Since Hubble's discovery that distant galaxies are moving away from us in 1929, giving rise to Hubble's Law(1) one of the major unanswered questions in cosmology has been what will happen to the Universe in the future. Hubble's law shows and explains that an observer at each point in the Universe will see himself at the centre of the Universe. This explains why we see ourselves at the centre - galaxies far away from us (ones that are not significantly affected by the gravitational field of the Milky Way) always travel away from us. The real value of Hubble's law extends from that. It tells us that the Universe is expanding uniformly, isotropically, as shown in the following diagram.
This shows a system of galaxies uniformly expanding between the epochs t1 and t2. It is apparent
that at t2 the galaxies A, B and C (for example) are twice as far apart compared to t1, and thus
they must have twice the recessional velocity.
There is good observational evidence that the Universe is isotropic on the largest scales. The map of cosmic background radiation produced by the Cosmic Background Explorer (COBE)(2) below shows that the cosmic background radiation (an echo of the Big Bang) is uniform to one part in 100,000(3). The bright band in the centre of the map is radiation from the Galactic plane.
If the density of the Universe is sufficient to halt the expansion of the Universe then it would
eventually stop expanding and collapse down to a 'Big Crunch' (closed scenario). If the density
is less than than the required amount then the Universe will continue expanding forever, at an
accelerating rate (open scenario). The third possibility exists that if the density is just enough
to halt expansion then the 'size' of the Universe will increase ever more slowly to a definite limit
at an infinite time. (flat scenario, also the critical or Einstein-de Sitter model).
The parameter is known as the density parameter of the Universe, and is the ratio of the actual
density of the Universe divided by the critical density - the density which would cause a flat
Universe.
There are important implications for the past as well as the future of the Universe, depending
on which one of these scenarios turns out to be correct. There are some people, for example,
who believe that the Universe is continually oscillating in a series of Big Bangs/Crunches - and
that each Crunch is a new Bang(5).
To try and find the answer to our original question, one can imagine a simple, idealized Universe
such as a Newtonian model, asking the question, what is the deceleration due to gravity of a
galaxy located at the surface of a uniformly expanding sphere, which has a density equal to the
average density of the Universe.
Thus in principle it should be a simple matter to calculate the solution because the assumption
of isotropy makes the results of this calculation valid for the whole Universe.
Unfortunately there are many problems in producing such a solution. Firstly although
Newtonian mechanics works well on many of our everyday scales, it breaks down with the vast
distances and velocities of space. Secondly much is unknown about the Universe. It appears
that most of the mass of the Universe is in a form that we cannot directly observe; this is called
dark matter. The first problem is solved by using Einstein's general theory of relativity.
Prior to Hubble's momentous discovery Einstein had been working on applying his general
theory of relativity to the entire Universe. Most of his solutions showed the Universe either
contracting or expanding. However, this went against the prevailing belief of the time, which
was that the Universe was static and perfect. This came about for philosophical reasons, where
a dynamic Universe meant an uncertain world, which was not desirable. To resolve the dilemma
of fitting his theory to this belief he added a (permissible) arbitrary constant, called the
cosmological constant, that took the form of a hypothetical repulsive force acting against the pull
of gravity that would otherwise cause the Universe to contract. By setting this constant to a
certain value Einstein was able to formulate a static theory of the Universe which kept him and
his fellow men happy.
When Einstein heard of Hubble's discovery he was understandably upset, and he later called his
cosmological constant 'his biggest blunder'. However, in the last few months astronomers have
been collecting data that seems to imply that the cosmological constant is non-zero if it is to fit
in with the popular inflationary model of the early Universe. This will be discussed later.
The second problem I mentioned was the existence of dark matter, matter which cannot be seen.
The standard procedure for 'weighing' a galaxy, for example, is to consider the balancing of the
'centrifugal force' and the attractive gravitational force. However, when we observe giant spiral
galaxies such as NGC 5084 (see below) the density of matter at a particular point, especially in
the outer regions, seems to be more than would be expected from the amount of radiation being
emitted. This points to large amounts of dark matter in these outer regions, emitting very little
light.
