Abstract
An N=1 Poincare supergravity action, suitable for describing the Starobinsky inflation, is proposed. It extends f(R) gravity to supergravity in its old-minimal version. The action is parametrized by a single holomorphic potential and a single non-holomorphic potential, and can be dualized into the standard matter-coupled supergravity action, with the "matter" given by two chiral superfields. The action extends the earlier proposals for embedding the Starobinsky inflation into supergravity, and can be further generalized to include quantum corrections to the inflation. Our approach assumes the gravitational origin of inflaton and quintessence in the context of supergravity, by using a single chiral scalar curvature superfield.
Highlights
The most recent (March 2013) PLANCK satellite mission data [1] combined with the WMAP9 polarization and lensing data [2] yield ns = 0.960 ± 0.007 for the CMB spectral index, r < 0.08 for the CMB tensor-to-scalar-ratio with the 95% level of confidence, and fNL = 2.7 ± 5.8 with the 68% level of confidence for the CMB non-Gaussianity parameter
The Starobinsky inflationary model based on the (R + R2) gravity [3] perfectly fits the bill, so it inspired renewed interest to that model in the recent literature in the context of supergravity
As was demonstrated in Ref. [39], the new-minimal version of supergravity can be successfully used for embedding the scalar potential (2), while the dual version of that theory has a dynamical massive vector multiplet whose loweset real scalar field component plays the role of inflaton
Summary
It means that the ghosts can be avoided in the theory (1) despite of the presence of the higher derivatives It demonstrates the ”accidental” drop of the spin-0 part of metric in the Einstein-Hilbert action (describing only the propagating spin-2 part of metric) versus more general actions that are non-linear in R. It gives rise to the scaling invariance of the Starobinsky inflation in the large R limit This scaling invariance is not exact for finite (large) values of R, and its violation is exactly measured by the slow-roll parameters, in full correspondence to the nearly conformal spectrum of the CMB perturbations presumably associated with the scalaron field. In order to properly supersymmetrize f (R) gravity to the form suitable for its viable applications to inflation, reheating and dark energy, we need a generic N = 1 locally supersymmetric action subject to the following neccessary conditions:.
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