Axially Symmetric Universe with Chaplygin Gas in Hoyle-Narlikar C-Field Cosmology

Abstract In this paper, we explore how an axially symmetric space-time described by the Bhattacharya and Karade metric evolves within Hoyle-Narlikar’s Creation Field (C-field) theory of gravitation. We view the universe as filled with a Chaplygin Gas, which is a candidate for dark energy. This gas is coupled with the creation field to examine the dynamic effects of ongoing matter creation. We find exact solutions to the modified Einstein field equations by assuming a power-law relationship between the metric potentials (B=A^n). We derive the model's physical parameters, including matter density, thermodynamic pressure, spatial volume, and total mass. A key finding is that the matter density (ρ) remains constant (ρ=√K), Additionally, the total mass (M) of the universe increases linearly over time, which supports the idea of continuous matter creation. We also calculate the cosmographic parameters and find constant values for deceleration (q=2), jerk (j=10), and snap (s=-80 These values indicate a decelerating era, even with the presence of dark energy fluid. Furthermore, cosmographic parameters including deceleration, jerk, and snap are evaluated and found to remain constant during the evolution of the model. The obtained results suggest that the model represents a decelerating universe despite the presence of dark energy fluid, and provides useful insights into anisotropic cosmological models in C-field theory.