Observational Constraints on Fractal Gravity with Specific Form of Deceleration Parameter

Objectives: In the framework of fractal gravity theory for the Bianchi Type V model, the phase transition and accelerated expansion of the universe are investigated using a specific form of the deceleration parameter. The field equations are solved by assuming nonzero fractal parameter and without cosmological constant. Methods: This study examines various physical parameters including density, pressure, and deceleration parameter. Based on the signature flip property of the deceleration parameter, we have derived the scale factor and the Hubble parameter. Observational data from the Hubble 𝐻(𝑧) and Pantheon datasets are utilized to constrain the model parameters. The optimal parameter values were determined by minimizing the Root Mean Squared Error (RMSE) criterion. Findings: Cosmographic analysis reveals that the model’s behavior exhibits a close correspondence with that of the Λ CDM model. The best-fit values derived from the Hubble dataset are 𝛾 = 53.00+2.4 −2.6, 𝜂 = 0.542+0.019 −0.021, 𝑙1 = −0.878+0.057 −0.054. For the Pantheon dataset, the corresponding best-fit are 𝛾 = 55.3+2.4 −2.6 , 𝜂 = 0.487+0.020 −0.024 , 𝑙1 = −0.896+0.067 −0.053 with 𝑅2 values 0.93 and 0.9967 for Hubble & Pantheon data sets respectively. The current values of 𝑞 obtained at 𝑧 = 0 are − 0.24 and − 0.35 for the Hubble and Pantheon dataset. Novelty: The deceleration parameter used here shows a transition from decelerating phase to an accelerating phase of expansion. As a result, the cosmological model that we have studied in fractal gravity is capable of explaining late time universe expansion without any dark energy component present in energy momentum tensor. Keywords: Bianchi Type-V (BV) space time; Fractal gravity; Barotropic fluid; Dark Energy; Root Means Square Error (RMSE)