D-term Model Research Articles

Tight constraints onF- andD-term hybrid inflation scenarios

We use present cosmological data from the cosmic microwave background, large-scale structure and deuterium at high redshifts to constrain supersymmetric F- and D-term hybrid inflation scenarios including possible contributions to the CMB anisotropies from cosmic strings. Using two different realizations of the cosmic string spectrum, we find that the minimal version of the D-term model is ruled out at high significance. F-term models are also in tension with the data. We also discuss possible non-minimal variants of the models.

An inflaton mass problem in string inflation from threshold corrections to volumestabilization

Inflationary models whose vacuum energy arises from a D-term are believed not to sufferfrom the supergravity eta problem of F-term inflation. That is, D-term models have thedesirable property that the inflaton mass can naturally remain much smaller than theHubble scale. We observe that this advantage is lost in models based on stringcompactifications whose volume is stabilized by a non-perturbative superpotential: theF-term energy associated with volume stabilization causes the eta problem to reappear.Moreover, any shift symmetries introduced to protect the inflaton mass will typically belifted by threshold corrections to the volume-stabilizing superpotential. Using thresholdcorrections computed by Berg, Haack, and Körs, we illustrate this point in the example ofthe D3–D7 inflationary model, and conclude that inflation is possible, but only forfine-tuned values of the stabilized moduli. More generally, we conclude that inflationarymodels in stable string compactifications, even D-term models with shift symmetries, willrequire a certain amount of fine-tuning to avoid this new contribution to the eta problem.

Hilltop inflation

We study ‘hilltop’ inflation, in which inflation takes place near a maximum of the potential.Viewed as a model of inflation after the observable Universe leaves the horizon(observable inflation), hilltop inflation is rather generic. If the potential steepensmonotonically, observable hilltop inflation gives a tiny tensor fraction . The usual F- and D-term models may easily be transmuted to hilltop models byPlanck-suppressed terms, making them more natural. The only commonly consideredmodel of observable inflation which is definitely not hilltop is tree-level hybrid inflation.Viewed instead as an initial condition, we explain that hilltop inflation is more genericthan seems to have been previously recognized, adding thereby to the credibilityof the idea that eternal inflation provides the pre-inflationary initial condition.

F-term strings in the Bogomolnyi limit are also BPS states

We derive the Bogomol'nyi equations for supersymmetric abelian F-term cosmic strings in four-dimensional flat space and show that, contrary to recent statements in the literature, they are BPS states in the Bogomol'nyi limit, but the partial breaking of supersymmetry is from N = 2. The second supersymmetry is not obvious in the N = 1 formalism, so we give it explicitly in components and in terms of a different set of N = 1 chiral superfields. We also discuss the appearance of a second supersymmetry in D-term models, and the relation to N = 2 F-term models. The analysis sheds light on an apparent paradox raised by the recent observation that D-term strings remain BPS when coupled to N = 1 supergravity, whereas F-term strings break the supersymmetry completely, even in the Bogomol'nyi limit. Finally, we comment on their semilocal extensions and their relevance to cosmology.