The Big Bang model of cosmology rests on two key ideas that date back to the early 20th century: General Relativity and the Cosmological Principle. By assuming that the matter
in the universe is distributed uniformly on the largest scales, one can use
General Relativity to compute the corresponding gravitational effects of
that matter. Since gravity is a property of spacetime in General Relativity,
this is equivalent to computing the dynamics of spacetime itself. The story
unfolds as follows:
Given
the assumption that the matter in the universe is homogeneous and isotropic
(The Cosmological Principle) it can be shown that the corresponding distortion
of spacetime (due to the gravitational effects of this matter) can only
have one of three forms, as shown schematically in the picture at left. It
can be "positively" curved like the surface of a ball and finite in extent;
it can be "negatively" curved like a saddle and infinite in extent; or it
can be "flat" and infinite in extent  our "ordinary" conception of space.
A key limitation of the picture shown here is that we can only portray the
curvature of a 2dimensional plane of an actual 3dimensional space! Note
that in a closed universe you could start a journey off in one direction
and, if allowed enough time, ultimately return to your starting point; in
an infinite universe, you would never return.
Before we discuss which of these three pictures describe our universe (if any) we must make a few disclaimers:
 Because the universe has a finite age (~13.7 billion years) we can only see a finite distance out into space: ~13.7 billion light years. This is our socalled horizon.
The Big Bang Model does not attempt to describe that region of space significantly
beyond our horizon  spacetime could well be quite different out there.
 It is possible that the universe has a more complicated global
topology than that which is portrayed here, while still having the same local
curvature. For example it could have the shape or a torus (doughnut). There
may be some ways to test this idea, but most of the following discussion
is unaffected.
Matter plays a central role in cosmology. It turns out that
the average density of matter uniquely determines the geometry of the universe
(up to the limitations noted above). If the density of matter is less than
the socalled critical density, the universe is open and infinite. If the
density is greater than the critical density the universe is closed and finite.
If the density just equals the critical density, the universe is flat, but
still presumably infinite. The value of the critical density is very small:
it corresponds to roughly 6 hydrogen atoms per cubic meter, an astonishingly
good vacuum by terrestrial standards! One of the key scientific questions
in cosmology today is: what is the average density of matter in our universe?
While the answer is not yet known for certain, it appears to be tantalizingly
close to the critical density.
Given
a law of gravity and an assumption about how the matter is distributed, the
next step is to work out the dynamics of the universe  how space and the
matter in it evolves with time. The details depend on some further information
about the matter in the universe, namely its density (mass per unit volume)
and its pressure (force it exerts per unit area), but the generic picture
that emerges is that the universe started from a very small volume, an event
later dubbed the Big Bang, with an initial expansion rate. For the most part
this rate of expansion has been slowing down (decelerating) ever since
due to the gravitational pull of the matter on itself. A key question for
the fate of the universe is whether or not the pull of gravity is strong
enough to ultimately reverse the expansion and cause the universe to collapse
back on itself. In fact, recent observations have raised the possibility
that the expansion of the universe might in fact be speeding up (accelerating),
raising the possibility that the evolution of the universe is now dominated
by a bizarre form of matter which has a negative pressure.
The picture above shows a number of possible scenarios for
the relative size of the universe vs. time: the bottom (green) curve represents
a flat, critical density universe in which the expansion rate is continually
slowing down (the curves becomes ever more horizontal). The middle (blue)
curve shows an open, low density universe whose expansion is also slowing
down, but not as much as the critical density universe because the pull of
gravity is not as strong. The top (red) curve shows a universe in which a
large fraction of the matter is in a form dubbed "dark energy"
which is causing the expansion of the universe to speed up (accelerate).
There is growing evidence that our universe is following the red curve.
Please avoid the following common misconceptions about the Big Bang and expansion:
 The Big Bang did not occur at a single point in space as an "explosion."
It is better thought of as the simultaneous appearance of space everywhere
in the universe. That region of space that is within our present horizon
was indeed no bigger than a point in the past. Nevertheless, if all of space
both inside and outside our horizon is infinite now, it was born infinite.
If it is closed and finite, then it was born with zero volume and grew from
that. In neither case is there a "center of expansion"  a point from which
the universe is expanding away from. In the ball analogy, the radius of the
ball grows as the universe expands, but all points on the surface of the
ball (the universe) recede from each other in an identical fashion. The interior
of the ball should not be regarded as part of the universe in this analogy.
 By definition, the universe encompasses all of space and time
as we know it, so it is beyond the realm of the Big Bang model to postulate
what the universe is expanding into. In either the open or closed universe,
the only "edge" to spacetime occurs at the Big Bang (and perhaps its counterpart
the Big Crunch), so it is not logically necessary (or sensible) to consider
this question.
 It is beyond the realm of the Big Bang Model to say what gave
rise to the Big Bang. There are a number of speculative theories about this
topic, but none of them make realistically testable predictions as of yet.
To
this point, the only assumption we have made about the universe is that its
matter is distributed homogeneously and isotropically on large scales. There
are a number of free parameters in this family of Big Bang models that must
be fixed by observations of our universe. The most important ones are: the
geometry of the universe (open, flat or closed); the present expansion rate
(the Hubble constant); the overall course of expansion, past and future,
which is determined by the fractional density of the different types of matter
in the universe. Note that the present age of the universe follows from the
expansion history and present expansion rate.
As noted above, the geometry and evolution of the universe
are determined by the fractional contribution of various types of matter.
Since both energy density and pressure contribute to the strength of gravity
in General Relativity, cosmologists classify types of matter by its "equation
of state" the relationship between its pressure and energy density. The basic
classification scheme is:
 Radiation: composed of massless or nearly massless particles
that move at the speed of light. Known examples include photons (light) and
neutrinos. This form of matter is characterized by having a large positive
pressure.
 Baryonic matter: this is "ordinary matter" composed primarily
of protons, neutrons and electrons. This form of matter has essentially no
pressure of cosmological importance.
 Dark matter: this generally refers to "exotic" nonbaryonic
matter that interacts only weakly with ordinary matter. While no such matter
has ever been directly observed in the laboratory, its existence has long
been suspected for reasons discussed in a subsequent page. This form of matter also has no cosmologically significant pressure.
 Dark energy:
this is a truly bizarre form of matter, or perhaps a property of the vacuum
itself, that is characterized by a large, negative pressure. This is the
only form of matter that can cause the expansion of the universe to accelerate,
or speed up.
One of the central challenges in cosmology today is to determine the relative
and total densities (energy per unit volume) in each of these forms of matter,
since this is essential to understanding the evolution and ultimate fate
of our universe.
Last updated: Tuesday, 03012005
