AdS and stabilized extra dimensions in multidimensional gravitational models with nonlinear scalar curvature terms 1/R and R^4

Abstract

We study multidimensional gravitational models with scalar curvature nonlinearities of the type 1/R and R^4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with warped product structure. Special attention is paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the 1/R model that configurations with stabilized extra dimensions do not provide a late-time acceleration (they are AdS), whereas the solution branch which allows for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R^4 model, we obtain that the stability region in parameter space depends on the total dimension D=dim(M) of the higher dimensional spacetime M. For D>8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singularity (and an antigravity sector beyond it) by a potential barrier of infinite height and width. This sector is smoothly connected with the stability region of a curvature-linear model. For D<8 an additional (metastable) sector exists which is separated from the conformal singularity by a potential barrier of finite height and width so that systems in this sector are prone to collapse into the conformal singularity. This second sector is not smoothly connected with the first (absolutely stable) one. Several limiting cases and the possibility for inflation are discussed for the R^4 model.

28 pages, minor cosmetic improvements, Refs. added; to appear in Class. Quantum Grav

References in corpus (107)

• The Hierarchy Problem and New Dimensions at a Millimeter
• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• de Sitter Vacua in String Theory
• Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Hierarchies from Fluxes in String Compactifications
• The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang
• Towards Inflation in String Theory
• Pre-Big-Bang in String Cosmology
• Brane Inflation
• The Pre-Big Bang Scenario in String Cosmology
• Further Evidence for Cosmological Evolution of the Fine Structure Constant
• Cosmic Evolution in a Cyclic Universe
• Can modified gravity explain accelerated cosmic expansion?
• Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
• 1/R gravity and Scalar-Tensor Gravity
• Constraining dark energy with SNe Ia and large-scale structure
• The Inflationary Brane-Antibrane Universe
• Cosmology from Maxima-1, Boomerang and COBE/DMR CMB Observations
• Modified gravity with $\ln R$ terms and cosmic acceleration
• On Physical Equivalence between Nonlinear Gravity Theories
• Moduli Stabilization from Fluxes in a Simple IIB Orientifold
• Where new gravitational physics comes from: M-theory?
• Extended Gravity Theories and the Einstein-Hilbert Action
• Quintessence without scalar fields
• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• Limits on the time variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars
• Gauge Theory and the Excision of Repulson Singularities
• Topological Inflation
• Racetrack Inflation
• Beauty is Attractive: Moduli Trapping at Enhanced Symmetry Points
• Accelerating Cosmologies from Compactification
• Inflation from D-\bar{D} brane annihilation
• Designing Cyclic Universe Models
• Monopoles as Big as a Universe
• Accelerating Cosmologies from S-Branes
• Inflation from Quantum Geometry
• Scales of Gravity
• Stabilization of Sub-Millimeter Dimensions: The New Guise of the Hierarchy Problem
• Rapid Asymmetric Inflation and Early Cosmology in Theories with Sub-Millimeter Dimensions
• R^4 terms in 11 dimensions and conformal anomaly of (2,0) theory
• Supersymmetry Breaking, M-Theory and Fluxes
• A Study of Accelerating Cosmologies from Superstring/M theories
• Hyperbolic Space Cosmologies
• Accelerating cosmologies from M/String theory compactifications
• Loop quantum gravity effects on inflation and the CMB
• On Brane Inflation With Volume Stabilization
• Modified Friedmann Equations in R${}^{-1}$-Modified Gravity
• Constraining Variations in the Fine-Structure Constant with the Cosmic Microwave Background
• The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models
• MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos
• Inflation in Realistic D-Brane Models
• Singular BPS Saturated States and Enhanced Symmetries of Four-Dimensional N=4 Supersymmetric String Vacua
• Branes and the Gauge Hierarchy
• On the Newtonian Limit in Gravity Models with Inverse Powers of R
• Exact Supersymmetric Massive and Massless White Holes
• Supergravity, Dark Energy and the Fate of the Universe
• Possible Constraints on the Time Variation of the Fine Structure Constant from Cosmic Microwave Background Data
• Loop Quantum Cosmology, Boundary Proposals, and Inflation
• Inflation from M-Theory with Fourth-order Corrections and Large Extra Dimensions
• Classical Stabilization of Homogeneous Extra Dimensions
• The spectrum of cosmological perturbations produced by a multi-component inflaton to second order in the slow-roll approximation
• Recombination of Intersecting D-Branes and Cosmological Inflation
• Loop Quantum Gravity and the Cyclic Universe
• Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity
• The Enhancon and the Consistency of Excision
• Volume Stabilization and the Origin of the Inflaton Shift Symmetry in String Theory
• The Power Spectrum for a Multi-Component Inflaton to Second-Order Corrections in the Slow-Roll Expansion
• M/String Theory, S-branes and Accelerating Universe
• Gravitational excitons from extra dimensions
• Constraints on Theories With Large Extra Dimensions
• Equation of State of Oscillating Brans-Dicke Scalar and Extra Dimensions
• Tensor-multi-scalar theories from multidimensional cosmology
• Problems with Time-Varying Extra Dimensions or "Cardassian Expansion" as Alternatives to Dark Energy
• Density perturbations arising from multiple field slow-roll inflation
• Gravity and antigravity in a brane world with metastable gravitons : Comment on hep-th/0002190 and hep-th/0003020
• Radion Stabilization in Compact Hyperbolic Extra Dimensions
• Topological $R^4$ Inflation
• Nonlinear multidimensional cosmological models with form fields: stabilization of extra dimensions and the cosmological constant problem
• Spontaneous decompactification
• Brane to bulk supersymmetry breaking and radion force at micron distances
• Holographic RG and Cosmology in Theories with Quasi-Localized Gravity
• Cosmological Effects of Radion Oscillations
• Stabilization of internal spaces in multidimensional cosmology
• Multidimensional cosmological models: cosmological and astrophysical implications and constraints
• Volume Stabilization and Acceleration in Brane Gas Cosmology
• Cosmological solutions in multidimensional model with multiple exponential potential
• Orientifolds, M-Theory, and the ABCD's of the Enhancon
• Born-Again Braneworld
• Tadpoles and Closed String Backgrounds in Open String Field Theory
• Asymptotical AdS from non-linear gravitational models with stabilized extra dimensions
• Multidimensional perfect fluid cosmology with stable compactified internal dimensions
• A note on dynamical stabilization of internal spaces in multidimensional cosmology
• R^4 corrections to conifolds and G_2 holonomy metrics
• Cosmology from Moduli Dynamics
• Flavordynamics with Conformal Matter and Gauge Theories on Compact Hyperbolic Manifolds in Extra Dimensions
• $R^4$ terms in supergravity and M-theory
• The Collapse of Large Extra Dimensions
• The Effective Potential of the N=0* Yang-Mills Theory
• Flux Compactifications: Stability and Implications for Cosmology
• A new wrinkle on the enhancon
• Oblate, Toroidal, and Other Shapes for the Enhancon
• Classical and Quantum Analysis of Repulsive Singularities in Four Dimensional Extended Supergravity
• Singular instantons in higher derivative theories
• Remarks on dimensional reduction of multidimensional cosmological models
• Quantum Probes of Repulsive Singularities in N = 2 Supergravity

