A four-dimensional ΛCDM-type cosmological model induced from higher dimensions using a kinematical constraint

Abstract

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 λ. 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 when the external space starts with a Big Bang (t=0), they expand only 1.49 times and stay at Planck length scales even in the present age of the universe (13.7 Gyr). 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.

12 pages, 8 figures; matches the version published in General Relativity and Gravitation

References in corpus (9)

• Dynamics of dark energy
• Varying constants, Gravitation and Cosmology
• A kinematical approach to dark energy studies
• Reconstruction of the deceleration parameter and the equation of state of dark energy
• Kinematic Constraints to the Transition Redshift from SNe Ia Union Data
• Comprehensive cosmographic analysis by Markov Chain Method
• Cosmic Jerk, Snap and Beyond
• Consistency among distance measurements: transparency, BAO scale and accelerated expansion
• Detecting the cosmic acceleration with current data

Cited by in corpus (7)

• Falsifying cosmological models based on a non-linear electrodynamics
• Phase space analysis of the bouncing universe with stringy effects
• The Dynamical Evolution of 3-Space in a Higher Dimensional Steady State Universe
• $\Lambda$CDM cosmology with a quiescent anisotropy in a higher dimensional steady state universe
• Role of internal space correlations in the dynamics of a higher-dimensional Bianchi type-I universe: shear scalar and Hubble parameter perspectives
• General solution of a cosmological model induced from higher dimensions using a kinematical constraint
• Anisotropic evolution of D-dimensional FRW spacetime