AAWSAP DIRD, Warp Drive, Dark Energy, and the Manipulation of Extra Dimensions, April 2010

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(5 .3)
MP, is the Planck mass12 (in our usual 4-dimensional spacetime) and r is the size of the
extra space dimensions. This remarkable result indicates that the Planck scale is, in
fact, a quantity that is derived from a more fundamental quantum gravity scale and
also the volume of the extra dimensions. Physically, this implies that the graviton is
diluted across the bulk with a diminished intersection with the familiar 3+1 dimensional
brane.
In this type of model the size of the internal space is of order 1/M and the effective
10:
2
cosmological constant is on the order A,11 ~ 8nM;; x
(Reference 36, 37). Setting
a
the value of the corresponding energy density equal to the known density of dark
energy, one finds that the extra-dimensional radius is r ~10-3cm. Similar results are
found in models with more complicated internal spaces. This is an important result in
the context of dimensional manipulation.
Note that extra dimensions that are accessible to all the Standard Model fields can also
be realized. These models are known as Universal Extra Dimensions (UED). In the case
of recent experimental constraints, a compactification scale as low as 1 TeV is allowed.
5.3 RANDALL SUNDRUM BRANE MODELS
The idea that the universe can be modeled as a (mem)brane existing in a higher
dimensional bulk spacetime has received a huge amount of attention in recent years
(Reference 38-46). It is possible that the brane energy density affects the spacetime
curvature, and an approximation can be achieved by first considering a model where
branes are located at the two ends of a periodic 5th dimension. To ensure stability of the
model two branes are required to balance the bulk energy. To get a stable metric, the
effects of the brane on the spacetime must be compensated by a negative cosmological
constant in the bulk. Thus, the 5th dimension can be considered a slice of Anti-deSitter
(AdS) 13 space bounded by flat branes, and the price of keeping the branes flat is to
introduce curvature into the 5th dimension. Such models are termed warped extra
dimensions.
The Randall-Sundrum (RSl) model (Reference 47, 48) proposes a novel geometrical
solution to the hierarchy problem. The hierarchy problem questions why gravity is so
much weaker than the weak force (which is 1032 times stronger), and why the Higgs
boson is so much lighter than the Planck mass. In the RSl setup, the Standard Model
fields are now confined to one of two 3-branes which lie at the endpoints (i.e., fixed
points) of an S1 /Z2 orbifold, 14 except for the Higgs field. One of the branes physically
corresponds to "our" universe and is sometimes referred to as the IR or "visible" brane.
The closer a Standard Model field is to the visible brane, the greater its coupling to the
12 2.18 x 10-s kg.
13 Anti-deSitter space is a Lorentzian manifold with a constant negative scalar curvature. In terms of General
Relativity, this is a solution to Einstein's field equation with an attractive cosmological constant.
14 An 5 1/22 corresponds to a circular extra dimension with an additional symmetry. This type of projection is
popular in a number of higher dimensional models due to its ability to mathematically "project" out certain
phenomenologically undesirable fields.
11
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