Gravity on codimension 2 brane worlds

Abstract

We compute the matching conditions for a general thick codimension 2 brane, a necessary previous step towards the investigation of gravitational phenomena in codimension 2 braneworlds. We show that, provided the brane is weakly curved, they are specified by the integral in the extra dimensions of the brane energy-momentum, independently of its detailed internal structure. These general matching conditions can then be used as boundary conditions for the bulk solution. By evaluating Einstein equations at the brane boundary we are able to write an evolution equation for the induced metric on the brane depending only on physical brane parameters and the bulk energy-momentum tensor. We particularise to a cosmological metric and show that a realistic cosmology can be obtained in the simplest case of having just a non-zero cosmological constant in the bulk. We point out several parallelisms between this case and the codimension 1 brane worlds in an AdS space.

24 pages

References in corpus (53)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• An Alternative to Compactification
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Cosmological parameters from SDSS and WMAP
• The Einstein Equations on the 3-Brane World
• Non-conventional cosmology from a brane-universe
• Brane cosmological evolution in a bulk with cosmological constant
• Cosmological Expansion in the Presence of an Extra Dimension
• Study of the anomalous acceleration of Pioneer 10 and 11
• Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration
• Cosmology of One Extra Dimension with Localized Gravity
• Is there Supernova Evidence for Dark Energy Metamorphosis ?
• Topological Black Holes in Anti-de Sitter Space
• The case for dynamical dark energy revisited
• Towards a Naturally Small Cosmological Constant from Branes in 6D Supergravity
• General brane cosmologies and their global spacetime structure
• Localizing Gravity on a String-Like Defect in Six Dimensions
• Global structure of exact cosmological solutions in the brane world
• Nonsingular global string compactifications
• An Early Proposal of "Brane World"
• Cosmological constraints on the dark energy equation of state and its evolution
• A Critical Cosmological Constant from Millimeter Extra Dimensions
• Warped Brane Worlds in Six Dimensional Supergravity
• Codimension Two Compactifications and the Cosmological Constant Problem
• Einstein gravity on the codimension 2 brane?
• 3-Branes and Uniqueness of the Salam-Sezgin Vacuum
• Can codimension-two branes solve the cosmological constant problem?
• Cosmology of codimension-two braneworlds
• Selftuning and its footprints
• Spheres, Deficit Angles and the Cosmological Constant
• Sidestepping the Cosmological Constant with Football-Shaped Extra Dimensions
• Can we be tricked into thinking that w is less than -1?
• A Conical Tear Drop as a Vacuum-Energy Drain for the Solution of the Cosmological Constant Problem
• General Axisymmetric Solutions and Self-Tuning in 6D Chiral Gauged Supergravity
• Football Shaped Extra Dimensions and the Absence of Self-Tuning
• Warped compactification on Abelian vortex in six dimensions
• Gravity on a 3-brane in 6D Bulk
• A comment on the self-tuning of cosmological constant with deficit angle on a sphere
• 4d-Flat Compactifications With Brane Vorticities
• Quasi-Thick Codimension 2 Braneworld
• Using globular clusters to test gravity in the weak acceleration regime
• Brane solutions of a spherical sigma model in six dimensions
• Localized gravity and mass hierarchy in D=6 with the Gauss-Bonnet term
• Effective Theory on Non-Abelian Vortices in Six Dimensions
• Can we live in a self-tuning universe?
• QED from six-dimensional vortex and gauge anomalies
• Nonsingular 4d-flat branes in six-dimensional supergravities
• Zero modes of six-dimensional Abelian vortices
• Cosmology of intersecting brane world models in Gauss-Bonnet gravity
• Higher codimension braneworlds from intersecting branes
• A cigar-like Universe
• Regular compactifications and Higgs model vortices
• No-boundary Codimension-two Braneworld

Cited by in corpus (66)

