Although the neutralino and SUSY are well-motivated, other particle
candidates for dark matter also exist. The axion is a particle proposed
in 1977 by Roberto Peccei and Helen Quinn to solve the so-called
"strong-CP problem."
[37]
In a
nutshell, the strong force Lagrangian contains a term that can give an
arbitrarily large electric dipole moment to the neutron; since no
electric dipole moment for the neutron has ever been observed, Peccei
and Quinn postulated that a new symmetry prevents the appearance of such
a term (much like a gauge symmetry keeps the photon massless). They
further theorized that this symmetry is slightly broken which leads to a
new, very light scalar particle, the axion. Although this particle is
extremely light (theories place its mass in the *µ*eV range),
it can exist in sufficient numbers to act as cold dark matter. Since
axions should couple to photons, axions can be searched for with
precisely tuned radio frequency (RF) cavities; inside the magnetic field
of an RF cavity the axion can be converted into a photon which shows up
as excess power in the cavity. And in a unique blend of particle and
astro-physics, limits on axions have been placed through observations of
red giant stars; axions, if they existed, would offer another cooling
mechanism which can be constrained by studying how quickly red giant
stars cool.
[38]
Although the axion has never been observed directly, several experiments
such as ADMX and CARRACK are continuing the search and setting new
limits on axion parameters.
[39,
40]

If axions exist and SUSY is also correct, then the axino (the
supersymmetric partner of the axion) is by a wide margin the LSP;
neutralinos would decay into axinos through
*a* +
.
[41]
However, axinos would also act as a significant source of hot dark
matter and thus could not compose the bulk of the dark matter.

One final exotic particle candidate for dark matter comes from theories
of extra spatial dimensions. The idea that our universe could have extra
spatial dimensions began in the 1920s with Theodor Kaluza and Oscar
Klein; by writing down Eisntein's general theory of relativity in five
dimensions, they were able to recover four dimensional gravity as well
as Maxwell's equations for a vector field (and an extra scalar particle
that they didn't know what to do with).
[42,
43]
Klein explained the non-observation
of this extra fifth dimension by compactifying it on a circle with an
extremely small radius (something like 10^{-35} cm so that it is
completely non-observable). Kaluza-Klein theories (as they came to be
known) were an initial quest for a grand unified theory; however, the
emergence of the weak and strong nuclear forces as fundamental forces of
nature relegated this type of approach to unification to the drawing
board. However, in the late 1990s two new scenarios with extra
dimensions appeared. Arkani-Hamed, Dvali, and Dimpoulos tried to solve
the hierarchy problem by assuming the existence of large extra
dimensions (initially on the scale of mm or smaller); they made the bold
assertion that the electroweak scale is the only fundamental scale in
nature and that the Planck scale appears so small due to the presence of
these extra dimensions.
[44]
Lisa Randall and Raman Sundum, on the other hand, proposed infinitely large
extra dimensions that were unobservable at low energies; gravity, they
explained, was weak precisely because it was the only force that could
"leak-out" into this extra dimension.
[45]

What do extra dimensions have to do with candidates for dark matter? In
theories in which extra dimensions are compactified, particles which can
propagate in these extra dimensions have their momenta quantized as
*p*^{2} ~ 1 / *R*^{2}, where *p* is the
particle's momentum and *R* is the size of the extra
dimension. Therefore, for each particle free to move in these extra
dimensions, a set of fourier modes, called Kaluza-Klein states, appears:

(6) |

where *R* is the size of the compactified extra dimension,
*m*_{0} is the regular standard model mass of the particle,
and *n* is the mode number. Each standard model particle is then
associated with an infinite tower of excited Kaluza-Klein states. If
translational invariance along the fifth dimension is postulated, then a
new discrete symmetry called Kaluza-Klein parity exists and the Lightest
Kaluza-Klein particle (LKP) can actually be stable and act as dark
matter. In most models the LKP is the first excitation of the photon; in
the Universal Extra Dimensions (UED) model, if the LKP has mass between
500 and 1200 GeV, then the LKP particle can exist in sufficient numbers
to act as the dark matter.
[46]
Additional motivations for extra dimensional theories of dark matter
include proton stability and the cancellation of gauge anomalies from
three generations of fermions.
[47]

Many other theories have been proposed to account for the universe's dark matter, most of which are not as promising as those already discussed. These include Q-balls, mirror particles, WIMPzillas, and branons among many others. [48, 49, 50] However, the neutralino remains the most studied and most theoretically motivated dark matter candidate. In the next section we will discuss how particles like the neutralino (the SUSY LSP) can be produced in the early universe and how to determine if they exist today in sufficient density to act as the dark matter.