Dynamical Dark Energy Signatures from a New Transition $Om(z)$ Parametrization in Flat FLRW Cosmology

We investigate a cosmic scenario using a new transition parameterization of the $Om(z)$ diagnostic, $Om(z) = \frac{z^l}{(1+z)^m}$, in the spatially flat Friedmann Lema\^itre Robertson-Walker (FLRW) framework. Using observational datasets such as Observational Hubble Data (OHD), Pantheon Plus (PP), and SH0ES, we analyze the evolution of the $Om(z)$ function to probe deviations from the standard $\Lambda$CDM model and constrain free parameter space {$H_0$, l, m } using Markov Chain Monte Carlo (MCMC) analysis with the emcee sampler. Our analysis reveals a clear transition in the slope of $Om(z)$ from negative to positive at transition redshift values $z_t \approx 1.41$, $0.65$, and $0.33$ for the OHD, OHD+PP, and OHD+PP$\&$SH0ES datasets, respectively. This behavior suggests a dynamical evolution of dark energy, indicating a transition from a quintessence-like phase to a phantom regime. From the combined OHD+PP$\&$SH0ES dataset, we obtain a best-fit value of the Hubble constant $H_0 = 73.01 \pm 0.36 \, \mathrm{km\,s^{-1}\,Mpc^{-1}}$, which is consistent with the SH0ES calibration and supports the viability of our model. Additionally, our analysis indicates that the current age of the Universe is approximately $13 \sim 14$ Gyr from all available combinations of datasets, which is consistent with observational expectations. Further, we find that the deceleration-to-acceleration transition, which marks the beginning of cosmic acceleration, is inferred to occur within the redshift interval $z_t \in [0.5, 0.8]$, highlighting the emergence of dark energy as the dominant component in the Universe's recent expansion history. Our transition $Om(z)$ parameterization captured progressive cosmological changes and enabled seamless interpolation over cosmic epochs.