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Horizon crossing and inflation with large η

William H. Kinney
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Abstract

I examine the standard formalism of calculating curvature perturbations in inflation at horizon crossing, and derive a general relation which must be satisfied for the horizon crossing formalism to be valid. This relation is satisfied for the usual cases of power-law and slow roll inflation. I then consider a model for which the relation is strongly violated, and the curvature perturbation evolves rapidly on superhorizon scales. This model has Hubble slow roll parameter $η= 3$, but predicts a scale-invariant spectrum of density perturbations. I consider the case of hybrid inflation with large $η$, and show that such solutions do not solve the ``$η$ problem'' in supergravity. These solutions correspond to field evolution which has not yet relaxed to the inflationary attractor solution, and may make possible new, more natural models on the string landscape.

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William H. Kinney. 2005-07-19. Horizon crossing and inflation with large η. https://doi.org/10.1103/physrevd.72.023515

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