A particular form of the time-dependent deceleration parameter is used to examine the accelerated expansion of the universe and the phase transition in this expansion in the context of $f(R,T)$ gravity theory for the flat FRW model. The modified field equations are solved under the choice of $f(R,T)=R+2f\left(T\right)$. The best fit values of the model parameters that would be consistent with the recent observational datasets that are estimated. For this estimation, 57 points from Cosmic Chronometers (CC) datasets and 1048 points from Pantheon supernovae datasets are used. Bayesian analysis and likelihood function are applied together with Markov Chain Monte Carlo (MCMC) method at $1\sigma$ and $2\sigma$ confidence levels. Then, the physical behavior of parameters such as density, pressure and cosmographic parameters corresponding to these constrained values of the model parameters are analyzed. Looking at the deceleration parameter, it is seen that the universe has passed from a decelerating expansion phase to an accelerating phase. As a result, it has been shown that the cosmological model $f(R,T)$ that we discussed can explain the accelerating expansion of the late universe well without resorting to any dark energy component in the energy-momentum tensor.

We present an investigation of a scalar field dark energy model in the context of the FLRW universe, focusing on the parameterization of the deceleration parameter q(z) to study the evolution of cosmic acceleration. By employing extensive observational datasets—including 30 independent cosmic chronometer measurements, 17 additional baryon acoustic oscillation data points, and standard candle datasets from Pantheon Type Ia supernovae, Quasars, and Gamma-Ray Bursts—we provide constraints on cosmological parameters using advanced Markov chain Monte Carlo methods. Our analysis identifies a transition redshift of $$z_t = 0.62$$ z t = 0.62 , marking the shift from decelerated to accelerated expansion, with a current deceleration parameter of $$q_0 = -0.59$$ q 0 = - 0.59 . The equation of state parameter confirms the dynamical behavior of quintessence, deviating slightly from a cosmological constant. Furthermore, the model demonstrates strong consistency with $$\Lambda $$ Λ CDM at lower redshifts while revealing distinct deviations at higher redshifts, which provides valuable insights into the late-time dynamics of the universe. By examining the evolution of cosmography parameters, energy density, pressure, and the scalar field equation of state, this study contributes the relevance of scalar field models as promising candidates for dark energy.