Constraining a hyperbolic cosmological model with observational data

In this study, we investigate the dynamic evolution of the universe through a hyperbolic cosmological model based on a spatially flat FLRW metric. By using observational datasets, including CC, Pantheon+, and BAO datasets, we constrain model parameters and examine distinct characteristics, such as the transition in the deceleration parameter. The transition redshifts are z(l) = 0.74(-0.30)(+0.28), z(l) = 0.33(-0.02)(+0.02), and z(l) = 0.36(-0.03)(+0.03) for the CC, Pantheon+, and BAO datasets, respectively. Also, the present values of the deceleration parameter are determined to be q(0) = -0.38(-0.06)(+0.06), q(0) = -0.27(-0.11)(+0.10), and q(0) = -0.29(-0.01)(+0.01) for the CC, Pantheon+, and BAO datasets, respectively. Our findings indicate quintessence-like behavior and suggest potential deviations from standard cosmological expectations. The hyperbolic model emerges as a compelling alternative, underscoring its compatibility with quintessence scenarios and shedding light on the nature of dark energy and the universe's destiny.