Planckian hypersurfaces, inflation and bounces
  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.
