R2 inflation from scale invariant supergravity and anomaly free superstrings with fluxes

Abstract

The R 2 scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the non-supersymmetric case the conformally coupled scalars belong to an SO(1, 1 + n)/SO(1 + n) manifold, while in the supersymmetric case the scalar manifold becomes isomorphic to the Kählerian space M n =SU (1, 1 + n)/U (1) × SU (1 + n). In both cases when the underlying scale symmetry is preserved the vacuum corresponds to de Sitter space. Once the scale symmetry is broken by quantum effects, a transition to flat space becomes possible. We argue that the scale violating terms are induced by anomalies related to a U (1) R symmetry. The anomaly is resolved via the gauging of a Peccei-Quinn axion shift symmetry. The theory describes an inflationary transition from de Sitter to flat Minkowski space, very similar to the Starobinsky inflationary model. The extension to metastable de Sitter superstring vacua is also investigated. The scalar manifold is extended to a much richer manifold, but it contains always M n as a sub-manifold. In superstrings the metastability is induced by axions that cure the anomalies in chiral N = 1 (or even N = 0) supersymmetric vacua via a Green-Schwarz/Peccei-Quinn mechanism generalized to four dimensions. We present some typical superstring models and discuss the possible stabilization of the no-scale modulus.

ℛ2 supergravity

“…This poses severe restrictions on the dual standard supergravity theory which, in fact, cannot be an arbitrary scale invariant theory of supergravity. For example, we find that only certain cases are possible among the ones worked out in [1]. Moreover, one conformally coupled chiral superfield (that we call S) and another one that we call the chiral superfield T , are not matter fields but have a pure gravitational origin.…”

“…While demanding conformal invariance (Weyl local gauge symmetry) would require spin two ghosts arising from the Weyl square term [4,5], the rigid scale invariant R 2 theory propagates only physical massless modes in de Sitter space, in contrast with the R + R 2 theory, which has in addition a Minkowski phase with a massive scalar, the inflaton. An Einstein term is then obtained through quantum effects as substantiated by the analysis of [1]. Further restrictions that follow from the supersymmetric extensions of these theories are the aim of the present investigation.…”

“…Recently, various authors [1][2][3] considered pure R 2 theories of gravity coupled to matter. These theories are particularly interesting also in regard to cosmology because they naturally accommodate for de Sitter universes.…”

“…Further restrictions that follow from the supersymmetric extensions of these theories are the aim of the present investigation. In particular, in this note we implement the analysis of [1] by requiring that pure R 2 supergravity be effectively derived solely in terms of the geometry of curved superspace. This poses severe restrictions on the dual standard supergravity theory which, in fact, cannot be an arbitrary scale invariant theory of supergravity.…”

Helical phase inflation via non-geometric flux compactifications: from natural to starobinsky-like inflation

“…Specifically, by introducing one additional parameter, the Starobinsky model can interpolate to quadratic or natural inflation [44][45][46][47][48][49][50][51][52][53][54]. The problem of trans-Planckian field excursion has been carefully considered in quadratic and natural inflation, while it usually is ignored for Starobinsky-like inflation, since the tensor-to-scalar ratio is lower than the Lyth bound r ∼ 0.01.…”