Stability Behavior of Bianchi Type I Cosmological Models with Variable G under a Creation Field

Abstract

This paper introduces a modification of Einstein’s field equations through the incorporation of a massless scalar field, referred to as the C-field. It investigates a cosmological model with a variable gravitational constant (G) within the framework of Bianchi type I space-time, taking into account the presence of a creation field. To construct a deterministic model, the study assumes G= V^n where V=DEF represents the volumetric function, in accordance with the principles of steady-state cosmology and the creation field. The model satisfies conservation laws, demonstrates an increasing creation field over time, avoids singularities, and offers a natural explanation for inflationary dynamics and isotropisation. Graphical analyses are employed to illustrate the evolution of key cosmological parameters. Furthermore, the model explores acceleration properties, revealing an expanding and accelerating universe consistent with observational evidence. The universe is assumed to be filled with a perfect fluid, characterised by the equation P=γρ , where γa constant within the range is γϵ [0,1]. Different values of γ correspond to distinct cosmological scenarios: γ=0 represents a dust-dominated universe, γ=1 corresponds to the Zel’dovich universe or stiff matter, and γ=1/3 describes a radiation-dominated (non-relativistic) fluid. The results for these scenarios are analysed and discussed in detail.