Cosmological evolution of general scalar fields and quintessence

Abstract

We study the cosmological evolution of scalar fields with arbitrary potentials in the presence of a baryotropic fluid ͑matter or radiation͒ without making any assumption on which term dominates. We determine what kind of potentials V() permits a quintessence interpretation of the scalar field and to obtain interesting cosmological results. We show that all model dependence is given in terms of ϵϪVЈ/V only and we study all possible asymptotic limits: approaching zero, a finite constant, or infinity. We determine the equation of state dynamically for each case. For the first class of potentials, the scalar field quickly dominates the universe behavior, with an inflationary equation of state allowing for a quintessence interpretation. The second case gives the extensively studied exponential potential, while in the last case, when approaches infinity, if it does not oscillate, then the energy density redshifts faster than the baryotropic fluid, but if oscillates, then the energy density redshift depends on the specific potential. PACS number͑s͒: 98.80.Cq, 95.35.ϩd, 98.80.Hw *

Cosmological evolution of general scalar fields in a brane-world cosmology

“…The success of this approach has often been established by demonstrating the existence of attractor solutions by investigating the asymptotic dynamics of the system being studied. For example in the context of usual 4D Einstein gravity, particular potentials have been discussed [7,8,9,10,11,12,13], whereas others have adopted an approach which does not specify a particular potential [1,14,15]. However, recent higherdimensional unification scenarios based on brane-worlds suggest that the gravitational law could be different from Einstein's during the early stages of our Universe.…”

“…In Sec. II, we review the key equations of motion and define variables which will allow us to analyse the asymptotic behaviour of this system and point out an intriguing duality with the equations obtained in the context of scaling solutions in standard Friedman cosmologies [1,11]. In Sec.…”

“…Since the modification of the cosmic expansion law arising through the quadratic energy density term becomes important during the early stage of the universe, we concentrate on this stage. In order to classify the asymptotic behaviour of the solutions, we follow the model independent approach as first proposed in [1,14]. Earlier work investigating the impact of these ρ 2 corrections has concentrated on models with particular potentials [34,35,36,37,38,39,40].…”

“…Assuming both the scalar field and fluid are confined to the brane, we find a range of behaviour depending on the form of the potential. Generalising an approach developed for a standard Friedmann cosmology, in [1], we show that the potential dependence V (φ) can be described through a parameter λ ≡ − √ 2m . For the case where λ asymptotes to zero, we show that the solution exhibits stable inflationary behaviour.…”

Friedmann cosmology with nonpositive-definite Higgs potentials

“…Cosmological models with one scalar field with positively defined potential are well studied models, see for example [2,51,54,55,56]. Let us remind the main features of the phase portraits of these models.…”