2009/02/11 by F. Darabi, Darabi, F.
Computer Science · Physics and Astronomy · #Black Holes and Theoretical Physics #Computational Physics and Python Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.0902.1863
20 pages, "Trends in General Relativity and Quantum Cosmology" Editor: Charles V. Benton, Nova Science Publishers, New York (2006)
arxiv created 2009/02/11 · openalex publication_date 2009/02/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a (4+D)-dimensional Kaluza-Klein cosmology with a Robertson-Walker type metric having two scale factors a and R, corresponding to D-dimensional internal space and 4-dimensional universe, respectively. By introducing an exotic matter in the form of perfect fluid with an special equation of state, as the space-time part of the higher dimensional energy-momentum tensor, a four dimensional effective decaying cosmological term appears as λ∼ R-m with 0 ≤ m≤ 2, playing the role of an evolving dark energy in the universe. By taking m=2, which has some interesting implications in reconciling observations with inflationary models and is consistent with quantum tunneling, the resulting Einstein's field equations yield the exponential solutions for the scale factors a and R. These exponential behaviors may account for the dynamical compactification of extra dimensions and the accelerating expansion of the 4-dimensional universe in terms of Hubble parameter, H. The acceleration of the universe may be explained by the negative pressure of the exotic matter. It is shown that the rate of compactification of higher dimensions as well as expansion of 4-dimensional universe depends on the dimension, D. We then obtain the corresponding Wheeler-DeWitt equation and find the general exact solutions in D-dimensions. A good correspondence between the solutions of classical Einstein's equations and the solutions of quantum Wheeler-DeWitt equation in any dimension, D, is obtained based on Hartle's point of view concerning the classical limits of quantum cosmology.