Creation of matter in the universe and groups of type E7

Abstract

Abstract:We relate the mechanism of matter creation in the universe after inflation to a simple and universal mathematical property of extended N > 1 supergravities and related compactifications of superstring theory. We show that in all such models, the inflaton field may decay into vector fields due to a nonminimal scalar-vector coupling. This coupling is compulsory for all scalars except N = 2 hyperscalars. The proof is based on the fact that all extended supergravities described by symmetric coset spaces G H have duality groups G of type E7, with exception of U(p, n) models. For N = 2 we prove separately that special geometry requires a non-minimal scalar-vector coupling. Upon truncation to N = 1 supergravity, extended models generically preserve the non-minimal scalar-vector coupling, with exception of U(p, n) models and hyperscalars. For some string theory/supergravity inflationary models, this coupling provides the only way to complete the process of creation of matter in the early universe.

Degeneration of groups of type E 7 and minimal coupling in supergravity

“…The present paper is intended to generalize the results of [5], because we believe that the issue of minimal coupling in N 2 extended supergravities deserves some attention.…”

“…Indeed, such theories never 2 exhibit a constant f αβ , and in [5] this fact was pointed out to be a consequence of electric-magnetic-duality, which requires a special coupling of the non-linear sigma model of scalars to the vector sector [6,7]. The kinetic vector matrix N ΛΣ which occurs in N 2, D = 4 extended supergravities is not holomorphic,…”

“…In presence of matter coupling, there is another way of obtaining sub-theories, namely to consistently reduce the matter sector but not the gravitino multiplet(s); section 8 deals with such cases. The list of examples produced by the systematic approach of the present investigation is much larger than the ones given in [5,10,11], and it is of some interest also because some truncations correspond to orbifolds and orientifolds of string theories with larger supersymmetry, as discussed in section 9, in which the further truncation N = 2 → N = 1 is considered. Comments on the "degeneration" of the so-called Freudenthal duality are then given in section 10.…”

“…The 20 is the rank-3 antisymmetric self-real irrep. of SU (1,5). The commuting SU(3) factor can be interpreted as the part of the R-symmetry truncated away in the supersymmetry reduction N = 8 → N = 5.…”

“…This problem was recently addressed in [5], where it was pointed out that in N = 1 supergravity obtained by reduction from higher-dimensional and/or higher-supersymmetric theories the non-minimal vector scalar couplings (1.2) are generic.…”