Modified Supergravity and Early Universe: The Meeting Point of Cosmology and High-Energy Physics

Abstract

We review the new theory of modified supergravity, dubbed the F (R) supergravity, and some of its recent applications to inflation and reheating in the early universe cosmology. The F (R) supergravity is the N = 1 locally supersymmetric extension of the f (R) gravity in four space-time dimensions. A manifestly supersymmetric formulation of the F (R) supergravity exist in terms of N = 1 superfields, by using the (old) minimal Poincaré supergravity in curved superspace. We find the conditions for stability, the absence of ghosts and tachyons. Three models of the F (R) supergravity are studied. The first example is devoted to a recovery of the standard (pure) N = 1 supergravity with a negative cosmological constant from the F (R) supergravity. As the second example, a generic R 2 supergravity is investigated, and the existence of the AdS bound on the scalar curvature is found. As the third (and most important) example, a simple viable realization of chaotic inflation in supergravity is found. Our approach is minimalistic since it does not introduce new exotic fields or new interactions, beyond those already present in (super)gravity. The universal reheating mechanism is automatic. We establish the consistency of our approach and also apply it to preheating and reheating after inflation. The Higgs inflation and its correspondence to the Starobinsky inflation are established in the context of supergravity. We briefly review other relevant issues such as non-Gaussianity, CP -violation, origin of baryonic asymmetry, lepto-and baryo-genesis. The F (R) supergravity has promise for possible solutions to those outstanding problems too.

New actions for modified gravity and supergravity

“…[1,2] for a review -in agreement with all known observations. The f (R) gravity is known to be classically equivalent to the scalar-tensor gravity [3], so that in the context of inflation or dark energy it amounts to quintessence.…”

“…We use the notation of Ref. [2] and briefly comment on its relation to the more standard notation of Ref. [16] in Sec.…”

“…The "fifth force" at present due to exchange of the extra scalar (dubbed scalaron in the context of f (R) gravity) can be effectively screened on local scales (like the Solar system) but can allow the enhancement of gravity on cosmological scales due to the so-called chameleon effect [4]. Gravitational instabilities in f (R) gravity can also be avoided by demanding the proper signs of the first and second derivatives of the function f , thus making it free of ghosts and tachyons [2]. The coupling of f (R) gravity to matter fields after a transformation to the Einstein frame gives rise to the couplings of inflaton (scalaron) to all matter fields and thus leads to the universal reheating after inflation in the early universe [5].…”

“…2 Besides having the manifest local N = 1 supersymmetry, the action (4) has the so-called auxiliary freedom [22] because the auxiliary fields do not propagate in this theory. It distinguishes the action (4) from other possible supersymmetric extensions of Eq.…”

Starobinsky model inN=2supergravity

“…The Starobinsky inflaton (dubbed scalaron) φ of the mass M is thus identified with the spin-0 part of metric and has geometrical origin. This interpretation is obscure in the quintessence picture, but it is essential for fixing the inflaton interactions with other (matter) fields during reheating after inflation -it is known as the universal reheating mechanism (in the original picture) [2].…”