Although superstring theory promises to synthesize general relativity with the other fundamental forces of nature, it introduces a number of surprising features - such as the existence of microscopic strings, rather than particles, as the fundamental units of matter, along with the existence of several extra spatial dimensions in the universe. Could our observable universe really be built from such a bizarre collection of ingredients?

Naïvely, one might expect the extra dimensions to conflict
with the observed behavior of gravity. To be successful, string
theory, like general relativity, must reduce to Newton's law of
gravity in the appropriate limit. In Newton's formulation,
gravity can be described by force lines that always begin and end
on masses. If the force lines could spread in *n* spatial
dimensions, then at a radius *r* from the center, they would
intersect a hypersphere with surface area proportional to
*r*^{n-1}. An equal number of force lines would cross the
hypersphere at each radius, which means that the density of force
lines would be proportional to 1 / *r*^{n-1}. For *n*
= 3, this reproduces the familiar Newtonian force law,
*F* 1 /
*r*^{2},
which has been tested (along with its Einsteinian generalization)
to remarkable accuracy over a huge range of distances, from
astronomical scales down to less than a millimeter
[30,
31].

An early response to this difficulty was to assume that the extra
spatial dimensions are curled up into tiny closed circles rather
than extending to macroscopic distances. Because gravity has a
natural scale, known as the Planck length,
*l*_{P}
[ *G* /
*c*^{3}]^{1/2}
10^{-35} m [where
is Planck's
constant divided by 2],
physicists assumed that *l*_{P} sets
the scale for these extra dimensions. Just as the surface of a
soda straw would appear one-dimensional when viewed from a large
distance - even though it is really two-dimensional - our
space would appear three-dimensional if the extra dimensions were
"compactified" in this way. On scales much larger than the
radii of the extra dimensions, *r*_{c}, we would fail to notice
them: The strength of gravity would fall off in its usual 1 /
*r*^{2}
manner for distances *r* >> *r*_{c}, but would
fall off as
1 / *r*^{n-1} for scales *r* << *r*_{c}
[32]. The
question remained, however, what caused this compactification,
and why this special behavior affected only some but not all
dimensions.

Recently Arkani-Hamed, Dimopoulos, and Dvali
[33]
realized that there is no necessary relation between
*l*_{P} and
*r*_{c}, and that experiments only require
*r*_{c} 1 mm.
Shortly afterward, Randall and Sundrum
[34,
35]
discovered that the extra dimensions could even be infinite in
extent! In the Randall-Sundrum model, our observable universe
lies on a membrane, or "brane" for short, of three spatial
dimensions, embedded within some larger multidimensional space.
The key insight is that the energy carried by the brane will
sharply affect the way the gravitational field behaves. For
certain spacetime configurations, the behavior of gravity along
the brane can appear four-dimensional (three space and one time),
even in the presence of extra dimensions. Gravitational force
lines would tend to "hug" the brane, rather than spill out into
the "bulk" - the spatial volume in which our brane is
embedded. Along the brane, therefore, the dominant behavior of
the gravitational force would still be 1 / *r*^{2}.

In simple models, in which the spacetime geometry along our brane
is highly symmetric, such as the Minkowski spacetime of special
relativity, the effective gravitational field along our brane is
found to mimic the usual Einsteinian results to high accuracy
[36,
37].
At very short distances there are
calculable (and testable) deviations from standard gravity, and
there may also be deviations for very strong gravitational
fields, such as those near black holes. There are also
modifications to the cosmological predictions of gravity. In the
usual case, when Einstein's equations are applied to a homogeneous
and isotropic spacetime, one finds
*H*^{2}
- *k* /
*a*^{2},
where *k* is a constant connected to the curvature of the
universe. If instead we lived on a brane embedded within one
large extra dimension, then
*H*^{2}
+
^{2} -
*k* / *a*^{2}, where
is a constant
[38].

Under ordinary conditions,
decreases as
the universe
expands, and so the new term in the effective Einstein equations
should have minimal effects at late times in our observable
universe. But we saw above that during an inflationary epoch,
constant, and in
these early moments the departures from the ordinary Einsteinian case
can be dramatic. In particular, the
^{2}
term would allow inflation to occur
at lower energies than are usually assumed in ordinary
(nonembedded) models, with potential energy functions that are
less flat than are ordinarily needed to sustain inflation.
Moreover, the spectrum of primordial perturbations would get
driven even closer to the scale-invariant shape, with
*n*_{s} = 1.00
[39,
40].
Brane cosmology thus leads to some interesting effects during the early
universe,
making inflation even more robust than in ordinary scenarios.