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

Abstract

We study the cosmology of a general scalar field and barotropic fluid during the early stage of a brane-world where the Friedmann constraint is dominated by the square of the energy density. 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. On the other hand if it approaches a finite constant, then V (φ) ∝ 1 φ 2 . For λ → ∞ asymptotically, we find examples where it does so both with and without oscillating. In the latter case, the barotropic fluid dominates the scalar filed asymptotically. Finally we point out an interesting duality which leads to identical evolution equations in the high energy ρ 2 dominated regime and the low energy ρ dominated regime.

Early universe dynamics in semi-classical loop quantum cosmology

“…In particular, the modified evolution equations for spatially flat models can be recast, after appropriate field redefinitions, into the classical Einstein equations for a minimally coupled, self-interacting scalar field. A similar correspondence between standard relativistic cosmology and the high-energy limit of the Randall-Sundrum type II braneworld [56] has also been identified recently [57,58,59,60] and it would be interesting to explore possible relationships between these apparently unrelated scenarios further.…”

Loop cosmological dynamics and dualities with Randall-Sundrum braneworlds

“…[26] it was established that if a cosmological model with a modified Friedmann equation of the form H 2 = (κ/3)ρ(φ)G 1 (φ) has a scaling solution (a 1 (φ), b 1 (φ), V 1 (φ)), then a necessary and sufficient condition for different cosmological model with H 2 = (κ/3)ρ(φ)G 2 (φ) and scaling solution (a 2 (φ), b 2 (φ), V 2 (φ)) to satisfy eq. (25) and to be the dual is that…”

“…Cosmological models/phases related via (25) are said to be dual to each other. This property is immensely useful to establish correspondence between different cosmological phases [23] or between different models [25,26]. Here we would study its symmetries for different phases of the scalar field dynamics.…”

“…For that we would derive scaling solutions in LQC which are useful to study the stability properties of cosmological models [24,25,26,27]. As has been further established in Ref.…”

Confronting quintessence models with recent high-redshift supernovae data

“…Furthermore in such a tracking regime the equation of state of quintessence w remains almost constant. Moreover there are particular models, usually called scaling models [9][10][11], in which w mimics the equation of state of the dominant component throughout the cosmological evolution. These properties allow quintessence models to alleviate the fine tuning problem of XCDM models, although in any case the scale of the quintessence potential has always to be tuned in order to reproduce the data.…”