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In the recently developed theory by Steven Weinberg and Abdus
Salam, that unifies the electromagnetic and weak forces, the
vacuum is not empty. This peculiar situation comes about because
of the existence of a new type of field, called the Higgs
field. The Higgs field has an important physical consequence
since its interaction with the W, W and Z particles (the carriers
of the weak force) causes them to gain mass at energies below
100 billion electron volts (100 Gev). Above this energy they
are quite massless just like the photon and it is this characteristic
that makes the weak and electromagnetic forces so similar
at high energy.
On a somewhat more abstract level, consider Figures 1 and
2 representing the average energy of the vacuum state. If
the universe were based on the vacuum state in Figure 1, it
is predicted that the symmetry between the electromagnetic
and weak interactions would be quite obvious. The particles
mediating the forces would all be massless and behave in the
same way. The corresponding forces would be indistinguishable.
This would be the situation if the universe had an average
temperature of 1 trillion degrees so that the existing particles
collided at energies of 100 Gev. In Figure 2, representing
the vacuum state energy for collision energies below 100 Gev,
the vacuum state now contains the Higgs field and the symmetry
between the forces is suddenly lost or 'broken'. Although
at low energy the way in which the forces behave is asymmetric,
the fundamental laws governing the electromagnetic and weak
interactions remain inherently symmetric. This is a very remarkable
and profound prediction since it implies that certain symmetries
in Nature can be hidden from us but are there nonetheless.
During the last
10 years physicists have developed even more powerful theories
that attempt to unify not only the electromagnetic and weak
forces but the strong nuclear force as well. These are called
the Grand Unification Theories (GUTs) and the simplist one
known was developed by Howard Georgi, Helen Quinn,and Steven
Weinberg and is called SU(5), (pronounced 'ess you five').
This theory predicts that the nuclear and 'electroweak' forces
will eventually have the same strength but only when particles
collide at energies above 1 thousand trillion GeV corresponding
to the unimaginable temperature of 10 thousand trillion trillion
degrees! SU(5) requires exactly 24 particles to mediate forces
of which the 8 massless gluons of the nuclear force, the 3
massless intermediate vector bosons of the weak force and
the single massless photon of the electromagnetic force are
12. The remaining 12 represent a totally new class of particles
called Leptoquark bosons that have the remarkable property
that they can transform quarks into electrons. SU(5) therefore
predicts the existence of a 'hyperweak' interaction; a new
fifth force in the universe! Currently, this force is 10 thousand
trillion trillion times weaker than the weak force but is
nevertheless 100 million times stronger than gravity. What
would this new force do? Since protons are constructed from
3 quarks and since quarks can now decay into electrons, through
the Hyperweak interaction, SU(5) predicts that protons are
no longer the stable particles we have always imagined them
to be. Crude calculations suggest that they may have half-lives
between 10(29) to 10(33) years. An immediate consequence of
this is that even if the universe were destined to expand
for all eternity, after 'only' 10(32) years or so, all of
the matter present would catastrophically decay into electrons,
neutrinos and photons. The Era of Matter, with its living
organisms, stars and galaxies, would be swept away forever,
having represented but a fleeting episode in the history of
the universe. In addition to proton decay, SU(5) predicts
that at the energy characteristic of the GUT transition, we
will see the affects of a new family of particles called supermassive
Higgs bosons whose masses are expected to be approximately
1 thousand trillion GeV! These particles interact with the
12 Leptoquarks and make them massive just as the Higgs bosons
at 100 GeV made the W, W and Z particles heavy. Armed with
this knowledge, let's explore some of the remarkable cosmological
consequences of these exciting theories.
The
GUT Era
To see how these
theories relate to the history of the universe, imagine if
you can a time when the average temperature of the universe
was not the frigid 3 K that it is today but an incredable
10 thousand trillion trillion degrees (10(15) GeV). The 'Standard
Model' of the Big Bang, tells us this happened about 10(-37)
seconds after Creation. The protons and neutrons that we are
familiar with today hadn't yet formed since their constituent
quarks interacted much too weakly to permit them to bind together
into 'packages' like neutrons and protons. The remaining constituents
of matter, electrons, muons and tau leptons, were also massless
and traveled about at essentially light-speed; They were literally
a new form of radiation, much like light is today! The 12
supermassive Leptoquarks as well as the supermassivs Higgs
bosons existed side-by-side with their anti-particles. Every
particle-anti particle pair that was annihilated was balanced
by the resurrection of a new pair somewhere else in the universe.
