Exact Bianchi type-I inflationary model with non-minimally coupled scalar field

Abstract

In the present work, we try to build up an inflationary model within the framework of Bianchi type-I spacetime using a non-minimally coupled, homogeneous, self-interacting canonical scalar field. Specifically, using the Lie symmetry method, we are able to find some novel exact solutions to the Einstein field equations by assuming a power-law relationship between the scalar field and average scale factor. These symmetry-based solutions have been used to derive the values of some important parameters of the anisotropic universe. In this anisotropic model, we find that the volume of space expands with time in an inflationary scenario, depicting the Universe's accelerating phases. An important characteristic of this model is that it initially represents anisotropic spacetime and then isotropizes the spacetime as time goes on, which favors recent cosmological observations.

Kinematic parameters and Raychaudhuri equation in the Kantowski-Sachs model

“…In addition to the articles discussed previously, we found in the scientific literature a large number of works with anisotropic models [38][39][40][41][42][43][44] and we see that a complete set of these models includes those already mentioned previously: Bianchi type models [45,46] and the KS model, where the spatial hypersurfaces have the topology of the 2 − ordinary sphere and the real line, S 2 × R 1 . Its metric presents two scale factors of the Universe as follows q q j = --+ ds dt a t dr b t d d sin .…”