https://doi.org/10.1140/epjc/s10052-019-7492-y
Regular Article - Theoretical Physics
Anisotropic evolution of D-dimensional FRW spacetime
Department of Physical and Environmental Sciences, Colorado Mesa University, Grand Junction, Colorado, 81501, USA
* e-mail: chmiddle@coloradomesa.edu
Received:
13
June
2019
Accepted:
17
November
2019
Published online:
29
November
2019
We examine the time evolution of the 
dimensional Einstein field equations subjected to a flat Robertson-Walker metric where the 3D and higher-dimensional scale factors are allowed to evolve at different rates. We find the exact solution to these equations for a single fluid component, which yields two limiting regimes offering the 3D scale factor as a function of the time. The fluid regime solution closely mimics that described by 4D FRW cosmology, offering a late-time behavior for the 3D scale factor after becoming valid in the early universe, and can give rise to a late-time accelerated expansion driven by vacuum energy. This is shown to be preceded by an earlier volume regime solution, which offers a very early-time epoch of accelerated expansion for a radiation-dominated universe for 
. The time scales describing these phenomena, including the transition from volume to fluid regime, are shown to fall within a small fraction of the first second when the fundamental constants of the theory are aligned with the Planck time. This model potentially offers a higher-dimensional alternative to scalar-field inflationary theory and a consistent cosmological theory, yielding a unified description of early- and late-time accelerated expansions via a 5D spacetime scenario.
© The Author(s), 2019
