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 Rn with 1<n<2, regardless of whether the duality is exact or approximate. The R2-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 m2ϕ2-inflation which breaks the shift symmetry with a monomial, and corresponds to effectively logarithmic corrections to an R+R2 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.
Highlights
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
We investigated the duality between scalar field theories being coupled minimally and non-minimally to gravity and f (R)-Lagrangians
We further demonstrated how to obtain an expression for an f (R)-Lagrangian driving chaotic inflation within the accessible range of inflationary e-folds
Summary
Adding a term of type R2−γ with γ 1 to a Starobinsky f (R) can induce a chaotic regime and change the predictions for the spectral index ns and tensor-to-scalar ratio r to those of φm models, depending on the specific value of γ as depicted in figure 1. This confirms the findings of [31, 33, 34, 36, 47] but without omitting the R2-term in the first place. This confirms the findings of [35], where parametric methods are used to obtain an f (R)-theory corresponding to m2φ2-inflation and it is found that a linear logarithmic correction is not sufficient but a squared term is necessary
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