Density perturbations in f(R) gravity theories in metric and Palatini formalisms

Understand

We make a detailed study of matter density perturbations in both metric and Palatini formalisms in theories whose Lagrangian density is a general function, f(R), of the Ricci scalar.

• We derive these equations in a number of gauges.
• We show that for viable models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived under a sub-horizon approximation are valid even for super-Hubble scales provided the oscillating mode (scalaron) does not dominate over the matter-induced mode.
• Such approximate equations are especially reliable in the Palatini formalism because of the absence of scalarons.