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 $\varphi =\sqrt{3/2}M\log f_R$, where $M$ is the reduced Planck mass and $f_R=df/dR>0$.

The potential is $V(\varphi )=3M^2{m}^2[1-e^{-\sqrt{2/3}\varphi /M}{]}^2/4$. Near its minimum, expanding the exponential gives $V\simeq m^2{\varphi }^2/2$, 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.^[ref]