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Register a new userInflation and Supersymmetry Breaking in Higgs-$R^2$ Supergravity
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We propose a new construction of the supergravity inflation as an UV completion of the Higgs-$R^2$ inflation. In the dual description of $R^2$-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singlet scalar fields. We also discuss supersymmetry breaking and its transmission to the visible sector as a result of the couplings of the dual chiral superfields and the non-minimal gravity coupling of the Higgs fields.
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We elaborate on integrable dynamical systems from scalar-gravity Lagrangians that include the leading dilaton tadpole potentials of broken supersymmetry. In the static Dudas-Mourad compactifications from ten to nine dimensions, which rest on these leading potentials, the string coupling and the space-time curvature become unbounded in some regions of the internal space. On the other hand, the string coupling remains bounded in several corresponding solutions of these integrable models. One can thus identify corrected potential shapes that could grant these features generically when supersymmetry is absent or non-linearly realized. On the other hand, large scalar curvatures remain present in all our examples. However, as in other contexts, the combined effects of the higher-derivative corrections of String Theory could tame them.
We discuss supergravity inflation in braneworld cosmology for the class of potentials $V(phi)=alpha phi^nrm{exp}(-beta^m phi^m)$ with $m=1,~2$. These minimal SUGRA models evade the $eta$ problem due to a broken shift symmetry and can easily accommodate the observational constraints. Models with smaller $n$ are preferred while models with larger $n$ are out of the $2sigma$ region. Remarkably, the field excursions required for $60$ $e$-foldings stay sub-planckian $Deltaphi <1$.
It has recently been suggested that the Standard Model Higgs boson could act as the inflaton while minimally coupled to gravity - given that the gravity sector is extended with an $alpha R^2$ term and the underlying theory of gravity is of Palatini, rather than metric, type. In this paper, we revisit the idea and correct some shortcomings in earlier studies. We find that in this setup the Higgs can indeed act as the inflaton and that the tree-level predictions of the model for the spectral index and the tensor-to-scalar ratio are $n_ssimeq 0.941$, $rsimeq 0.3/(1+10^{-8}alpha)$, respectively, for a typical number of e-folds, $N=50$, between horizon exit of the pivot scale $k=0.05, {rm Mpc}^{-1}$ and the end of inflation. Even though the tensor-to-scalar ratio is suppressed compared to the usual minimally coupled case and can be made compatible with data for large enough $alpha$, the result for $n_s$ is in severe tension with the Planck results. We briefly discuss extensions of the model.
We study the supersymmetry breaking patterns in four-dimensional $mathcal{N}=2$ gauged supergravity. The model contains multiple (Abelian) vector multiplets and a single hypermultiplet which parametrizes SO$(4,1)/{rm{SO}}(4)$ coset. We derive the expressions of two gravitino masses under {it{general}} gaugings and prepotential based on the embedding tensor formalism, and discuss their behaviors in some concrete models. Then we confirm that in a single vector multiplet case, the partial breaking always occurs when the third derivative of the prepotential exists at the vacuum, which is consistent with the result of Ref.~cite{Antoniadis:2018blk}, but we can have several breaking patterns otherwise. The discussion is also generalized to the case of multiple vector multiplets, and we found that the full ($mathcal{N}=0$) breaking occurs even if the third derivative of the prepotential is nontrivial.
The supersymmetric extension of Starobinsky $R+alpha R^2$ models of inflation is particularly simple in the new minimal formalism of supergravity, where the inflaton has no scalar superpartners. This paper is devoted to matter couplings in such supergravity models. We show how in the new minimal formalism matter coupling presents certain features absent in other formalisms. In particular, for the large class of matter couplings considered in this paper, matter must possess an R-symmetry, which is gauged by the vector field which becomes dynamical in the new minimal completion of the $R+alpha R^2$ theory. Thus, in the dual formulation of the theory, where the gauge vector is part of a massive vector multiplet, the inflaton is the superpartner of the massive vector of a nonlinearly realized R-symmetry. The F-term potential of this theory is of no-scale type, while the inflaton potential is given by the D-term of the gauged R-symmetry. The absolute minimum of the potential is always exactly supersymmetric, so in this class of models if realistic vacua exist, they must be always metastable. We also briefly comment on possible generalizations of the examples discussed here and we exhibit some features of higher-curvature supergravity coupled to matter in the old minimal formalism.
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