) significantly deviates from zero in severalcases, (iii) the inclusion of local $H_0$ not only increases the fitted valueof $H_0$ (as expected) but also affects the gap between predictions of $f(R)$models and the $\Lambda$CDM model, and (iv) the relevant quantitiescharacterizing the (accelerated) expansion of the universe obtained in ourmodels are consistent with those obtained in a model-independent way by others.Our investigation and results present a compelling case for pursuing furtherresearch on $f(R)$ models with future observations to come.

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