Brane cosmological evolution in a bulk with cosmological constant

Abstract

We consider the cosmology of a ``3-brane universe'' in a five dimensional (bulk) space-time with a cosmological constant. We show that Einstein's equations admit a first integral, analogous to the first Friedmann equation, which governs the evolution of the metric in the brane, whatever the time evolution of the metric along the fifth dimension. We thus obtain the cosmological evolution in the brane for any equation of state describing the matter in the brane, without needing the dependence of the metric on the fifth dimension. In the particular case $p=w\rho$, $(w=constant)$, we give explicit expressions for the time evolution of the brane scale factor, which show that standard cosmological evolution can be obtained (after an early non conventional phase) in a scenario à la Randall and Sundrum, where a brane tension compensates the bulk cosmological constant. We also show that a tiny deviation from exact compensation leads to an effective cosmological constant at late time. Moreover, when the metric along the fifth dimension is static, we are able to extend the solution found on the brane to the whole spacetime.

12 pages, Latex; references added, minor modifications

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• Brane-world Singularities
• Intermediate inflation on the brane and warped DGP models
• Mass spectrum of primordial black holes from inflationary perturbation in the Randall-Sundrum braneworld: a limit on blue spectra
• The dynamics of scalar-tensor cosmology from RS two-brane model
• Effects of the Generalized Uncertainty Principle on the Inflation Parameters
• Inflationary solutions in the brane-world and their geometrical interpretation
• Brane-Bulk Interaction and Holographic Principle
• Brane inflation and the robustness of the Starobinsky inflationary model
• Stochastic inflation on the brane
• Braneworld inflation with effective α-attractor potential
• Domain wall cosmology and multiple accelerations
• Degeneracy of consistency equations in braneworld inflation
• Initial Kaluza-Klein fluctuations and inflationary gravitational waves in braneworld cosmology
• Inflation with Planck: a survey of some "exotic" inflationary models
• Quark-hadron phase transition in a chameleon Brans-Dicke model of brane gravity
• A no-go for no-go theorems prohibiting cosmic acceleration in extra dimensional models
• Supersymmetry and Brane Cosmology
• Primordial Nucleosynthesis as a Test of the Friedmann Equation in the Early Universe
• Hubble Law and Brane Matter after Ekpyrosis
• On the possibility of braneworld quintessential inflation
• Exact Solutions in Five-Dimensional Axi-dilaton Gravity with Euler-Poincare Term
• Effective theory for close limit of two branes
• Bulk black holes radiating in non-Z_2 brane-world spacetimes
• Abundance of Asymmetric Dark Matter in Brane World Cosmology
• Manybody treatment of white dwarf and neutron stars on the brane
• Vacuum Brane and the Bulk Dynamics in Dilatonic Brane World
• Sneutrino inflation in Gauss-Bonnet brane-world cosmology, the gravitino problem and leptogenesis
• Induced Curvature in Brane Worlds by Surface Terms in String Effective Actions with Higher-Curvature Corrections
• Brane worlds and dark matter
• Multiple-scales analysis of cosmological perturbations in brane-worlds
• Braneworld cosmological solutions and their stability
• Cosmological braneworld solutions with bulk scalar field in DGP setup
• Reformulation and Interpretation of SMS Braneworld
• Simple inflationary models in Gauss-Bonnet brane-world cosmology
• FLRW Universes from "Wave-Like" Cosmologies in 5D
• A Varying-e Brane World Cosmology
• Holographic Cosmic Quintessence on Dilatonic Brane World
• Holographic Friedmann Equation and $\mathcal{N}=$4 SYM theory
• Dynamical Instabilities of the Randall-Sundrum Model
• Curvaton Dynamics in Brane-worlds
• Brane Cosmology in an Arbitrary Number of Dimensions
• On interactions of higher spin fields with gravity and branes in AdS_5
• Global p-Brane World: A New Approach to Stable Mass Hierarchy
• Holographic Cosmological Backgrounds, Wilson Loop (De)confinement and Dilaton Singularities
• Geometry of deformations of branes in warped backgrounds
• Supergravity Brane Cosmologies
• Which action for brane worlds?
