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

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UNCLASSIFIED//P6R OFFIOIIIL W&li Q~•kY
Higgs, and therefore the greater the mass. The second brane is the UV or "hidden"
brane. The line element in RSl is described by the metric:
(5.4)
Y/µvis the metric tensor for the D-dimensional Minkowski spacetime, the AdS curvature
radius is given by 1/k and the interbrane separation is given by r. The 5th dimension is
compactified on the orbifold of length a, where a < qi < a. The orbifold fixed points
located at qi= 0 and 4>= a correspond to the location of the visible and the hidden
brane.
The exponential factor is referred to as the warp factor and is an appealing feature in
the RSl model, as it can both generate a TeV mass scale from the Planck scale in the
higher dimensional theory and reduce the effective gravitational strength on the visible
brane through the suppression factor e-2krl.SI while retaining a bulk width that is only a
couple of orders of magnitude above the Planck scale. In addition to the stabilization of
the interbrane separation, the quantum effects from the bulk fields (aka the Casimir
energy) can also provide a mechanism for the generation of dark energy on the visible
brane.
5.4 EXTRA DIMENSION SUMMARY
Although there is still no direct evidence of extra spatial dimensions, there is the
possibility that the experiments planned at the Large Hadron Collider could detect
particle decay signatures that would indicate the presence of higher dimensions. In fact,
all the theoretical groundwork has been performed by theorists, and as soon as the LHC
is running smoothly it could, in principle, demonstrate the existence of higher
dimensions in a relatively short period of time. Any such discovery would represent a
truly radical alteration of our understanding of nature, and many new questions will
emerge regarding the potential role extra dimensions could play in advanced
technologies (which will be discussed in more detail later in this paper).
6. Dark Energy as a Higher Dimensional Artifact
As discussed earlier, the vacuum of spacetime can be visualized as a sea of quantum
fields never fully at rest due to the Heisenberg Uncertainty Principle. The oscillations of
the vacuum radiate energy over a range of frequencies in much the same way that an
oscillating electron emits electromagnetic energy, and in this way, there exists a ground
state energy associated with space itself. The vacuum potential for a periodic scalar
field in the ADD model described above is given by (Reference 48-50):
+
T}C
00 d
4
2
n,r 2
2
V = - L
,,, fo -(
k)4 log[ k +( -
) + m ] •
(6.1)
2
2,r
R
11=
where k is the momentum modes of the quantum fields, R is the radius of the 5th
dimension, and mis the mass of the field. The prime on the summation indicates the
n = 0 term is excluded. The integral over the continuous momentum modes of the
UNCLASSIFIED//FQR OFFIOIAL ~81: 6Ht,•
12