**5.2 WIMPZILLAS - Size Does Matter**

The simple assumption that the dark matter (DM) is a thermal relic is
surprisingly
restrictive. The limit _{X} 1 implies that the mass of a
DM relic must be less than about 500 TeV
[6]. The standard
lore is that the hunt for DM should concentrate on particles with mass
of the order of the weak scale and with interactions with ordinary
matter on the scale of the weak force. This has been the driving force
behind the vast effort in DM detectors.

But recent developments in understanding how
matter is created in the early universe suggests the possibility
that DM might be naturally composed of *nonthermal* supermassive
states. The supermassive dark matter (WIMPZILLA)
*X* may have a mass many orders of magnitude larger than the
weak scale, possibly as large as the Grand Unified Theory (GUT)
scale. It is very intriguing that these
considerations resurrect the possibility that the dark matter might be
charged or even strongly interacting!

The second condition for WIMPZILLAS is that the particle must not have been
in equilibrium when it froze out (i.e., it is not a thermal
relic), otherwise _{X} would be larger than one.
A sufficient condition for nonequilibrium is that the
annihilation rate (per particle) must be smaller than the expansion
rate: *n* |*v*| <
*H*, where *n* is the number density, |*v*| is
the annihilation rate times the Møller flux factor, and *H* is the
expansion rate. Conversely, if the WIMPZILLA was created at some
temperature *T*_{*} *and* _{X} < 1, then it is easy to show that
it could not have attained equilibrium. To see this, assume *X*s
were created in a radiation-dominated universe at temperature
*T*_{*}.
Then _{X} is
given by _{X} =
_{}
(*T*_{*}/*T*_{0}) *M _{X} n_{X}*(

This implies that if a nonrelativistic particle with
*M _{X}* 200
TeV was created at

An attractive origin for WIMPZILLAS is during the defrosting phase after
inflation. It is important to realize that it is not necessary to
convert a significant fraction of the available energy into massive
particles; in fact, it must be an infinitesimal amount. If a fraction
of the available energy
density is in the form of a
massive, stable *X* particle, then _{X} = _{}
(*T _{RH} / T*

In one extreme we might assume that the vacuum energy of inflation is
immediately converted to radiation, resulting in a reheat temperature
*T _{RH}*. In this case

A second (and more plausible) scenario is that reheating is not
instantaneous, but is the result of the decay of the inflaton
field. In this approach the radiation is produced as the inflaton
decays. The WIMPZILLA density is
found by solving the coupled system of equations for the inflaton
field energy, the radiation density, and the WIMPZILLA mass density. The
calculation has been recently reported in Ref.
[8], with
result _{X} ~
*M _{X}*

The large difference in WIMPZILLA masses in the two reheating scenarios
arises because the peak temperature is much larger in the second
scenario, even with identical *T _{RH}*. Because the temperature
decreases as

Figure 9. The evolution of energy densities and
T/M as a function
of the scale factor. Also shown is _{X}X/X.
_{EQ} |

Another way to produce WIMPZILLAS after inflation is in a preliminary stage
of reheating called ``preheating''
[9], where nonlinear
quantum effects may lead to an extremely effective dissipational
dynamics and explosive particle production. Particles can be created
in a broad parametric resonance with a fraction of the energy stored
in the form of coherent inflaton oscillations at the end of inflation
released after only a dozen oscillation periods. A crucial
observation for our discussion is that particles with mass up to
10^{15} GeV may be created during preheating
[10,
11,
12],
and that their distribution is nonthermal. If these particles are stable,
they may be good candidates for WIMPZILLAS.

To study how the creation of WIMPZILLAS takes place in preheating, let us
take the simplest chaotic inflation potential:
*V* () =
*M*_{}^{2} ^{2} / 2 with
*M*_{} ~
10^{13} GeV. We assume
that the interaction term between the WIMPZILLA and the inflaton field is of
the type *g*^{2}^{2}
|*X*|^{2}. Quantum fluctuations of the *X* field with
momentum during
preheating *approximately* obey the
Mathieu equation, *X'' _{k}* + [

For a reheating temperature of the order of 100 GeV, the present
abundance of WIMPZILLAS with mass *M _{X}* ~
10

Another possibility which has been recently investigated is the production of very massive particles by gravitational mechanisms [15, 16]. In particular, the desired abundance of WIMPZILLAS may be generated during the transition from the inflationary phase to a matter/radiation dominated phase as the result of the expansion of the background spacetime acting on vacuum quantum fluctuations of the dark matter field [15]. A crucial side-effect of the inflationary scenarios is the generation of density perturbations. A related effect, which does not seem to have attracted much attention, is the possibility of producing matter fields due to the rapid change in the evolution of the scale factor around the end of inflation. Contrary to the first effect, the second one contributes to the homogeneous background energy density that drives the cosmic expansion, and is essentially the familiar ``particle production'' effect of relativistic field theory in external fields.

Very massive particles may be created in a nonthermal state with sufficient abundance to achieve critical density today by the classical gravitational effect on the vacuum state at the end of inflation. Mechanically, the particle creation scenario is similar to the inflationary generation of gravitational perturbations that seed the formation of large-scale structures. However, the quantum generation of energy density fluctuations from inflation is associated with the inflaton field, which dominated the mass density of the universe, and not a generic sub-dominant scalar field.

If 0.04
*M _{X}* /

The observation of anisotropy in the cosmic background radiation
does not fix *H _{e}* uniquely, but using

The distinguishing feature of this mechanism [15] is the capability of generating particles with mass of the order of the inflaton mass even when the WIMPZILLA interacts only extremely weakly (or not at all!) with other particles, including the inflaton. This feature makes the gravitational production mechanism quite model independent and, therefore, more appealing to us than the one occurring at preheating.

WIMPZILLAS can also be produced in theories where inflation is completed by a first-order phase transition [17]. In these scenarios, the universe decays from its false vacuum state by bubble nucleation [18]. When bubbles form, the energy of the false vacuum is entirely transformed into potential energy in the bubble walls, but as the bubbles expand, more and more of their energy becomes kinetic and the walls become highly relativistic. Eventually the bubble walls collide.

During collisions, the walls oscillate through each other
[19]
and the kinetic energy is dispersed into low-energy scalar waves
[19,
20].
If these soft scalar quanta carry quantum numbers
associated with some spontaneously broken symmetry, they may even lead
to the phenomenon of nonthermal symmetry restoration
[21]. We
are, however, more interested in the fate of the potential energy of
the walls, *M _{P}* = 4

Suppose now that the WIMPZILLA is some fermionic degree of freedom *X* and
that it couples to the inflaton field by the Yukawa coupling *g*
bar*X* *X*. One
can treat (the
bubbles or walls) as a
classical, external field and the WIMPZILLA as a quantum field in the
presence of this source. This amounts to ignoring the backreaction of
particle production on the evolution of the walls, but this is
certainly a good approximation in our case. The number of WIMPZILLA
particles created in the collisions from the wall's potential energy
is *N _{X}* ~

In conclusion, a large fraction of the DM in the universe may be made of WIMPZILLAS of mass greatly exceed the electroweak scale - perhaps as large as the GUT scale. This is made possible by the fact that the WIMPZILLAS were created in a nonthermal state and never reached chemical equilibrium with the primordial plasma.

ACKNOWLEDGEMENTS

This work was supported in part by the Department of Energy, as well as NASA under grant number NAG5-7092. The hospitality of Tom Ferbel and the inquisitiveness of the students were greatly appreciated.