Planckian hypersurfaces, inflation and bounces

Abstract

When the different wavelengths of the scalar and tensor modes of the geometry are all assigned on the same space-like hypersurface the maximally amplified frequencies of the spectrum remain smaller than the Planck mass only if the duration of a stage of accelerated expansion and the corresponding tensor to scalar ratio are severely constrained. All the different wavelengths can be initialized on the same space-like hypersurface at the onset of inflation but this strategy and the related conclusions are plausible only for classical inhomogeneities. We argue that a whole class of potential constraints is easily evaded provided the different wavelengths of the quantum fields are assigned as soon as they cross the corresponding Planckian hypersurfaces. In this case the Cauchy data for the mode functions depend on the wavenumber so that larger wavelengths start evolving earlier while shorter wavelengths are assigned later. Within this strategy the duration of a conventional inflationary phase and the corresponding tensor to scalar ratio are not constrained but the large-scale power spectra inherit specific large-scale corrections that remain however unobservable.