Parametric Resonance in the Einstein frame: the Jordan-frame Doppelgänger

Abstract

Modified $f(R)$ theories of gravity have been investigated for quite a long time in the literature as a possible explanation for the inflationary period of the universe. The correspondence to General Relativity with an extra scalar field $\tilde{\varphi }$ in the so-called Einstein Frame via a conformal transformation is a major tool in this class of theories. Here, we assume three different potentials $V(\tilde{\varphi })$ and a parametric-resonance coupling between $\tilde{\varphi }$ and a secondary scalar field $\tilde{\psi }$ such that one can have both inflation and preheating in the Einstein frame. We study the instability resonance band structure for our models. Further, we determine the correspondent mechanism -- and the function $f(R)$ itself -- in the Jordan frame, that is possibly related to the so-called vacuum awakening mechanism.

7 pages, 4 figures. Comments are welcome