During this period, the particles that mediated the strong,
weak and electromagnetic forces were completely massless so
that these forces were no longer distinguishable. An inhabitant
of that age would not have had to theorize about the existence
of a symmetry between the strong, weak and electromagnetic
interactions, this symmetry would have been directly observable
and furthermore, fewer types of particles would exist for
the inhabitants to keep track of. The universe would actually
have beed much simpler then!
As the universe
continued to expand, the temperature continued to plummet.
It has been suggested by Demetres Nanopoulis and Steven Weinberg
in 1979 that one of the supermassive Higgs particles may have
decayed in such a way that slightly more matter was produced
than anti-matter. The remaining evenly matched pairs of particles
and anti-particles then annihilated to produce the radiation
that we now see as the 'cosmic fireball'.
Exactly what
happened to the universe as it underwent the transitions at
10(15) and 100 GeV when the forces of Nature suddenly became
distinguishable is still under investigation, but certain
tantalizing descriptions have recently been offered by various
groups of theoriticians working on this problem. According
to studies by Alan Guth, Steven Weinberg and Frank Wilczyk
between 1979 and 1981, when the GUT transition occured, it
occured in a way not unlike the formation of vapor bubbles
in a pot of boiling water. In this analogy, the interior of
the bubbles represent the vacuum state in the new phase, where
the forces are distinguishable, embedded in the old symmetric
phase where the nuclear, weak and electromagnetic forces are
indistinguishable. Inside these bubbles, the vacuum energy
is of the type illustrated by Figure 2 while outside it is
represented by Figure 1. Since we are living within the new
phase with its four distinguishable forces, this has been
called the 'true' vacuum state. In the false vacuum state,
the forces remain indistinguishable which is certainly not
the situation that we find ourselves in today!
Cosmic
Inflation
An exciting
prediction of Guth's model is that the universe may have gone
through at least one period in its history when the expansion
was far more rapid than predicted by the 'standard' Big Bang
model. The reason for this is that the vacuum itself also
contributes to the energy content of the universe just as
matter and radiation do however, the contribution is in the
opposite sense. Although gravity is an attractive force, the
vacuum of space produces a force that is repulsive. As Figures
1 and 2 show, the minimum energy state of the false vacuum
at 'A' before the GUT transition is at a higher energy than
in the true vacuum state in 'B' after the transition. This
energy difference is what contributes to the vacuum energy.
During the GUT transition period, the positive pressure due
to the vacuum energy would have been enormously greater than
the restraining pressure produced by the gravitational influence
of matter and radiation. The universe would have inflated
at a tremendous rate, the inflation driven by the pressure
of the vacuum! In this picture of the universe, Einstein's
cosmological constant takes on a whole new meaning since it
now represents a definite physical concept ; It is simply
a measure of the energy difference between the true and false
vacuum states ('B' and 'A' in Figures 1 and 2.) at a particular
time in the history of the universe. It also tells us that,
just as in de Sitter's model, a universe where the vacuum
contributes in this way must expand exponentially in time
and not linearly as predicted by the Big Bang model. Guth's
scenario for the expansion of the universe is generally called
the 'inflationary universe' due to the rapidity of the expansion
and represents a phase that will end only after the true vacuum
has supplanted the false vacuum of the old, symmetric phase.
A major problem
with Guth's original model was that the inflationary phase
would have lasted for a very long time because the false vacuum
state is such a stable one. The universe becomes trapped in
the cul-de-sac of the false vacuum state and the exponential
expansion never ceases. This would be somewhat analogous to
water refusing to freeze even though its temperature has dropped
well below 0 Centigrade. Recent modifications to the original
'inflationary universe' model have resulted in what is now
called the 'new' inflationary universe model. In this model,
the universe does manage to escape from the false vacuum state
and evolves in a short time to the familiar true vacuum state.
