Disentangling the $f(R)$ - Duality

Motivated by UV realisations of Starobinsky-like inflation models, we study generic exponential plateau-like potentials to understand whether an exact f(R)-formulation may still be obtained when the asymptotic shift-symmetry of the potential is broken for larger field values. Potentials which break the shift symmetry with rising exponentials at large field values only allow for corresponding f(R)-descriptions with a leading order term Rn with 1<n<2, regardless of whether the duality is exact or approximate. The R(2)-term survives as part of a series expansion of the function f(R) and thus cannot maintain a plateau for all field values. We further find a lean and instructive way to obtain a function f(R) describing m(2)phi(2)-inflation which breaks the shift symmetry with a monomial, and corresponds to effectively logarithmic corrections to an R+R(2) model. These examples emphasise that higher order terms in f(R)-theory may not be neglected if they are present at all. Additionally, we relate the function f(R) corresponding to chaotic inflation to a more general Jordan frame set-up. In addition, we consider f(R)-duals of two given UV examples, both from supergravity and string theory. Finally, we outline the CMB phenomenology of these models which show effects of power suppression at low-ℓ.