A study of accelerating and anisotropic cosmological models in certain modified theories of gravitation (Journal of Advances and Scholarly Researches in Allied Education, 2023)
Anisotropic and spatially homogenous cosmological models are important tools for explaining the universe's large-scale characteristics. Bianchi space-times have a uniform spatial structure and are globally hyperbolic. On the one hand, the asymptotic behaviour of the most rigid Bianchi space-time (Bianchi I and II space time) is straightforward and well-defined. Nonetheless, the asymptotic behaviour of generic Bianchi space time (Bianchi VIll and IX space-time) is considered to remain chaotic and oscillatory at their initial singularity over an extended period of time.Numerous hoovers Bianchi VIll and IX space-times display extraordinarily complicated aceillatory behaviour around their original singularity; even little changes to such a space-time's initial Cauchy data produce a significant shift in its asymptotic behaviour. Bianchi space-times are asymptotically silent, defying Misner's notion. Bianchi spaces l X are critical for modelling spatially homogeneous and anisotropic cosmologies. Dirac was the first to propose the idea of a variable gravitational constant G in the framework of relativity. Lau proposed changes to relate the G and A variants within the framework of general relativity. Because a variation in the A equations is technically followed by a variation in G, the significance of the change allows us to continue using Einstein's field without modification.