An extension of Einstein’s → general relativity
derived from relaxing the hypothesis that the
→ Hilbert-Einstein action for the
→ gravitational field is strictly linear. This was done by
replacing the → Ricci scalar,
R, with a non-linear function of R:
S = (1/2κ)∫d4x (-g)1/2f(R) +
Sm,
where κ ≡ 8πG and Sm is the matter part
of the action.
The case of
f(R) = R represents the simplest type of f(R) gravity theories.
The discovery of → dark energy
in 1998 stimulated the idea that → cosmic acceleration
today may originate from some modification of
gravity to general relativity. Dark energy models based on f(R) theories have been
extensively studied as the simplest modified gravity scenario to
realize the late-time acceleration. There are three versions of f(R) modified
gravity: metric (or second order) formalism, Palatini (or first order) formalism, and
metric-affine gravity.
See also: f(R), function of the → Ricci scalar;
→ gravity.
