f(R) gravity
= f(R) gravity
{c}
An f(R) theory replaces the Ricci scalar in the gravitational action by a smooth function $f(R)$. Its metric field equation is
$$
f'(R)R_{ab}-\frac12f(R)g_{ab}
+(g_{ab}\Box-\nabla_a\nabla_b)f'(R)=8\pi T_{ab}.
$$
= f(R) gravity
{c}
An f(R) theory replaces the Ricci scalar in the gravitational action by a smooth function $f(R)$. Its metric field equation is
$$
f'(R)R_{ab}-\frac12f(R)g_{ab}
+(g_{ab}\Box-\nabla_a\nabla_b)f'(R)=8\pi T_{ab}.
$$