A Four-Dimensional ΛCDM-Type Cosmological Model Induced from Higher Dimensions Using a Kinematical Constraint

Details A Four-Dimensional ΛCDM-Type Cosmological Model Induced from Higher Dimensions Using a Kinematical Constraint A Four-Dimensional ΛCDM-Type Cosmological Model Induced from Higher Dimensions Using a Kinematical Constraint

2012-01-22

arxiv.org/abs/1201.4545v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, 6 figures

Scientific paper

A class of cosmological solutions of higher dimensional Einstein field equations with the energy-momentum tensor of a homogeneous, isotropic fluid as the source are considered with an anisotropic metric that includes the direct sum of a 3-dimensional (physical, flat) external space metric and an n-dimensional (compact, flat) internal space metric. A simple kinematical constraint is postulated that correlates the expansion rates of the external and internal spaces in terms of a real parameter \lambda. A specific solution for which both the external and internal spaces expand at different rates is given analytically for n=3. Assuming that the internal dimensions were at Planck length scales at the beginning t=0, the external space starts with a Big Bang and the external and internal spaces both reach the same size after 10^{-176} Gyr. Then during the lifetime of the observed universe (13.7 Gyr), the external dimensions would expand 10^{59} times while the internal dimensions expand only 1.49 times. The effective four dimensional universe would exhibit a behavior consistent with our current understanding of the observed universe. It would start in a stiff fluid dominated phase and evolve through radiation dominated and pressureless matter dominated phases, eventually going into a de Sitter phase at late times.

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