Types of Universes
After Albert Einstein
formulated his general theory of relativity, Alexander Friedman (Russian
mathmetician) developed
models for the structure of expanding universes based on GTR (Georges Lemaitre
[Belgian Roman Catholic priest and physicist/astronomer]
also investigated various models for expanding universes. Lemaitre's
primeval atom is
sometimes credited as the forerunner
of what has eventually come to be called the Big Bang
Theory). Einstein, Friedman, and Lemaitre worked roughly at around
the same time (the 1920's). Friedman using the GTR and taking
the Cosmological Principle, found
three basic styles for expanding universes.
Friedman, GTR, and the Geometry (Shape) of the Universe
We demonstrate some properties of
Friedman universes with two-dimensional analogies.
Recall that in order to determine the locations of
events in our Universe we must specify four things
(---> our Universe has four dimensions);
we must specify the position
and time of an event, that is, we must specify the space-time
position of events.
Interestingly, the framework within which we
place these space-time events
for the Universe can have different shapes. We have
flat space (Euclidean, critical universe),
postive curvature space (e.g.,
a sphere, the closed universe), and
negative curvature space (e.g., a saddle, open universe)
universes.
Graphically, in two-dimensions,
positive curvature
and
negative curvature universes.
Abstract as these concepts are, our Universe may have one of these shapes
(topologies). Hmm, but so what. Well, the different shapes are indicative
of the ultimate fate of the Universe.
If we can determine the
geometry (shape) of our Universe, we can infer what will
happen to our Universe
in the distant future.
What Are Some Differences Between Universes of Different Shapes?
|
- Flat universes ---> expanding universe and will stop expanding after
an infinite amount of time; the flat universe is
the dividing line between open and
closed universes.
- Closed universes ---> expanding, but will reach a maximum size and
then collapse
- Open universes ---> expanding universe which will expand forever and
is infinite in spatial extent
|
Scale Factor
We now show what each solution looks like in terms of what is referred to as
the scale factor
for the universe R(t). The scale factor, R(t),
tells us how much bigger or smaller the Universe is today than it was yesterday
and so on.
- Scale Factor ===> Size = R(t) x Size (in the past)
where Size (in the past) is usually the size of the universe at some point
in the past.
In terms of the scale factor R(t), the evolution of the various solutions
for the universe look like:
The closed universes correspond to the bottom curve.
Open universes correspond to the top curve.
The flat universe (the critical universe) separates things into
closed and open universes.
In terms of a Hubble plot (that is the speed of recession versus
the distance), we have:
A great deal of effort was directed toward determining the which of
the above models was the correct one for our Universe. The
types of methods used
to determine the correct universe model fall into two
categories:
- Dynamical Tests
where we check to see if the Universe exceeds
its escape speed by measuring the expansion rate of the Universe (the
Hubble constant, H) and the mass of the Universe
- Topological Tests
where we try and measure the shape
of the Universe
We will spend a fair amount of time on both methods.
