Brane cosmological evolution in a bulk with cosmological constant

Binétruy, P.; Deffayet, Cédric; Ellwanger, Ulrich; Langlois, David

doi:10.1016/s0370-2693(00)00204-5

Cited by 1,007 publications

(1,227 citation statements)

References 17 publications

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“…This is a difficult task because of the presence of the Lovelock tensor. An easier approach is to solve the 5-dimensional field equations in suitable coordinates and impose the junction conditions, following the Randall-Sundrum case [2], as generalized to the Gauss-Bonnet case in ref. [15].…”

Section: Jhep10(2003)066mentioning

confidence: 99%

Brane cosmology with curvature corrections

Kofinas

Maartens

Papantonopoulos

2003

J. High Energy Phys.

115

123

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Abstract:We study the cosmology of the Randall-Sundrum brane-world where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. The combined effect of these curvature corrections to the action removes the infinite-density big bang singularity, although the curvature can still diverge for some parameter values. A radiation brane undergoes accelerated expansion near the minimal scale factor, for a range of parameters. This acceleration is driven by the geometric effects, without an inflaton field or negative pressures. At late times, conventional cosmology is recovered.

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Section: Jhep10(2003)066mentioning

confidence: 99%

Brane cosmology with curvature corrections

Kofinas

Maartens

Papantonopoulos

2003

J. High Energy Phys.

115

123

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“…(40), the effects that lead to the quadratic dependence of the Friedmann equation (39) on the energy density of the scalar field modify only the oscillator potential (41), whereas the non-linear term on the right-hand side arises through the bulk black hole contribution. Thus, in principle, a similar approach to that outlined above in Section 3 may be developed for analytically investigating the importance of these terms on braneworld cosmologies.…”

Section: Braneworld Scenariosmentioning

confidence: 99%

Ermakov-Pinney equation in scalar field cosmologies

2002

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It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the non-linear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed. reviews, see, e.g., [3]). The simplest mechanism for inflation utilises the potential energy associated with the self-interaction of a scalar inflaton field to drive the accelerated expansion. High redshift observations of type Ia supernovae suggest that the universe is experiencing another phase of accelerated expansion at the present epoch [4]. This, combined with the CMB data, presents a picture of the universe dominated by a dark energy component [5,6]. One possible source of this dark energy is a scalar quintessence field that interacts with baryonic and non-baryonic matter in such a way that its potential energy is currently dominating the cosmic dynamics [7]. The observations favour a model of structure formation where 70% of the energy density of the universe is presently in the form of quintessence [6]. The remaining fraction of the energy density is comprised of visible and cold dark matter which collectively act as a pressureless perfect fluid.The ekpyrotic scenario has recently been proposed as an alternative to the standard inflationary cosmology [8]. In this scenario the big bang is interpreted as the collision of two domain walls or branes travelling through a fifth dimension. Before the collision, the effective dynamics on the four dimensional branes is described by Einstein's gravity minimally coupled to a self-interacting scalar field. The field parametrizes the separation between the branes and at early times slowly rolls down a negative potential. This results in an accelerated collapse of the universe and since the field is minimally coupled, its energy density is related to the Hubble parameter by the standard Friedmann equation. Thus, self-interacting scalar fields play a central role in modern cosmology and in view of the above developments, it is important to investigate cosmologies that contain both a scalar field and a perfect fluid.In this paper, we develop an analytical approach to models of this type by expressing the cosmological field equations in terms of an Ermakov system [9,10,11]. In general, an Ermakov system is a pair of coupled, second-order, non-linear ordinary differential equations (ODEs) [11] and such systems often arise in studies of nonlinear optics [12], nonlinear elasticity [13], molecular structures [14] and quantum cosmology [15]. (For further references, see, e.g., Refs. [16]). In the one-dimensional case, the two equations decouple and the system reduces to a single equation known as the Ermakov-Pinney equation [9,17]. This is given by 1

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“…Friedmann branes, for example, are known to be embeddible into any of the Schwarzschild / Reissner-Nordström / Vaidya -anti de Sitter bulks (depending on the energy-momentum in the bulk; for a systematic treatment see [3]). Cosmological evolution has been extensively studied in this scenario (for symmetric embeddings see [7], [8] and references therein; for asymmetric embeddings [3], [9] and references therein). The matter in the bulk affects the cosmological evolution on the brane through a "comoving mass" and a bulk pressure [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Black holes and dark energy from gravitational collapse on the brane

Gergely

2007

J. Cosmol. Astropart. Phys.

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The gravitational collapse of a pressureless fluid in general relativity (Oppenheimer-Snyder collapse) results in a black hole. The study of the same phenomenon in the brane-world scenario has shown that the exterior of the collapsing dust sphere cannot be static. We show that by allowing for pressure, the exterior of a fluid sphere can be static. The gravitational collapse on the brane proceeds according to the modified gravitational dynamics, turning the initial nearly dust-like configuration into a fluid with tension. The tension arises from the non-linearity of the dynamical equations in the energy-momentum tensor, and it vanishes in the general relativistic limit. Below the horizon the tension turns the star into dark energy. This transition occurs right below the horizon for astrophysical black holes and far beyond the horizon for intermediate mass and galactic black holes. Further, both the energy density and the tension increase towards infinite values during the collapse. The infinite tension however could not stop the formation of the singularity.

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Brane cosmological evolution in a bulk with cosmological constant

Cited by 1,007 publications

References 17 publications

Brane cosmology with curvature corrections

Brane cosmology with curvature corrections

Ermakov-Pinney equation in scalar field cosmologies

Black holes and dark energy from gravitational collapse on the brane

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