Cosmology of a Class Models in Teleparallel Gravity

Abstract

The great theoretical and experimental research activity currently carried out in cosmology and particle physics is entirely devoted to understanding the true nature of dark energy , the cause of the accelerated universe . Although the cosmological constant^is the simplest candidate for dark energy, it is still a challenging problem to explain the very small value of ^ consistent with today’s dark energy scale.this was one of the bigest problem’s in the lamda CDM model,besides the problem’s that we discocted earlear Acording to the first chapiter we saw that in the theory of Eeinstein there is no gravitational force interaction in general relativity, but gravitational field wich can be expressed by the torsion-less Levi–Civita metric–connection, whose curvature determines the intensity of the gravitational field. On the other hand, in the teleparallel description of gravitation,the presence of a gravitational field is expressed by the flatWeitzenbock connection, whose torsion is now the entity responsible for determining the intensity of the gravitational field. The gravitational interaction, therefore, can be described either, in terms of curvature, or in terms of torsion. Whether gravitation requires a curved or a torsioned spacetime, therefore, is a matter of convention. In general space time can in principle present two different properties curvature and Torsion but the torsion is absent in GR theory . makes the theory incomplit in some physicits vision and need to be extanded .This extension in GR was by adding exra degrees of freedom like the scalar field f like the Horndesky theories in the third chapitre, wich turned out to be a generalisation of the Galileon fields to curved space .