Exact Solutions of Some Dynamical Variables in FRW Universe with Scalar
  Field Dynamics
  The inflationary epoch and the late time acceleration of the expansion rate
of universe can be explained by assuming a gravitationally coupled scalar
field. In this article, we propose a new method of finding exact solutions in
the background of flat Friedmann-Robertson-Walker (FRW) cosmological models by
considering both scalar field and matter. We consider different forms of scalar
field potential as a function of scale factor. Our method provides analytical
expressions for equation of state parameter of scalar field, deceleration
parameter and Hubble parameter. This method can be applied to various other
forms of scalar field potential, to the early radiation dominated epoch and
very early scalar field dominated inflationary dynamics. Since the method
produces exact analytical expression for $H(a)$ (i.e., H(z) as well) one can
use this result to constrain the model parameters using Hubble parameter data
at different redshifts. As an extension of the method, we also consider the
inverse problem of reconstructing scalar field potential energy by assuming any
general analytical expression of scalar field equation of state parameter as a
function of scale factor.
