1202.3598 (Amine Benachour)

On the f(R) theories equivalent to general relativity, for spacetimes
with a constant Ricci scalar    [PDF]

Amine Benachour

We show how one can obtain the f(R) modified theories of gravity strictly
equivalent to GR, in the sense that both theories have exactly the same
solutions, which lead to a constant Ricci scalar. Precisely for a vacuum
solutions and more general one, we demonstrate that when the f(R) function and
its first derivative take certain value at some point k,the f(R) theory and GR,
are equivalent for the description of spacetimes with Ricci scalar R=k. We show
how this allow us to construct such functions, and gives the possibility to
fixe, the conditions on the parameters of any given class of f(R) functions so
that the class and GR will have exactly the same solutions. The well-known
model R+{\alpha}{\beta}^{1-p}R^{p},for dark energy is discussed as an
illustration.

View original: http://arxiv.org/abs/1202.3598