We don't really
know how exactly long the inflationary phase may have lasted
but the time required for the universe to double its size
may have been only 10(-34) seconds. Conceivably, this inflationary
period could have continued for as 'long' as 10(-24) seconds
during which time the universe would have undergone 10 billion
doublings of its size! This is a number that is truely beyond
comprehension. As a comparison, only 120 doublings are required
to inflate a hydrogen atom to the size of the entire visible
universe! According to the inflationary model, the bubbles
of the true vacuum phase expanded at the speed of light. Many
of these had to collide when the universe was very young in
order that the visible universe appear so uniform today. A
single bubble would not have grown large enough to encompass
our entire visible universe at this time; A radius of some
15-20 billion light years. On the other hand, the new inflationary
model states that even the bubbles expanded in size exponentially
just as their separations did. The bubbles themselves grew
to enormous sizes much greater than the size of our observable
universe. According to Albrecht and Steinhardt of the University
of Pennsylvania, each bubble may now be 10(3000) cm in size.
We should not be too concerned about these bubbles expanding
at many times the speed of light since their boundaries do
not represent a physical entity. There are no electrons or
quarks riding some expandind shock wave. Instead, it is the
non-material vacuum of space that is expanding. The expansion
velocity of the bubbles is not limited by any physical speed
limit like the velocity of light.
GUMs
in GUTs
A potential
problem for cosmologies that have phase transitions during
the GUT Era is that a curious zoo of objects could be spawned
if frequent bubble mergers occured as required by Guth's inflationary
model. First of all, each bubble of the true vacuum phase
contains its own Higgs field having a unique orientation in
space. It seems likely that no two bubbles will have their
Higgs fields oriented in quite the same way so that when bubbles
merge, knots will form. According to Gerhard t'Hooft and Alexander
Polyakov, these knots in the Higgs field are the magnetic
monopoles originally proposed 40 years ago by Paul Dirac and
there ought to be about as many of these as there were bubble
mergers during the transition period. Upper limits to their
abundance can be set by requiring that they do not contribute
to 'closing' the universe which means that for particles of
their predicted mass (about 10(16) GeV), they must be 1 trillion
trillion times less abundant than the photons in the 3 K cosmic
background. Calculations based on the old inflationary model
suggest that the these GUMs (Grand Unification Monopoles)
may easily have been as much as 100 trillion times more abundant
than the upper limit! Such a universe would definitly be 'closed'
and moreover would have run through its entire history between
expansion and recollapse within a few thousand years. The
new inflationary universe model solves this 'GUM' overproduction
problem since we are living within only one of these bubbles,
now almost infinitly larger than our visible universe. Since
bubble collisions are no longer required to homogenize the
matter and radiation in the universe, very few, if any, monopoles
would exist within our visible universe.
Horizons
A prolonged
period of inflation would have had an important influence
on the cosmic fireball radiation. One long-standing problem
in modern cosmology has been that all directions in the sky
have the same temperature to an astonishing 1 part in 10,000.
When we consider that regions separated by only a few degrees
in the sky have only recently been in communication with one
another, it is hard to understand how regions farther apart
than this could be so similar in temperature. The radiation
from one of these regions, traveling at the velocity of light,
has not yet made it across the intervening distance to the
other, even though the radiation may have started on its way
since the universe first came into existence. This 'communication
gap' would prevent these regions from ironing-out their temperature
differences.
With the standard,
Big Bang model, as we look back to earlier epochs from the
present time, the separations between particles decrease more
slowly than their horizons are shrinking. Neighboring regions
of space at the present time, become disconnected so temperature
differences are free to develope. Eventually, as we look back
to very ancient times, the horizons are so small that every
particle existing then literally fills the entire volume of
its own, observable universe. Imagine a universe where you
occupy all of the available space! Prior to the development
of the inflationary models, cosmologists were forced to imagine
an incredably well-ordered initial state where each of these
disconnected domains (some 10(86) in number) had nearly identical
properties such as temperature. Any departure from this situation
at that time would have grown to sizable temperature differences
in widely separated parts of the sky at the present time.
