  We examine the time evolution of the D=d+4 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 d=1. 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.
