A four-dimensional {\Lambda}CDM-type cosmological model induced from higher dimensions using a kinematical constraint

TL;DR

This paper presents a higher-dimensional cosmological model with a kinematical constraint linking external and internal space expansion rates, resulting in a universe consistent with observations and featuring a transition from early stiff fluid to late-time de Sitter acceleration.

Contribution

It introduces a novel higher-dimensional Einstein field solution with a simple kinematical constraint, demonstrating realistic cosmological evolution including late-time acceleration.

Findings

Internal dimensions remain at Planck scale over cosmic time.

Model reproduces standard cosmological phases: stiff fluid, radiation, matter, and de Sitter.

External universe expansion aligns with observational data.

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 {\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 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.