  Quintessential inflation refers to an attempt to unify inflation and
late-time cosmic acceleration using a single scalar field. In this letter we
consider two different classes of quintessential inflation, one of which is
based upon a Lagrangian with non-canonical kinetic term $k^2(\phi)\partial^\mu
\phi \partial_\mu \phi$ and a steep exponential potential while the second
class uses the concept of steep brane world inflation. We show that in both
cases the Lyth bound can be evaded, despite the large tensor-to-scalar ratio of
perturbations. The post-inflationary dynamics is consistent with
nucleosynthesis constraint in these cases.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology;High Energy Physics - Theory