Bianchi-I cosmology within f(T ): Reconstruction method and dynamical study

Abstract

This paper is fundamentally devoted to the cosmological reconstruction and dynamic studying in homogeneous BIANCHI-I space-time under the f(T ) background. Its content is supported by the fact that in the General Relativity description of the standard cosmological paradigm, the evolution from an anisotropic universe into an Friedmann– Lemaitre–Robertson–Walker (FLRW) one can be achieved by a period of inflationary expansion. Nowadays, modified gravity theories like f(T ) are widely accepted to provide a real description of some universe evolution phases like inflation era, matter-dominated era, etc. So, we aim to examine here what f(T ) gravity model can accommodate with an anisotropic universe, an expanding universe and even the transition between both evolutions. To reach this goal, we use a reconstruction method based on dynamic equations in Bianchi-I space-time by assuming a particular form for the metric anisotropy and by specifying some time functions describing average scale factor. Most of the obtained models are consistent with certain known results in the literature but other add new results in this work. In the second part of this work, the dynamical behaviors of the Bianchi-I space-time are addressed through the reconstruction of an autonomous dynamical system. For an aleatory choice of anisotropic fluid, the numerical analysis of the system shows that the metric anisotropy decreases with expansion. Then, an attractor point is reached and becomes unstable by the end of inflation. Such interesting properties found in this work on Bianchi-I space-time are often interpreted as graceful exit from inflation which doesn’t occur in ordinary FLRW space-time.