  In the first part of this paper, we outline the construction of an
inflationary cosmology in the framework where inflation is described by a
universally evolving scalar field, with the Lagrangian ${\cal
L}_\phi=-{1/2}(\partial\phi)^2 -V(\phi)$. By considering a generic situation
that inflaton attains a nearly constant velocity, during inflation, $m_P^{-1}
(d\phi/dN)\equiv \alpha$ (where $N\equiv \ln a$ is the e-folding time), we find
the conditions that have to satisfied by the (reconstructed) scalar potential
to be consistent with the WMAP inflationary data. In the second part of this
paper, we introduce a novel approach of constructing dark energy within the
context of the standard scalar-tensor gravity. The assumption that a scalar
field might roll with a nearly constant velocity, during inflation, can also be
applied to {\it quintessence} or dark energy models. For the minimally coupled
quintessence, $\alpha_Q\equiv dA(Q)/d(\kappa Q)=0$ (where $A(Q)$ is the
standard matter-quintessence coupling), the dark energy equation of state in
the range $-1\le w_{DE} < -0.82$ can be obtained for $0\le \alpha < 0.63$. For
$\alpha<0.1$, the model allows for only modest evolution of dark energy density
with redshift. The effect of the matter-quintessence coupling can be
significant only if $|\alpha_Q| \gtrsim 0.1$, while a small coupling
$|\alpha_Q|< 0.1$ will have almost no effect on cosmological parameters. The
best fit value of $\alpha_Q$ in our model is found to be $\alpha_Q \simeq
0.06$, but it may contain significant numerical errors, viz $\alpha_Q=0.06\pm
0.35$, which thereby implies the consistency of our model with general
relativity (for which $\alpha_Q=0$) at $1\sigma$ level.
