Cosmology on a Three-Brane

Abstract

In this paper a general solution is found for a five dimensional orbifold spacetime that induces a $k=0$ cosmology on a three-brane. Expressions for the energy density and pressure on the brane in terms of the brane metric are derived. Given a metric on the brane it is possible to find five dimensional spacetimes that contain the brane. This calculation is carried out for an inflationary universe and for a metric that corresponds to a radiation dominated universe in standard cosmology. It is also shown that any $k=0$ cosmology can be embedded in a flat five dimensional orbifold spacetime and the equation of the three-brane surface is derived. For an inflationary universe it is shown that the surface is the usual hyperboloid representation of de Sitter space, although it is embedded in an orbifold spacetime.

11 pages, LaTex. New solutions with a cosmological constant have been added

References in corpus (9)

• The Einstein Equations on the 3-Brane World
• Brane cosmological evolution in a bulk with cosmological constant
• Cosmology of Brane Models with Radion Stabilization
• Brane New World
• Cosmological Expansion in the Randall-Sundrum Brane World Scenario
• Brane-world solutions, standard cosmology, and dark radiation
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Cited by in corpus (26)

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• Strong Brane Gravity and the Radion at Low Energies
• Bulk Gravitational Field and Cosmological Perturbations on the Brane
• Braneworld Instantons
• de Sitter in non-supersymmetric string theories: no-go theorems and brane-worlds
• Braneworld cosmological models with anisotropy
• Asymptotic behavior of a scalar field with an arbitrary potential trapped on a Randall-Sundrum's braneworld: the effect of a negative dark radiation term on a Bianchi I brane
• Disappearing Dark Matter in Brane World Cosmology: New Limits on Noncompact Extra Dimensions
• Gravity on branes
• Supersymmetry Breaking and Stability in String Vacua: brane dynamics, bubbles and the swampland
• On linearized gravity in the Randall-Sundrum scenario
• Reinventing spacetime on a dynamical hypersurface
• Variation of G, ${\Lambda }_{(4)}$ and Vacuum Energy From Brane-World Models
• Gravitational waves in cosmological models of Hořava-Witten theory
• Brane-world models emerging from collisions of plane waves in 5D
• Inflationary solutions in the brane-world and their geometrical interpretation
• FLRW Universes from "Wave-Like" Cosmologies in 5D
• Static solutions in the R^4 brane world
• Shedding light on dark bubble cosmology
• New Perspectives on Moving Domain Walls in (A)dS_(5) Space
• New exact cosmologies on the brane
• Cosmological predictions from the Misner brane
• Limits on the integration constant of the dark radiation term in Brane Cosmology
• An Investigation of Equivalence between the Bulk-based and the Brane-based Approaches for Anisotropic Models