Parameterized Hubble parameter with observational constraints in fractal gravity

Abstract

In the present paper, the dynamical aspects of the cosmological model of the Universe have been studied in fractal gravity, which is an effective quantum field theory. The parameterized Hubble parameter, given by $H\left(z\right)=\frac{H_0}{2}(1+{(1+z)}^n),$ is used to solve the field equations, where $H_0$ and $n$ are model parameters. We have obtained the approximate best-fit values of the model parameters using the least squares method, incorporating observational constraints from available datasets such as Hubble $H\left(z\right)$ and Pantheon, by applying the root mean square error (RMSE) formula.

For the approximate best fit values obtained from the model parameters, we observe that the deceleration parameter $q\left(z\right)$ exhibits a signature-flipping (transition) point within the range $0.5\le z_{da}\le 1.668,$ marking the transition from a decelerated universe to an accelerated expanding universe. In addition, we discuss various physical parameters, including pressure, energy density, and energy conditions.