Unfortunately, some agency would have to set-up these finely-tuned
initial conditions by violating causality. The contradiction
is that no force may operate by transmitting its influence
faster than the speed of light. In the inflationary models,
this contradiction is eliminated because the separation between
widely scattered points in space becomes almost infinitly
small compared to the size of the horizons as we look back
to the epoc of inflation. Since these points are now within
each others light horizons, any temperature difference would
have been eliminated immediatly since hotter regions would
now be in radiative contact with colder ones. With this exponentially-growing,
de Sitter phase in the universe's early history we now have
a means for resolving the horizon problem.
Instant
Flat Space
Because of the
exponential growth of the universe during the GUT Era, its
size may well be essentially infinite for all 'practical'
purposes . Estimates by Albrecht and Steinhardt suggest that
each bubble region may have grown to a size of 10(3000) cm
by the end of the inflationary period. Consequently, the new
inflationary model predicts that the content of the universe
must be almost exactly the 'critical mass' since the sizes
of each of these bubble regions are almost infinite in extent.
The universe is, for all conceivable observations, exactly
Euclidean (infinite and flat in geometry) and destined to
expand for all eternity to come. Since we have only detected
at most 10 percent of the critical mass in the form of luminous
matter, this suggests that 10 times as much matter exists
in our universe than is currently detectable. Of course, if
the universe is essentially infinite this raises the ghastly
spectre of the eventual annihilation of all organic and inorganic
matter some 10(32) years from now because of proton decay.
In spite of
its many apparent successes, even the new inflationary universe
model is not without its problems. Although it does seem to
provide explainations for several cosmological enigmas, it
does not provide a convincing way to create galaxies. Those
fluctuations in the density of matter that do survive the
inflationary period are so dense that they eventually collapse
into galaxy-sized blackholes! Neither the precise way in which
the transition to ordinary Hubbel expansion occurs nor the
duration of the inflationary period are well determined.
If the inflationary
cosmologies can be made to answer each of these issues satisfactorily
we may have, as J. Richard Gott III has suggested, a most
remarkable model of the universe where an almost infinite
number of 'bubble universes' each having nearly infinite size,
coexist in the same 4-dimensional spacetime; all of these
bubble universes having been brought into existence at the
same instant of creation. This is less troublesome than one
might suspect since, if our universe is actually infinite
as the available data suggests, so too was it infinite even
at its moment of birth! It is even conceivable that the universe
is 'percolating' with new bubble universes continually coming
into existence. Our entire visible universe, out to the most
distant quasar, would be but one infinitessimal patch within
one of these bubble regions. Do these other universes have
galaxies, stars, planets and living creatures statistically
similar to those in our universe? We may never know. These
other universes, born of the same paroxicism of Creation as
our own, are forever beyond our scrutiny but obviously not
our imaginations!
Beyond
The Beginning...
Finally, what
of the period before Grand Unification? We may surmise that
at higher temperatures than the GUT Era, even the supermassive
Higgs and Leptoquark bosons become massless and at long last
we arrive at a time when the gravitational interaction is
united with the weak, electromagnetic and strong forces. Yet,
our quest for an understanding of the origins of the universe
remains incomplete since gravity has yet to be brought into
unity with the remaining forces on a theoretical basis. This
last step promises to be not only the most difficult one to
take on the long road to unification but also appears to hold
the greatest promise for shedding light on some of the most
profound mysteries of the physical world. Even now, a handful
of theorists around the world are hard at work on a theory
called Supergravity which unites the force carriers (photons,
gluons, gravitons and the weak interaction bosons) with the
particles that they act on (quarks, electrons etc). Supergravity
theory also predicts the existence of new particles called
photinos and gravitinos. There is even some speculation that
the photinos may fill the entire universe and account for
the unseen 'missing' matter that is necessary to give the
universe the critical mass required to make it exactly Euclidean.
The gravitinos, on the other hand, prevent calculations involving
the exchange of gravitons from giving infinite answers for
problems where the answers are known to be perfectly finite.
Hitherto, these calculations did not include the affects of
the gravitinos.
Perhaps during
the next decade, more of the details of the last stage of
Unification will be hammered out at which time the entire
story of the birth of our universe can be told. This is, indeed,
an exciting time to be living through in human history. Will
future generations forever envy us our good fortune, to have
witnessed in our lifetimes the unfolding of the first comprehensive
theory of Existence?
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