Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-01-11
Physics
High Energy Physics
High Energy Physics - Theory
53 pages, 7 figures; LaTeX
Scientific paper
The F(R) supergravity theories are the N=1 locally supersymmetric extensions of the well studied f(R) gravity theories in four space-time dimensions, which are often used for `explaining' inflation and Dark Energy. A manifestly supersymmetric description of F(R) supergravities exist in terms of N=1 superfields, by using the (old) minimal Poincar'e supergravity in curved superspace. We find that any F(R) supergravity is classically equivalent to the Poincar'e-type matter-coupled N=1 supergravity via the superfield Legendre-Weyl-K"ahler transformation. The (non-trivial) K"ahler potential and the scalar superpotential of the inflaton superfield are determined in terms of the original holomorphic F(R) function. The conditions for stability, the absence of ghosts and tachyons are also found. No-scale F(R) supergravity is constructed too. Three different examples of F(R) supergravity theories are studied in detail. The first example is devoted to a recovery of the standard (pure) N=1 supergravity with a negative cosmological constant from F(R) supergravity. As the second example, a generic quadratically-generated F(R) supergravity is investigated, and the existence of the AdS bound on its scalar curvature is discovered. As the third example, a simple viable realization of chaotic inflation in supergravity is given, via an embedding of the Starobinsky inflationary model into the F(R) supergravity. It is also found that F(R) supergravity can have a positive cosmological constant in the low-curvature regime. Our approach does not introduce new exotic fields or new interactions, beyond those already present in (super)gravity. A nonminimal scalar-curvature coupling in gravity and supergravity, Higgs inflation and its correspondence to Starobinsky inflation in f(R) gravity and F(R) supergravity, respectively, are established too.
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