Résumé:
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 .
