Exact solutions of embedding the 4D Universe in a 5D Einstein manifold

Abstract

One of the simplest way to extend 4D cosmological models is to add another spatial dimension to make them 5D. In particular, it has been shown that the simplest of such 5D models, i.e., one in which the right hand side of the Einstein equation is empty, induces a 4D nonempty Universe. Accordingly, the origin of matter in the 4D real Universe might be mathematically attributed to the existence of one (fictitious) extra spatial dimension. Here we consider the case of an empty 5D Universe possessing a cosmological constant $\Lambda$ and obtain exact solutions for both positive and negative values of $\Lambda$. It is seen that such a model can naturally reduce to a power law $\Lambda$CDM model for the real Universe. Further, it can be seen that, the arbitrary constants and functions appearing in this model are endowed with definite physical meanings.

3 pages, no figure. v3: title changed and typos corrected; v4: accepted by IJMPD

References in corpus (30)

• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• The Cosmological Constant and Dark Energy
• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• 4D Gravity on a Brane in 5D Minkowski Space
• Cosmological Constant - the Weight of the Vacuum
• Heterotic and Type I String Dynamics from Eleven Dimensions
• Eleven-Dimensional Supergravity on a Manifold with Boundary
• Differentiating between Modified Gravity and Dark Energy
• Cosmological model with viscosity media (dark fluid) described by an effective equation of state
• Cosmological Evolution in 1/R-Gravity Theory
• Modified Friedmann Equations in R${}^{-1}$-Modified Gravity
• Application of the Campbell-Magaard theorem to higher-dimensional physics
• Palatini Formulation of Modified Gravity with $\ln R$ Terms
• Equivalence Between Space-Time-Matter and Brane-World Theories
• Modified equation of state, scalar field, and bulk viscosity in Friedmann universe
• Universe Models with a Variable Cosmological "Constant" and a "Big Bounce"
• $R^2$ corrections to the cosmological dynamics of inflation in the Palatini formulation
• Palatini formulation of the $R^{-1}$modified gravity with an additionally squared scalar curvature term
• The Cosmological Constant and Quintessence from a Correlation Function Comoving Fine Feature in the 2dF Quasar Redshift Survey
• Universe Evolution in a 5D Ricci-flat Cosmology
• Reconstruction of $5D$ Cosmological Models From Equation of State of Dark Energy
• Three Components Evolution in a Simple Big Bounce Cosmological Model
• Hamiltonian formalism in Friedmann cosmology and its quantization
• The Big Bang as a Phase Transition
• Using (4+1) split and energy conditions to study the induced matter in 5D Ricc-flat cosmology
• Reconstruction of Five-dimensional Bounce cosmological Models From Deceleration Factor
• Correspondence Between $5D$ Ricci-Flat Cosmological Models and Quintessence Dark Energy Models

Cited by in corpus (1)

• Exact solutions of embedding the four-dimensional perfect fluid in a five- or higher-dimensional Einstein spacetime and the cosmological interpretations