• Scaling solution, radion stabilization, and initial condition for brane-world cosmology
• Classic tests of General Relativity described by brane-based spherically symmetric solutions
• Constraints on brane and bulk ideal fluid in Randall-Sundrum cosmologies
• The Inflationary Energy Scale in Braneworld Cosmology
• Cosmological dynamics of a non-minimally coupled bulk scalar field in DGP setup
• Constraints on Brane-World Inflation from the CMB Power Spectrum: Revisited
• Fluid inflation with brane correction
• Primordial perturbations from slow-roll inflation on a brane
• Role of Chaplygin gas as geometrical dark energy in anisotropic brane gravity
• Brane cosmology and the self-tuning of the cosmological constant
• Assisted chaotic inflation in brane-world cosmology
• Inflationary Attractor in Braneworld Scenario
• F-Term Hybrid Inflation, the η-problem and Extra Dimensions
• F-term Braneworld inflation in Light of Five-year WMAP observations
• Leading order corrections to the cosmological evolution of tensor perturbations in braneworld
• Dilaton tadpoles and mass in warped models
• Generalized Friedmann Equations for a Finite Thick Brane
• Effect of extrinsic curvature on quark--hadron phase transition
• Transition from decelerated to accelerated cosmic expansion in braneworld universes
• Numerical study of curvature perturbations in a brane-world inflation at high-energies
• Brane Cosmology and Motion of Test Particles in Five-Dimensional Warped Product Spacetimes
• Quadratic energy-momentum squared gravity: constraints from big bang nucleosynthesis
• Second-order corrections to slow-roll inflation in the brane cosmology
• Brane World Cosmology In Jordan-Brans-Dicke Theory
• A covariant approach to braneworld holography
• Gravitino dark matter in brane-world cosmology
• Accelerated expansion from braneworld models with variable vacuum energy
• Braneworld setup and embedding in teleparallel gravity
• Chaotic Inflationary Universe on Brane
• Shortcuts in Domain Walls and the Horizon Problem
• Effects of sterile neutrino and extra-dimension on big bang nucleosynthesis
• The consistency relation in braneworld inflation
• Asymptotic states in brane cosmology with a nonlocal anisotropic stress
• Standard Cosmology on the Anti-de Sitter boundary
• Quantum creation and inflationary universes: a critical appraisal
• Dark matter in supersymmetric models with axino LSP in Randall-Sundrum II brane model
• Axino dark matter in brane world cosmology
• Test of patch cosmology with WMAP
• Comment on 4D Lorentz invariance violations in the brane-world
• Holographic Fluids from 5D Dilaton Gravity
• Second order brane cosmology with radion stabilization
• Inflation in anisotropic brane universe using tachyon field
• Randall-Sundrum limit of f(R) brane-world models
• Quark-hadron phase transition in Brans-Dicke brane gravity
• Generalized Holographic Cosmology
• Linearized Israel Matching Conditions for Cosmological Perturbations in a Moving Brane Background
• Brane-world inflation: slow-roll corrections to the spectral index
• Braneworld inflation from an effective field theory after WMAP three-year data
• Gravitational collapse and evolution of holographic black holes
• Curvature corrections to the low energy effective theory in 6D regularized braneworlds
• Gravitational particle production in braneworld cosmology
• Localization of gravity in brane world cosmologies
• Braneworld cosmology in the sourced-Taub background
• Big bang of the brane universe
• Bulk Higgs field in a Randall-Sundrum model with nonvanishing brane cosmological constant
• Ellipsoidal universe in the brane world
• Gauss-Bonnet braneworld and WMAP three year results
• A homogeneous brane-world universe
• Scalar Kinks in Warped Extra Dimensions
• Graviton Emission into Non-Z_2 Symmetric Brane World Spacetimes
• On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case
• Misner-brane cosmology
• Brane cosmology in teleparallel and $f(T)$ gravity
• Domain wall universe in the Einstein-Born-Infeld theory
• Holographic Description of Heavy-Quark Potentials in an Inflationary Braneworld Scenario
• Comments on SUSY inflation models on the brane
• Tachyon Logamediate inflation on the brane
• Dynamical Evolution of the Extra Dimension in Brane Cosmology
• A Scalar-Tensor Bimetric Brane World Cosmology
• Non-Vacuum AdS Cosmologies and the Approach to Equilibrium of Entanglement Entropy
• Clockwork Cosmology
• AdS/CFT on the brane
• Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes
• Formation Of Emergent Universe in Brane Scenario as a Consequence of Particle Creation
• High-Energy theory for close Randall Sundrum branes
• D-term inflation in D-brane cosmology
• Can local bulk effects explain the galactic dark matter?
