Universe’s accelerated expansion in f(T,B) gravity: An observational perspective

This study explores the cosmic evolution and accelerated expansion of the Universe using the modified teleparallel gravity model [Formula: see text]. We employ two parameterized forms of the deceleration parameter: [Formula: see text] and [Formula: see text]. Using MCMC simulations, we perform a Bayesian analysis to constrain the model parameters with observational data from CC, DESI DR2 BAO and Pantheon+. Our results show that the Hubble parameter [Formula: see text] lies in the range [Formula: see text], the transition redshift [Formula: see text] spans [Formula: see text] and the present deceleration parameter [Formula: see text] is constrained between [Formula: see text]. The derived Hubble parameter [Formula: see text], energy density, pressure and EoS parameter [Formula: see text] exhibit behavior that is consistent with observational data, which confirms the compatibility of these models with current cosmological observations. Energy condition reveals that the SEC is violated, while the NEC, WEC and DEC are satisfied, which align with the observed cosmic acceleration. Additionally, the state finder parameters [Formula: see text] and trajectories in the r–q plane showcase the models’ evolution from a Quintessence-like phase to a [Formula: see text]CDM point. Our results demonstrate that the proposed framework accurately predicts the age of the Universe, consistent with observational data. The [Formula: see text] gravity model, combined with [Formula: see text] parameterizations, is revealed to be an effective tool for describing the Universe’s transition from deceleration to acceleration and exploring its cosmic evolution.