Exploring B(z)CDM models beyond ΛCDM: Observational data and cosmographic analysis

With its model-independent approach, cosmography has emerged as an invaluable tool for faithfully representing a wealth of astrophysical observations, free from theoretical biases. This study employs cosmography to investigate two innovative cosmological models, $B\left(z\right)$CDM models 1 and 2, which introduce novel corrections to the standard $\Lambda$CDM model, $B\left(z\right)=sin\left(z\right)$ and $B\left(z\right)=log(1+z)$, respectively. By analyzing a variety of observational datasets, including 31 measurements from cosmic chronometers ($CC$), 1048 data points from the $Pantheon$ dataset, 6 measurements from baryon acoustic oscillations ($BAO$), and data from cosmic microwave background ($CMB$) measurements, we derive constraints on model parameters and assess their compatibility with real-world observations. We find that the present values of the deceleration parameter for $B\left(z\right)$CDM models 1 and 2 are $q_0=-0.54_{-0.23}^{+0.24}$ and $q_0=-0.56_{-0.40}^{+0.45}$, respectively, for the combined datasets. The results reveal intriguing transitions in the expansion of the universe, confirming the presence of DE and quintessence-like behavior within the framework of $B\left(z\right)$CDM models.