• Anisotropy in Born-Infeld brane cosmology
• New properties of scalar field dynamics in brane isotropic cosmological models
• Teleparallel Gravity in Five Dimensional Theories
• Pre-big bang on the brane
• WMAP Bounds on Braneworld Tachyonic Inflation
• Brane Cosmology With Generalized Chaplygin Gas in The Bulk
• Tensorial perturbations in the bulk of inflating brane worlds
• Two-Brane Randall-Sundrum Model in AdS_5 and dS_5
• Gauss-Bonnet brane-world cosmology without $Z_2$-symmetry
• A note on brane cosmology
• Dynamic domain walls in Maxwell-Dilaton background
• Static solutions in the R^4 brane world
• Living on a dS brane: Effects of KK modes on inflation
• Existence and Stability of Non-Trivial Scalar Field Configurations in Orbifolded Extra Dimensions
• Inflationary Cosmology: Theory and Phenomenology
• Trace Anomaly Inflation in Brane Induced Gravity
• The five dimensional universal hypermultiplet and the cosmological constant problem
• Domain walls in Born-Infeld-dilaton background
• The 4d effective action of 5d gauged supergravity with boundaries
• Slinky evolution of domain wall brane cosmology
• Five-Dimensional Black Hole String Backgrounds and Brane Universe Acceleration
• High-energy effective theory for matter on close Randall Sundrum branes
• Spherically Symmetric Thick Branes in Vacuum
• Bulk scalar field in DGP braneworld cosmology
• Separation Distribution of Vacuum Bubbles in de Sitter Space
• Modified Gravity Models Admitting Second Order Equations of Motion
• Gravitational and cosmological properties of a brane-universe
• New Perspectives on Moving Domain Walls in (A)dS_(5) Space
• Braneworld Cosmological Perturbations in Teleparallel Gravity
• Complementary cosmological tests of RSII brane models
• Particle creation in the presence of a warped extra dimension
• Origin of Small Cosmological Constant in Brane-World
• Brane Cosmology and KK Gravitinos
• Supersymmetric hybrid inflation in the braneworld scenario
• Hydrogen-like Spectrum of Spontaneously Created Brane Universes with deSitter Ground State
• Polytropic Inspired Inflation on the Brane
• A new source for a braneworld cosmological constant from a modified gravity model in the bulk
• Comparison of results on $N_{\mathrm{eff}}$ from various Planck likelihoods
• Self-tuning of the cosmological constant in brane-worlds with $P(X,\varphi )$
• Considering Late-Time Acceleration in some Cosmological Models
• Condition for Primordial Black Hole Formation in Randall-Sundrum Cosmology
• Simple brane-world inflationary models: an update
• Cosmology of Horava-Lifshitz f(R) Gravity
• Helical phase inflation and its observational constraints
• Non-Abelian brane cosmology
• WMAP and Supergravity Inflationary Models
• New exact cosmologies on the brane
• Thermodynamics of Gravitationally Induced Particle Creation Scenario in DGP Braneworld
• Boundary Terms for Massive General Relativity
• Radiative constraints on brane quintessence
• Defining perturbations on submanifolds
• Implications of quantum gravity for dark matter in the brane-world scenario
• Oscillating cosmic evolution and constraints on big bang nucleosynthesis in the extended Starobinsky model
• Non-singular flat universes in braneworld and Loop Quantum Cosmology
• The generality of inflation in some closed FRW models with a scalar field
• Effect of the Chameleon Scalar Field on Brane Cosmological Evolution
• Cosmology on a cosmic ring
• 3D black holes on a 2-brane in 4D Minkowski space
• Randall-Sundrum brane cosmology: modification of late-time cosmic dynamics by exotic matter
