Inhomogeneous compact extra dimensions and de Sitter cosmology

Abstract

In the framework of multidimensional $f(R)$ gravity, we study the metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even higher energy scales. It is shown that in the presence of a scalar field, varying in the extra factor space ${\mathbb{M}}_2$, it is possible to obtain a variety of inhomogeneous metrics in ${\mathbb{M}}_2$. Each of these metrics leads to a certain value of the 4D cosmological constant ${\Lambda }_4$, and in particular, it is possible to obtain ${\Lambda }_4=0$, as is confirmed by numerically obtained solutions. A nontrivial scalar field distribution in the extra dimensions is an important feature of this family of models.

arXiv comment15 pages, 9 figures

References in corpus (28)

• An Alternative to Compactification
• The Hierarchy Problem and New Dimensions at a Millimeter
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Dimensionless constants, cosmology and other dark matters
• Bounce cosmology from $F(R)$ gravity and $F(R)$ bigravity
• Dark energy from modified F(R)-scalar-Gauss-Bonnet gravity
• String Gas Cosmology and Structure Formation
• Fermion Generations from "Apple-Shaped" Extra Dimensions
• On cosmological-type solutions in multi-dimensional model with Gauss-Bonnet term
• Self-stabilization of extra dimensions
• Pure geometric thick $f(R)$-branes: stability and localization of gravity
• Brane world corrections to Newton's law
• Mass hierarchy and localization of gravity in extra time
• Quantum Creation of a Universe with $\Omega \ne 1$: Singular and Non-Singular Instantons
• Quantum Cosmology and Higher-Order Lagrangian Theories
• Multidimensional world, inflation and modern acceleration
• On the validity of constraints on light elementary particles and extra-dimensional physics from the Casimir effect
• Effects of spatial curvature and anisotropy on the asymptotic regimes in Einstein-Gauss-Bonnet gravity
• Multidimensional cosmology and asymptotical AdS
• Scalar field localization on deformed extra space
• Compactifying de Sitter Naturally Selects a Small Cosmological Constant
• Deformed compact extra space as dark matter candidate
• Classical evolution of subspaces
• On cosmology in nonlinear multidimensional gravity with multiple factor spaces
• Cosmologies from nonlinear multidimensional gravity with acceleration and slowly varying G
• Inflationary limits on the size of compact extra space
• Global strings in extra dimensions: a full map of solutions, matter trapping and the hierarchy problem

Cited by in corpus (6)

• Tensor Perturbations and Thick Branes in Higher-dimensional $f(R)$ Gravity
• Self-tuning inflation
• Dirac type relativistic quantum mechanics for massive photons
• Cosmological baryon/lepton asymmetry in terms of Kaluza-Klein extra dimensions
• Flexible extra dimensions
• Studies of the Inhomogeneous Cosmology in Higher Dimensional space-time with a Cosmological Constant