Abstract
The minimal Starobinsky supergravity with the inflaton (scalaron) and the goldstino in a massive vector supermultiplet is coupled to the dilaton-axion chiral superfield with the no-scale K\"ahler potential and a superpotential. The Kachru-Kallosh-Linde-Trivedi (KKLT)-type mechanism in the presence of a constant term in the superpotential is applied to stabilize the dilaton/axion during inflation, and it is shown to lead to an instability. The instability is cured by adding the alternative Fayet-Iliopoulos (FI) term that does not lead to the gauged $R$-symmetry. Other stabilization mechanisms, based on the Wess-Zumino (WZ)-type superpotential, are also studied in the presence of the FI term. A possible connection to a D3-brane is briefly discussed too.
Highlights
The instability is cured by adding the alternative Fayet-Iliopoulos (FI) term that does not lead to the gauged R symmetry
Cosmological inflation offers a simple solution to basic problems of standard cosmology and current cosmological observations of the cosmic microwave background (CMB) radiation
As we found in the previous section, the coupling of the vector superfield to the chiral superfield converts a single-field inflation into a multifield inflation, while it leads to the instability resulting in a significant reduction of the duration of inflation, measured by the e-foldings number Ne, and, to an unacceptable change in the predicted CMB power spectrum measured by the scalar index ns and the tensor-to-scalar ratio r, both depending upon Ne
Summary
Cosmological inflation offers a simple solution to basic problems of standard cosmology and current cosmological observations of the cosmic microwave background (CMB) radiation. We do not address those unsolved problems but check whether the minimal formulation of the Starobinsky inflation in supergravity is compatible with its coupling to the chiral dilaton-axion superfield Φ, described by the no-scale Kähler potential K and a superpotential W. In the case of the no-scale Kähler potential, we find a different situation because both dilaton and axion have 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]) It is the purpose of this paper to achieve the moduli stabilization of dilaton and axion with the Kähler potential (3) by using a suitable superpotential and the alternative FI term in the minimal Starobinsky supergravity coupled to the dilatonaxion superfield.. Spontaneous supersymmetry breaking after inflation is studied in Appendix C
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