Cited by in corpus (26)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Bouncing Universes in String-inspired Gravity
• On Wormhole Throats in $f(R)$ Gravity Theory
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Conserved Quantities in $f(R)$ Gravity via Noether Symmetry
• Bouncing inflation in nonlinear $R^2+R^4$ gravitational model
• Conditions and instability in $f(R)$ gravity with non-minimal coupling between matter and geometry
• Acceleration of the Universe via f(R) Gravities and The Stability of Extra Dimensions
• f(R) Gravities à la Brans-Dicke
• Gauge Formulation for Higher Order Gravity
• Scalar-multi-tensorial equivalence for higher order $f\left(R,{\nabla }_{\mu }R,{\nabla }_{{\mu }_1}{\nabla }_{{\mu }_2}R,...,{\nabla }_{{\mu }_1}...{\nabla }_{{\mu }_n}R\right)$ theories of gravity
• Gravitational Dust Collapse in $f(R)$ Gravity
• Emergence of symmetries
• Inflation from $(R+\gamma R^n-2\Lambda )$ Gravity in Higher Dimensions
• Cloud of strings in f(R) gravity
• Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity
• Inflation from higher dimensions
• Dark Energy and Cosmic Speed-Up from Consistent Modified Gravity
• On the problem of inflation in nonlinear multidimensional cosmological models
• 1/R multidimensional gravity with form-fields: stabilization of extra dimensions, cosmic acceleration and domain walls
• Probability for Primordial Black Holes in Multidimensional Universe with Nonlinear Scalar Curvature Terms
• Relaxation of hierarchy in higher-dimensional Starobinsky model
• The Compactification Problems of Additional Dimensions in Multidimensional Cosmological Theories