## 2 Field Equations in the Metric Formalism

We start with the 4-dimensional action in f (R) gravity:

where , is the determinant of the metric , and is a matter
Lagrangian
that depends on and matter fields . The Ricci scalar is defined by , where the
Ricci tensor is
In the case of the torsion-less metric formalism, the connections are the usual metric connections
defined in terms of the metric tensor , as
This follows from the metricity relation, .