Post-inflationary phases stiffer than radiation and Palatini formulation
  If the inflaton and the quintessence fields are identified, the background
geometry evolves through a stiff epoch undershooting the expansion rate of a
radiation-dominated plasma. For some classes of inflationary potentials this
scenario is at odds with the current observational evidence since the
corresponding tensor-to-scalar ratio is too large. Quintessential inflation is
analyzed when the gravitational action is supplemented by a contribution
quadratic in the Einstein-Hilbert term. In the Palatini formulation the
addition such a term does not affect the scalar modes during the inflationary
phase and throughout the course of the subsequent stiff epoch but it suppresses
the tensor power spectrum and the tensor-to-scalar ratio. While in the Palatini
formulation the power-law potentials leading to a quintessential inflationary
dynamics are again viable, the high-frequency spike of the relic graviton
spectrum is squeezed and the whole signal is suppressed at least when the
higher-order contributions appearing in the action are explicitly decoupled
from the inflaton.
