From WMAP to Planck: Exact reconstruction of 4- and 5-dimensional
  inflationary potential from high precision CMB measurements
  We make a more general determination of the inflationary observables in the
standard 4-D and 5-D single-field inflationary scenarios, by the exact
reconstruction of the dynamics of the inflation potential during the observable
inflation with minimal number of assumptions: the computation does not assume
the slow-roll approximation and is valid in all regimes if the field is
monotonically rolling down its potential. Making use of the {\em
Hamilton-Jacobi} formalism developed for the 5-D single-field inflation
model,we compute the scale dependence of the amplitudes of the scalarand tensor
perturbations by integrating the exact mode equation. We analyze the
implications of the theoretical uncertainty in the determination of the
reheating temperature after inflation on the observable predictions of
inflation and evaluate its impact on the degeneracy of the standard inflation
consistency relation.
