Abstract: We prove the necessary and the sufficient condition on the function f(R) leading to the equivalence of general relativity and the f(R) theory in the sense that for a spacetime with constant Ricci scalar, GR and the f(R) theory generated by any f(R) function satisfying this condition will necessarily have the same solutions. We show how this condition and its consequences allow to get such functions and give the possibility to ?fixe conditions on the parameters of any class of f(R) functions so that GR and this class of theories will have exactly the same solutions. The well-known model R + a[b^(1-p)]R^p for dark energy is presented as an illustration.
N° Revue: E-Print arxiv - Pagination: 1 à 9 - Date: 16/02/2012
URL: https://arxiv.org/abs/1202.3598
Mots cles: General relativity; f(R) Modi?ed theory of gravity; Ricci scalar; Common solutions; Equivalence.
co_auteurs: Aucun