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

Abstract

ABSTRACT Modified theories of gravity encompass a class of f(R) models that seek to elucidate the observed late-time accelerated expansion of the universe. In this study, 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, cosmic chronometer observations, baryonic acoustic oscillations data, data from H ii starburst galaxies, local measurements of the Hubble parameter (H0), and cosmic microwave background radiation data. We re-parametrize the f(R) models using a distortion/deviation parameter (b) which is a measure of their deviation from the lambda-cold dark matter (ΛCDM) model. Taking into account the ‘Hubble tension,’ we perform the study both with and without a Gaussian prior for H0 from local measurements, following the standard statistical procedures for constraining parameters and comparing models. Our findings are as follows: (i) in many cases the f(R) models are strongly favoured over the standard ΛCDM model, (ii) the deviation parameter (b) significantly deviates from zero in several cases, (iii) the inclusion of local H0 not only increases the fitted value of H0 (as expected) but also affects the gap between predictions of f(R) models and the ΛCDM model, and (iv) the relevant quantities characterizing the (accelerated) expansion of the universe such as transition redshift and the equations-of-state parameters, obtained in our models, are consistent with those obtained in a model-independent way by others. Our investigation and results present a compelling case for pursuing further research on f(R) models with future observations to come.