• A Novel Mass Hierarchy and Discrete Excitation Spectra from Quantum-Fluctuating D-branes
• 4D spacetimes embedded in 5D light-like Kasner universes
• Brane world solutions of perfect fluid in the background of a bulk containing dust or cosmological constant
• Thermodynamic Prescription of Cosmological Constant in Randall Sundrum-II Brane
• Deflation of Vacuum Energy During Inflation Due to Bulk-Brane Interaction
• Gravitational production of KK states
• Classical and quantum quintessence cosmology
• Dissipation and nonlocality in a general expanding braneworld universe
• Energy-momentum of a Cosmological Brane Model and the Gauge Hierarchy
• Thick branes via higher order field theory models with exponential and power-law tails
• The Dynamics of Brane-World Cosmological Models
• Graviton emission from the brane in the bulk in a model with extra dimension
• QCD phase transition with a power law chameleon scalar field in the bulk
• Cosmological Kaluza-Klein branes in black brane spacetimes
• Brane-world Cosmologies with non-local bulk effects
• Five-dimensional warped product space-time with time-dependent warp factor and cosmology of the four-dimensional universe
• Bounce scenarios in the Sotiriou-Visser-Weinfurtner generalization of the projectable Horava-Lifshitz gravity
• Ad$S_5$ with two boundaries and holography of $\mathcal{N}=$4 SYM theory
• Entanglement temperature for the excitation of SYM theory in (De)confinement phase
• Bouncing cosmological solutions and their stability
• Cosmological constraints from Gauss-Bonnet braneworld with large-field potentials
• On Braneworld Inflation Models in Light of WMAP7 data
• Warm constant-roll inflation in brane-world cosmology
• Universe Acceleration in Brane World Models
• Generalized virial theorem in warped DGP brane-world
• Cosmology of a Friedmann-Lamaître-Robertson-Walker 3-brane, Late-Time Cosmic Acceleration, and the Cosmic Coincidence
• 7D Randall-Sundrum cosmology, brane-bulk energy exchange and holography
• Friedmann equations from GUP-modified equipartition law
• Five-dimensional warped product space-time with time-dependent warping and a scalar field in the bulk
• Specific dynamics for the Domain-Walls in Einstein-Maxwell-Dilaton theory
• Glueball instability and thermalization driven by dark radiation
• Radiation back reaction on moving branes
• How does Inflation Depend Upon the Nature of Fluids Filling Up the Universe in Brane World Scenario
• Dynamics of the universe as a "test 3-brane" in a 5D bulk
• Quark-Hadron Phase Transition in DGP Brane Gravity with Bulk Scalar Field
• Vacuum Decay on a Brane World
• Generalized approach for the perturbative dynamical braneworld in $D$ dimensions
• Orbifold Branes in the $M_D\times M_{d^{+}}\times M_{d^{-}}$ Compactification of type II string on $S^1/Z_2$ and their cosmological applications
• Quark-hadron phase transition in DGP including BD brane
• Connection between two forms of extra-dimensional metrics revisited
• Chiral Symmetry of SYM theory in hyperbolic space at finite temperature
• New interpretation of matter-antimatter asymmetry based on branes and possible observational consequences
• A Note on the Generalized Friedmann Equations for a Thick Brane
• Cosmological constraints on parameters of one-brane models with extra dimension
• Constraints on parameters of models with extra dimension from primordial nucleosynthesis
• Closed inflationary universe in Patch Cosmology
• RS1 Cosmology as Brane Dynamics in an AdS/Schwarzschild Bulk
• Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World
