Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames

Understand

We investigate the dynamics of $f(R)$ gravity in Jordan and Einstein frames.

• First, we perform a phase-space singularities analysis in both frames.
• We show that, typically, anisotropic singularities are absent in the Einstein frame, whereas they may appear in the Jordan frame.
• We conciliate this apparent inconsistency by showing that the necessary conditions for the existence of the Einstein frame are namely the same ones assuring the absence of the anisotropic singularities in the Jordan frame.