We propose a logarithmic parametrization form of energy density for the scalar field dark energy in the framework of the standard theory of gravity, which supports the necessary transition from the decelerated to the accelerated behavior of the Universe. The model under consideration is constrained by available observational data, including cosmic chronometers data-sets (CC), Baryonic Acoustic Oscillation (BAO) data-sets, and Supernovae (SN) data-sets, consisting of only two parameters $$\alpha $$α and $$\beta $$β . The combined CC+BAO+SN data-sets yields a transition redshift of $$z_{tr}=0.79^{+0.02}_{-0.02}$$z tr = 0 . 79 - 0.02 + 0.02 , where the model exhibits signature-flipping and is consistent with recent observations. For the combined data-sets, the present value of the deceleration parameter is calculated to be $$q_{0}=-0.43^{+0.06}_{-0.06}$$q 0 = - 0 . 43 - 0.06 + 0.06 . Furthermore, the analysis yields constraints on both the parameter density value for matter and the present value of the Hubble parameter, with values of $$\Omega _{m0}=0.25849^{+0.00026}_{-0.00025}$$Ω m 0 = 0 . 25849 - 0.00025 + 0.00026 and $$H_{0}=67.79_{-0.59}^{+0.59}$$H 0 = 67 . 79 - 0.59 + 0.59 km/s/Mpc, respectively, consistent with the results obtained from Planck 2018. Finally, the study investigates how the mass of a black hole evolves over time in a Universe with both matter and dark energy. It reveals that the black hole mass increases initially but stops increasing as dark energy dominates.

Despite the significant accomplishments of general relativity, numerous unresolved issues persist in our understanding of the cosmos. One of the most perplexing challenges is the ongoing accelerated expansion of the Universe, which continues to elude a complete explanation. Consequently, scientists have proposed various alternative theories to general relativity in pursuit of a deeper understanding. In our analysis, we delve into the recently proposed modified f(Q) gravity, where Q represents the nonmetricity scalar responsible for gravitational effects. Specifically, we investigate a cosmological model characterized by the functional form f(Q) = Q + αQⁿ, where α (with α ≠ 0) and n serve as free parameters. Utilizing this functional form, we construct our Hubble rate, incorporating a specific equation of state to describe the cosmic fluid. Furthermore, we leverage a dataset consisting of 31 data points from Hubble measurements and an additional 1048 data points from the Pantheon dataset. These data serve as crucial constraints for our model parameters, and we employ the Markov Chain Monte Carlo (MCMC) method to explore the parameter space and derive meaningful results. With our parameter values constrained, our analysis yields several noteworthy findings. The deceleration parameter suggests a recent accelerated phase in the cosmic expansion. In addition, the EoS parameter paints a portrait of dark energy exhibiting phantom-like characteristics. Furthermore, we delve into the application of cosmological diagnostic tools, specifically the statefinder and the Om(z) diagnostics. Both of these tools align with our previous conclusions, confirming the phantom-like behavior exhibited by our cosmological model. These results collectively contribute to our understanding of the dynamic interplay between gravity, dark energy, and the expanding cosmos.

In this paper, we propose a new parametrization of dark energy based on the Om(z) diagnostic tool behavior. For this purpose, we investigate a functional form of the Om(z) that predicts the popular dark energy dynamical models, namely phantom and quintessence. We also found the famous cosmological constant for specified values of the model’s parameters. We employed the Markov Chain Monte Carlo approach to constrain the cosmological model using Hubble, Pantheon samples, and BAO datasets. Finally, we used observational constraints to investigate the characteristics of dark energy evolution and compare our findings to cosmological predictions.