• Cosmic Acceleration Data and Bulk-Brane Energy Exchange
• Brane Bounce from logarithmic entropic corrections in the bulk
• Modern cosmologies from empty Kaluza-Klein solutions in 5D
• BPS brane cosmology in N=2 supergravity
• Self-gravitating branes again
• 5-dimensional braneworld with gravitating Nambu-Goto matching conditions
• New Classes of Cosmic Energy and Primordial Black-Hole Formation
• Energy-momentum tensor of bouncing gravitons
• Cosmological solutions and observational constraints on 5-dimensional braneworld cosmology with gravitating Nambu-Goto matching conditions
• CMB Constraint on Radion Evolution in the Brane World Scenario
• On black holes in heterotic braneworlds
• Bouncing of gravitons emitted from the brane to the bulk back to the brane
• Density perturbations in braneworld cosmology and primordial black holes
• Traversable Lorentzian wormhole on the Shtanov-Sahni braneworld with matter obeying the energy conditions
• Curvaton reheating and intermediate inflation in brane cosmology
• Stability Analysis of DGP Brane-world Model with Agegraphic Dark Energy
• From WMAP to Planck: Exact reconstruction of 4- and 5-dimensional inflationary potential from high precision CMB measurements
• Cosmology in warped massive gravity
• Scalar cosmological perturbations in the Gauss-Bonnet braneworld
• Semi-realistic Bouncing Domain Wall Cosmology
• Correspondence Between DGP Brane Cosmology and 5D Ricci-flat Cosmology
• Tachyonic Universes in Patch Cosmologies with $\Omega >1$
• How much will we learn from the CMB ?
• The Global Structure of the Colliding Bubble Braneworld Universe
• The Hierarchy Problem and $\mathcal{N}=2$ $\mathcal{D}=5$ Supergravity
• Axion braneworld cosmology
• Minkowski Brane in Asymptotic dS${}_5$ Spacetime without Fine-tuning
• Constraints on $Ad{S}_5$ Embeddings
• Nambu-Goldstone boson phenomenology in Domain-Wall Standard Model
• Holographic Cosmology and Phase Transitions of SYM theory
• A note on supergravity inflation in braneworld
• Brane inflation and the fine-tuning problem
• A Study on Ricci Dark Energy in Bulk-Brane Interaction
• Cosmology of Dilatonic Brane World
• Analytical Solution for Bosonic Fields in the FRW Multiply Warped Braneworld
• Exact solutions of embedding the four-dimensional perfect fluid in a five- or higher-dimensional Einstein spacetime and the cosmological interpretations
• An Investigation of Equivalence between the Bulk-based and the Brane-based Approaches for Anisotropic Models
• Nonlinear matter terms in general scalar-tensor braneworld cosmology
• FLRW embeddings in ${\mathbb{R}}^{n+2}$, differential geometry and conformal photon propagator
• Angular Momentum of a Brane-world Model
• Quasi-homologous spherically symmetric branes and their symmetry breaking
• Brane cosmology with variable tension
• Effect of bulk Lorentz violation on anisotropic brane cosmologies
• Tunneling in Quantum Cosmology and Holographic SYM theory
• Chaotic inflation on the Randall-Sundrum 2-brane model
• Uniform rate inflation on the brane
• Conical singularities regularized in warped six-dimensional flux compactification and their induced brane cosmology
• Non-constant ground states for symmetry-breaking fields in brane world models
• Brane induced cosmological acceleration and crossing of w_{eff}=-1
• Conservation laws for colliding branes with induced gravity
• Hierarchy problem and the cosmological constant in a five-dimensional Brans-Dicke brane world model
• Induced cosmology on a codimension-2 brane in a conical bulk
• Cosmological predictions from the Misner brane