• Massive Gravity
• Brane-World Gravity
• Thick brane solutions
• Standard 4d gravity on a brane in six dimensional flux compactifications
• Charting the Landscape of Modified Gravity
• Codimension-two branes in six-dimensional supergravity and the cosmological constant problem
• Bulk Singularities and the Effective Cosmological Constant for Higher Co-dimension Branes
• Exact Black Holes and Gravitational Shockwaves on Codimension-2 Branes
• UV Caps and Modulus Stabilization for 6D Gauged Chiral Supergravity
• Tensor perturbations of $f(T)$-branes
• Casimir Energies for 6D Supergravities Compactified on T_2/Z_N with Wilson Lines
• Regularization of conical singularities in warped six-dimensional compactifications
• Codimension-2 Brane-Bulk Matching: Examples from Six and Ten Dimensions
• On braneworld cosmologies from six dimensions, and absence thereof
• Effective Field Theories and Matching for Codimension-2 Branes
• Induced cosmology on a regularized brane in six-dimensional flux compactification
• Brane-bulk matter relation for a purely conical codimension-2 brane world
• Large Dimensions and Small Curvatures from Supersymmetric Brane Back-reaction
• Thick brane in f(T,B) gravity
• Induced gravity on intersecting brane-worlds Part I: Maximally symmetric solutions
• Fermion generations, masses and mixings in a 6D brane model
• The 6D SuperSwirl
• Induced gravity on intersecting brane-worlds Part II: Cosmology
• Kicking the Rugby Ball: Perturbations of 6D Gauged Chiral Supergravity
• Gravitational Waves in a Codimension Two Braneworld
• The Effective Field Theory of Codimension-two Branes
• String-Like BTZ on Codimension-2 Braneworlds in the Thin Brane Limit
• Hybrid brane worlds in the Salam-Sezgin model
• Isolated Minkowski vacua, and stability analysis for an extended brane in the rugby ball
• Fermionic Kaluza-Klein modes in the string-cigar braneworld
• Bulk Axions, Brane Back-reaction and Fluxes
• Cosmological Evolution of a Purely Conical Codimension-2 Brane World
• MSLED, Neutrino Oscillations and the Cosmological Constant
• Gravitational resonances on $f(T)$-branes
• Black Holes on Thin 3-branes of Codimension-2 and their Extension into the Bulk
• Conservation equation on braneworlds in six dimensions
• First-order formalism for thick branes in $f(T,\mathcal{T})$ gravity
• Gravitational resonances on $f(R)$-brane
• Modified Friedmann Equation and Inflation in Warped Codimension-two Braneworld
• Supersymmetric codimension-two branes in six-dimensional gauged supergravity
• Footballs, Conical Singularities and the Liouville Equation
• Running with Rugby Balls: Bulk Renormalization of Codimension-2 Branes
• Instability of brane cosmological solutions with flux compactifications
• Regularized braneworlds of arbitrary codimension
• Unconventional cosmology on the (thick) brane
• Gravitational Kaluza-Klein modes in the String-Cigar Braneworld
• Technical Naturalness on a Codimension-2 Brane
• Gravitino in six-dimensional warped supergravity
• The cosmological constant problem in codimension-two brane models
• Warping with dilatation symmetry and self-tuning of the cosmological constant
• A 6D standing-wave Braneworld with normal matter as source
• Cosmology in Six Dimensions
• Geometrically contracted structure in teleparallel $f(T)$ gravity
• Sculpting the Extra Dimensions: Inflation from Codimension-2 Brane Back-reaction
• Localizing Gravity on the Triple Intersection of 7-branes in 10D
• Constraints for warped branes
• Codimension Two Branes and Distributional Curvature
• Bulk Renormalization and Particle Spectrum in Codimension-Two Brane Worlds
• A smoothed string-like braneworld in six dimensions
• String-like brane splitting in the context of $f(T,B)$ gravity
• Cosmological Kaluza-Klein branes in black brane spacetimes
• No-Go Theorems on Localization of Gravity around Higher Codimensional Branes in Noncompact Extra Dimensions
• Conical singularities regularized in warped six-dimensional flux compactification and their induced brane cosmology
• The End of the Road for Bulk Fields in Warped Randall-Sundrum Braneworlds
• Codimension-2 black hole solutions on a thin 3-brane and their extension into the bulk
• BTZ Solutions on Codimension-2 Braneworlds