Responses: Open or Closed? - The Fate of the Universe
Olbers’ Paradox
The example of Olbers’ Paradox should start getting you thinking about the nature of the
Universe. The fact that the night sky is actually dark contrasts with the Newtonian view that
space was static. The paradox can be solved by assuming that the Universe is expanding,
such that the light from distant galaxies has not had time (given the finite speed of light) to
reach us.
Space-time
Einstein’s general theory of relativity shows that gravity warps the actual fabric of space,
called space-time. One way to think about this is to imagine (try it out if the materials are
available!) a rubber sheet, stretched on a frame. If a heavy ball is placed in the centre of the
sheet, the sheet bends around the object. This is how we can think of gravity, bending the
material of space.
The key to this task is getting to grips with the Helpful Hints questions. Here is a summary of
the main points:
What are the possibilities for the curvature of space-time, and how do these relate to open or
closed Universes?
In this context, the actual shape of space is incredibly important, but is tricky to visualise.
Scientists usually consider a two-dimensional plane in these three-dimensional spaces, as it
is much easier to understand (see http://map.gsfc.nasa.gov/universe/bb_concepts.html).
The possible curvatures of space-time are flat, positively curved (like the surface of a
football) or negatively curved (like the surface of a saddle). The shape then dictates whether
the Universe is closed or open. Imagine standing on these three surfaces in turn, and
walking across them in a straight line. In the positively curved example, you will eventually
end up back where you started, so this is an example of a closed universe. In the negatively
curved example, walking in a straight line means you never return to where you started. This
is also true in the flat case, and these two spaces are examples of open universes.
What is the critical density of the Universe? If the density of the Universe equals the critical
density, what is the fate of the Universe? What other possibilities exist for the fate of the
Universe, and how do these relate to the density of the Universe?
The critical density is the average density of matter in the case of a flat universe. In this
universe, the size of the universe continues to increase forever, and the rate of this increase
actually depends on dark energy (see later questions). If the density of the Universe is
greater than the critical density, firstly the Universe is closed. In this case, the gravitational
pull of the matter in the Universe is strong enough to slow down the expansion of the
Universe, reverse it, and the Universe falls back on itself (ending in a Big Crunch!). In the
case where the density of the Universe is less than the critical density, the negatively curved
space applies, and the Universe still expands forever. So the shape, density and fate of the
Universe are all intricately linked.
How have satellites like WMAP (Wilkinson Microwave Anisotropy Probe) made
measurements of the density and curvature of the Universe?
WMAP is a current NASA mission to measure the fluctuations of the cosmic microwave
background radiation. The sizes of these fluctuations tell us directly about the shape of the
Universe, and in fact indicate that it is very close to the flat case. This also therefore means
that the total density of the Universe is very close to the critical density. Bear in mind
however, that we know relatively little about the constituent parts of the Universe, as only
about 4% of the Universe consists of atoms. Using the web resource here will give you lots
of information about the WMAP mission, so peruse the things that interest you the most.
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How do observations of distant supernovae indicate the existence of dark energy?
In 1998, measurements of observations of supernovae (stars reaching the end of their
lifetime and exploding) in distant galaxies were used to show that these galaxies are moving
away from us at a rate much greater than that predicted by Hubble’s Law. The explanation
for this behaviour is that the Universe is expanding at an accelerating rate. This can only be
true if an additional form of energy is present, which works in the opposite way to gravity.
This is where dark energy comes in. However, very little is known about it, all we know is
that it needs to constitute > 70% of the Universe!
Going Further
There is a proposed NASA mission called the Joint Dark Energy Mission, which currently has
three competing instruments to make measurements related to dark energy. You should
focus here on the differences between the instruments, and what they will actually measure
to further our current understanding of dark energy. An analysis of the possible strengths
and weaknesses of each approach may work well.
Summary
To summarise the key points:
• The density of matter in the Universe indicates the shape of space-time. This is turn
decides whether the Universe is open or closed.
• The expected fate of the Universe is a consequence of the density of matter and shape
of space-time. Open universes expand forever, and the rate of expansion is dependent
on the presence of dark energy. Closed universes have high density, which means that
gravity is strong enough to overcome expansion, and the universe ends in a Big Crunch.
• WMAP is a key mission in determining the parameters of the Universe that govern its
fate.
• Recent observations of distant supernovae indicated that the Universe is actually
accelerating. This behaviour can be attributed to dark energy, a concept that is still fairly
mysterious, and is currently under thorough scientific investigation.
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