Disentangling the f$(R)$ - Duality

Broy, Benedict; Pedro, Francisco; Westphal, Alexander

Preprint/Report

PUBDB-2014-04513

Disentangling the f$(R)$ - Duality

Broy, B. (Corresponding Author)DESY* ; Pedro, F.DESY* ; Westphal, A.DESY*

2014

This record in other databases:

Report No.: DESY-14-222; IFT-UAM/CSIC-14-124; arXiv:1411.6010

Abstract: 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 $R^{n}$ 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-$\ell$.

Keyword(s): inflation: model ; higher-order: 0 ; duality ; string model ; supergravity ; suppression ; Jordan ; ultraviolet