Arbitrary scalar field and quintessence cosmological models
  The mechanism of the initial inflationary scenario of the universe and of its
late-time acceleration can be described by assuming the existence of some
gravitationally coupled scalar fields $\phi $, with the inflaton field
generating inflation and the quintessence field being responsible for the late
accelerated expansion. Various inflationary and late-time accelerated scenarios
are distinguished by the choice of an effective self-interaction potential
$V(\phi )$, which simulates a temporarily non-vanishing cosmological term. In
this work, we present a new formalism for the analysis of scalar fields in flat
isotropic and homogeneous cosmological models. The basic evolution equation of
the models can be reduced to a first order non-linear differential equation.
Approximate solutions of this equation can be constructed in the limiting cases
of the scalar field kinetic energy and potential energy dominance,
respectively, as well as in the intermediate regime. Moreover, we present
several new accelerating and decelerating exact cosmological solutions, based
on the exact integration of the basic evolution equation for scalar field
cosmologies. More specifically, exact solutions are obtained for exponential,
generalized cosine hyperbolic, and power law potentials, respectively.
Cosmological models with power law scalar field potentials are also analyzed in
detail.
