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We show that the scale of the inflationary potential may be the electroweak scale or even lower, while still generating an acceptable spectrum of primordial density perturbations. Thermal effects readily lead to the initial conditions necessary for low scale inflation to occur, and even the moduli problem can be evaded if there is such an inflationary period. We discuss how low scale inflationary models may arise in supersymmetric theories or in theories with large new space dimensions.
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We discuss the phenomenological implications of hybrid natural inflation models in which the inflaton is a pseudo-Goldstone boson but inflation is terminated by a second scalar field. A feature of the scheme is that the scale of breaking of the Goldstone symmetry can be lower than the Planck scale and so gravitational corrections are under control. We show that, for supersymmetric models, the scale of inflation can be chosen anywhere between the Lyth upper bound and a value close to the electroweak breaking scale. Unlike previous models of low scale inflation the observed density perturbations and spectral index are readily obtained by the choice of the free parameters.
Low scale inflation has many virtues and it has been claimed that its natural realisation in supersymmetric standard model can be achieved rather easily. In this letter we have demonstrated that also in this case the dynamics of the hidden sector responsible for supersymmetry breakdown and the structure of the soft terms affects significantly, and in fact often spoils, the would-be inflationary dynamics. Also, we point out that the issue if the cosmological constant cancellation in the post-inflationary vacuum strongly affects supersymmetric inflation. It is important to note the crucial difference between freezing of the modulus and actually stabilising it - the first approach misses parts of the scalar potential which turn out to be relevant for inflation. We argue, that it is more likely that the low scale supersymmetric inflation occurs at a critical point at the origin in the field space than at an inflection point away from the origin, as the necessary fine-tuning in the second case is typically larger.
The relation between the Hubble constant and the scale of supersymmetry breaking is investigated in models of inflation dominated by a string modulus. Usually in this kind of models the gravitino mass is of the same order of magnitude as the Hubble constant which is not desirable from the phenomenological point of view. It is shown that slow-roll saddle point inflation may be compatible with a low scale of supersymmetry breaking only if some corrections to the lowest order Kahler potential are taken into account. However, choosing an appropriate Kahler potential is not enough. There are also conditions for the superpotential, and e.g. the popular racetrack superpotential turns out to be not suitable. A model is proposed in which slow-roll inflation and a light gravitino are compatible. It is based on a superpotential with a triple gaugino condensation and the Kahler potential with the leading string corrections. The problem of fine tuning and experimental constraints are discussed for that model.
In hybrid inflation, the inflaton generically has a tadpole due to gravitational effects in supergravity, which significantly changes the inflaton dynamics in high-scale supersymmetry. We point out that the tadpole can be cancelled if there is a supersymmetry breaking singlet with gravitational couplings, and in particular, the cancellation is automatic in no-scale supergravity. We consider the LARGE volume scenario as a concrete example and discuss the compatibility between the hybrid inflation and the moduli stabilization. We also point out that the dark radiation generated by the overall volume modulus decay naturally relaxes a tension between the observed spectral index and the prediction of the hybrid inflation.
We study whether the relaxion mechanism solves the Higgs hierarchy problem against a high scale inflation or a high reheating temperature. To accomplish the mechanism, we consider the scenario that the Higgs vacuum expectation value is determined after inflation. We take into account the effects of the Hubble induced mass and thermal one in the dynamics of the relaxion.
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