Scalaron (source code)

= Scalaron

The <scalaron> is the additional propagating scalar degree of freedom in a generic nonlinear $f(R)$ metric theory of <gravity>. In the model $f(R)=R+R^2/(6m^2)$, it can be expressed in the <Einstein frame> as a canonically normalized scalar $\phi=\sqrt{3/2}\,M\log f_R$, where $M$ is the <reduced Planck mass> and $f_R=df/dR>0$.

The potential is $V(\phi)=3M^2m^2[1-e^{-\sqrt{2/3}\phi/M}]^2/4$. Near its minimum, expanding the exponential gives $V\simeq m^2\phi^2/2$, identifying $m$ as the scalaron's small-oscillation mass. At large positive field values the potential flattens, providing the slow-roll mechanism of <Starobinsky inflation>.<Embedding (R+R^2)-Inflation into Supergravity by Sergei V. Ketov and Alexei A. Starobinsky>[Section I and the pure R-squared contribution to equation (26); scalar potential in the declared Einstein-frame convention]{ref}