Abstract
We prove (in superspace) the equivalence between the higher-derivative N=1 supergravity, defined by a holomorphic function F of the chiral scalar curvature superfield, and the standard theory of a chiral scalar superfield with a chiral superpotential W, coupled to the (minimal) Poincaré supergravity in four spacetime dimensions. The relation between the holomorphic functions F and W is found. It can be used as the technical framework for the possible scenario unifying the early Universe inflation and the present Universe acceleration. We speculate on the possible origin of our model as the effective supergravity generated by quantum superstrings, with a dilaton–axion field as the leading field component of the chiral superfield.
Highlights
Inflation in the early Universe [1] nicely predicts the homogeneity of our Universe at large scales, its large size and entropy, as well as an almost scale-invariant spectrum of cosmological perturbations, in good agreement with the high precision CMB measurements [2]
A mechanism of inflation is usually based on a ‘slow-roll‘ scalar field with a proper scalar potential [1]
The instabilities in the scenarios based on the 2nd-order curvature terms against adding the higher order scalar curvature terms were discussed in ref. [20] within perturbation theory
Summary
Inflation (i.e. a phase of ‘rapid’ accelerated expansion) in the early Universe [1] nicely predicts the homogeneity of our Universe at large scales, its large size and entropy, as well as an almost scale-invariant spectrum of cosmological perturbations, in good agreement with the high precision CMB measurements [2]. A mechanism (and details) of inflation is usually based on a ‘slow-roll‘ scalar field (inflaton) with a proper scalar potential [1] It follows from astronomical observations of Supernova Ia [3] that the present Universe is accelerating due to the mysterious ‘dark energy’ which violates the strong energy condition in General Relativity. In this Letter we would like to propose a possible geometrical origin of the inflaton and quintessence, as described by a single scalar field in the supergravity model modified by higher-order supercurvature terms. The latter may originate from quantum (non-perturbative) superstrings, though we do not have a compelling reason for that. ΕabcdRabcd because it does not vanish in supergravity due to the gravitino- (and matter-) induced torsion Tabc, with Rtor ∝ (∇T + T 2)
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