Abstract
We propose a limited class of models, describing interacting chiral multiplets with a non-minimal coupling to a vector multiplet, in curved superspace of $N=1$ supergravity. Those models are suitable for the inflationary model building in supergravity with inflaton assigned to a massive vector multiplet and spontaneous SUSY breaking in Minkowski vacuum after inflation, for any values of the inflationary parameters $n_s$ and $r$, and any scale of SUSY breaking.
Highlights
Success of the inflationary scenario for early Universe is, on the one hand, due to overcoming the theoretical problems of the standard (Einstein-Friedmann) cosmology and, on the other hand, due to its remarkable agreement with the CMB observational data (COBE, WMAP, PLANCK)
There is the so-called η-problem caused by the presence of the exponential factor eK in the scalar potential of supergravity with chiral superfields, which generically prevents slow roll
There are problems with ensuring the inflaton scalar potential to be bounded from below, and with getting SUSY breaking in a Minkowski vacuum after inflation too
Summary
Success of the inflationary scenario for early Universe is, on the one hand, due to overcoming the theoretical problems (horizon, flatness, structure formation) of the standard (Einstein-Friedmann) cosmology and, on the other hand, due to its remarkable agreement with the CMB observational data (COBE, WMAP, PLANCK). The minimal inflationary models with a single inflaton chiral superfield, with or without SUSY breaking after inflation, are possible [11, 12, 13] but require tuning both Kahler potential and a superpotential. Another approach, based on the use of non-linear realizations of SUSY and nilpotent chiral superfields, was introduced to the supergravity-based inflationary model building in [14]. The supergravity inflationary models of [15] have the single-field scalar potential given by an arbitrary real function squared. As is clear from (9), the absence of ghosts requires J′′(C) > 0
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