Disentangling thef(R)-duality

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 φ 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 twogiven 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.

F(R)-gravity and inflation

“…Different choices of n do not change the spectral index of Starobinsky inflation, but affect the value of the tensor-to-scalar ratio: in order to satisfy the Planck data we have to take 1/5 < n < 2 (see also the recent work in Ref. [34]). It is important to note that in the low curvature limit of the theory the scalar potentials under investigation correspond to Einstein's gravity in the frame of F (R)-gravity, even when n = 1.…”

“…By starting from this results, we can now reconstruct the spectral index and the tensor-to-scalar ratio which realize (34) and the corresponding models in the different representations.…”

Starobinsky-like two-field inflation

“…(2.8) and (2.9) can be further simplified by considering A as the new independent scalar field (instead of χ ) and doing the field redefinition 12) which leads to the canonical kinetic term of the scalar field ρ. We find…”

“…The predictions of the Starobinsky model (1.1) for the spectral indices n s ≈ 1 − 2/N e ≈ 0.964, r ≈ 12/N 2 e ≈ 0.004 and low non-Gaussianity are in agreement with the WMAP and PLANCK 2013 data (r < 0.13 and r < 0.11, respectively, at 95 % CL) [9], though they are in disagreement with the BICEP2 measurements (r = 0.2 + 0.07, −0.05) [10]. The enhancement of the tensor-toscalar-ratio r of the Starobinsky model to the higher values can be achieved via modification of the simplest Ansatz (1.1) by (matter) quantum corrections (beyond one loop) [11,12]. However, the Planck 2015 data [13] excludes a significant enhancement of r beyond r = 0.08.…”

Asymptotically safe inflation from quadratic gravity

“…k 2 ∼ R (see also [41]). In a recent investigation a similar approach has been successfully applied to study the quantum gravity modifications of the Starobinsky model [42] (see also [43][44][45][46][47][48] for other examples of quantum deformed quadratic gravity inflationary models).…”