Abstract
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.
Highlights
In a wide range of inflationary models the underlying dynamics is that of a single scalar field, with the inflaton rolling in some underlying potential [1,2,3,4]
In order to study the inflationary dynamics, the usual strategy is an expansion in the deviation from the scale invariance, formally expressed as the slow-roll approximation, which arises in two separate contexts
The first is in simplifying the classical inflationary dynamics of expansion and the lowest-order approximation ignores the contribution of the kinetic energy of the inflation to the expansion rate
Summary
In a wide range of inflationary models the underlying dynamics is that of a single scalar field, with the inflaton rolling in some underlying potential [1,2,3,4]. In [79], a phase-plane analysis was performed of the complete dynamical system corresponding to a flat FRW cosmological models with a perfect fluid and a self-interacting scalar field and it was shown that every positive and monotonous potential which is asymptotically exponential yields a scaling solution as a global attractor. The evolution equation is a firstorder, strongly non-linear differential equation, which, allows the possibility of considering analytical solutions in both the asymptotic limits of scalar-field kinetic or potential energy dominance and in the intermediate domain, respectively.
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