We review the implications of modern higher-dimensional theories of gravity
for astrophysics and cosmology. In particular, we discuss the latest
developments of space-time-matter theory in connection with dark matter,
particle dynamics and the cosmological constant, as well as related aspects of
quantum theory. There are also more immediate tests of extra dimensions,
notably involving perturbations of the cosmic 3K microwave background and the
precession of a supercooled gyroscope in Earth orbit. We also outline some
general features of embeddings, and include pictures of the big bang as viewed
from a higher dimension.Comment: 23 pages, 2 figures; to appear in Space Science Reviews; v3: typos
corrected and minor changes to text, expanded derivation of fundamental mode
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