Polonyi–Starobinsky supergravity with inflaton in a massive vector multiplet with DBI and FI terms

Abstract

We propose the Starobinsky-type inflationary model in the matter-coupled N = 1 four-dimensional supergravity with the massive vector multiplet that has inflaton (scalaron) and goldstino amongst its field components, whose action includes the Dirac-Born-Infeld-type kinetic term and the generalized (new) Fayet-Iliopoulos-type term, without gauging the R-symmetry. The N = 1 chiral matter ("hidden sector") is described by the modified Polonyi model needed for spontaneous supersymmetry breaking after inflation. We compute the bosonic action and the scalar potential of the model, and show that it can accommodate the positive (observed) cosmological constant (as the dark energy) and the spontaneous supersymmetry breaking at high scale after the Starobinsky inflation.

Generalized dilaton–axion models of inflation, de Sitter vacua and spontaneous SUSY breaking in supergravity

“…[12,13]. 4 Moreover, one can also combine both approaches and derive the supergravity-based inflationary models with inflaton in a massive vector multiplet in the presence of the FI term, with both F-type and D-type SUSY breaking needed for the hierarchy of scales [16,17]. In all those cases, the canonical Kähler potential and a linear superpotential for Polonyi superfield were chosen, like the original Polonyi model [18].…”

Minimal Starobinsky supergravity coupled to a dilaton-axion superfield

“…This phenomenon was first observed in Ref. [26] in the context of the so-called Polonyi-Starobinsky supergravity where a Polonyi chiral superfield with the canonical kinetic term and a linear superpotential were introduced for describing SSB and dark matter after inflation [27,28,29] towards combining our (early time) inflationary models with late time cosmology. In the case of the no-scale Kähler potential, we find a different situation because the dilaton-axion has to be trapped near a minimum of their scalar potential during the Starobinsky inflation driven by the scalaron, i.e., the masses of both dilaton and axion have to be larger than the Hubble scale during inflation (it is known as the moduli stabilization in the literature [30]).…”

“…But the double exponential in the e J -factor and the exponentials in the P function, defined by Eqs. (27) and (28) in terms of the canonical inflaton ϕ, destroy the flatness of the scalar potential and thus greatly reduce the e-foldings number of inflation. Therefore, we need the hierarchy of the two parameters, namely, g ≫ A.…”

“…The authors are grateful to Hiroyuki Abe for his collaboration on related work in Refs. [23,28] and Sergei Kuzenko for correspondence. S.A. was supported in part by a Waseda University Grant for Special Research Projects (Project number: 2019E-059).…”

“…Though we did our calculations with the DBI kinetic terms for the vector multiplet, in this paper we only use the Maxwell-type kinetic terms for simplicity, because the DBI structure does not significantly affect the Starobinsky inflation and the moduli stabilization in question, according to our findings (see also Refs. [18,23,28] for more).…”