Cosmic Model with Qeos and Anisotropic Bianchi Type- I Universe: A Mathematical Study

Abstract

On enormous scales, the current cosmos is thought to be homogenous and isotropic, but there is evidence of some anisotropy in its early stages. Homogeneous but anisotropic models such as the Bianchi ones are therefore of some interest. The solution to Einstein's field equations for gravity has been determined, and it requires the presence of both the cosmological constant and the quadratic equation of state (QEoS),which states that  where The model first slowed down but is now picking up speed. Also, the model is observed to approach isotropy at late times. We generate expressions for the Hubble parameter and state finder parameter and describe their significance at length. The cosmological model's physical characteristics are also examined. An intriguing aspect of the model is its dynamic cosmological parameter, which is enormous in the early cosmos, shrinks with time, and eventually approaches a constant. This has the potential to be useful in resolving the issue of the cosmological constant. When strings are present, a model of an accelerating universe can be built by presuming a negative value for the constant deceleration parameter and a decreasing vacuum energy density.For sufficiently enormous amounts of time, the threads vanish from the cosmos. Physical and geometrical model characteristics are also covered.