It is known that the density of matter visible in galaxies amounts to only 1% of the critical
density, ergo visible mass alone cannot close the Universe. However it is not known whether
the distribution of dark matter in the large-scale Universe is similar to that in galaxies, so there
is considerable uncertainty in the amount of dark matter in the Universe. Most estimates lie
between 10 and 20 times the visible mass of galaxies. Most opinions seem to suggest that a
closed Universe is unlikely because of this lack of mass; the observations discussed below also
seems to suggest that a closed Universe is not likely.
The results previously mentioned in connection with the cosmological constant were collected by the Supernova Cosmology Project, an international team of astrophysicists based at the Department of Energy's Ernest Orlando Lawrence Berkeley National Laboratory, consists of measurement of the redshifts and intrinsic brightnesses, which can be worked out by the time it takes for a supernova to decay. Distances combined with redshifts of the supernovae give the rate of expansion of the universe over its history, allowing a determination of how much the expansion rate is speeding up or slowing down. This depends on the predictability of Type Ia supernovae. They are so predictable, in fact, that the time at which the supernova explosion started can be determined just from looking at a spectrum.
The above graph shows the increasing redshift observed with very distant supernovae.
By studying very distant supernovae the team have discovered that the expansion of the Universe
seems to be increasing. Team member Robert Kirshner thinks that within billions of years from
now the stars seen in the sky today will be gone from view. "The Universe will be a very
different place to look at," he said. "It will be very lonely."
This supports the possibility that the cosmological constant is not zero after all, but for very
different reasons to Einstein's.
The question of what will happen in the future of the Universe is exciting, because in trying to answer it we are discovering more about the past and present Universe, too. An interesting fact is that we know that the density of the Universe is within a factor of ten of the critical density, so it is still possible to find that any three scenarios are valid. Although we do not yet understand enough or have enough data to draw any firm conclusions, we can hypothesize, and perhaps gain enough insight one day to really put these hypotheses to the test.
Sources:
http://www.nando.net/newsroom
http://www-supernova.lbl.gov
http://www.direct.ca/trinity
http://oposite.stsci.edu/pubinfo/pr
New Scientist, 9 November 1996
Our Evolving Universe by Malcolm S. Longhair
Acknowledgements:
Ed Copeland, Theoretical Physics, University of Sussex
Paul Roche, Astronomy Centre, University of Sussex
Image acknowledgements:
Uniform expansion: Malcolm Longhair
COBE microwave background radiation: NASA Goddard Space Flight Center
The three possibilities: Malcolm Longhair
Red shifts: The Supernova Cosmology Project
History of the Universe: NASA Goddard Space Flight Center - HqL-338
Dominic Hargreaves
28 August 1998
Notes:
1. Hubble's Law: v = H0 r, where v is the recessional velocity (usually measured in
kilometres/second), H0 is the Hubble constant, and r is the distance of the galaxy (usually
measured in megaparsecs).
2. The Cosmic Background Explorer Satellite is run by NASA. This image was taken in the millimetre band of wavelengths (microwaves). Observations have also been made throughout the near and far infrared bands.
3. The maximum variation in temperature on the image is 0.54 mK. The spectrum of the background radiation is that of a black body at 2.725 K, and is perfect to an accuracy of 0.03% of the maximum intensity in the wavelength range 0.5 to 2.5 mm.
4. The size of the Universe is something that needs considerable thought because it is not sufficient to give a 'diameter' of the Universe, because the Universe does not have an 'edge'. It is difficult to imagine, and is best described by thinking of the two dimensional surface of a sphere, which has no edge, being extended into a three dimensional space. This of course means that the model requires a fourth dimension of space, which explains why it is so difficult to visualize. However this description gives us some idea of the geometry of the Universe. For the purposes of our discussion the increasing size of the Universe can be thought of in this way, by imagining a balloon being blown up.
5. This theory has many advantages; for example it removes the anthropic problem - why
are have developed so successfully - because in an infinity of oscillations intelligent life is bound
to develop at some time. However, there are also a number of problems with this - not least, that
it seems to contradict the second law of thermodynamics - a most important, hitherto 'universal'
(no pun intended) law. As Sir Arthur Eddington, professor of astronomy at Cambridge
University said:
"The law that entropy always increases (the Second Law of Thermodynamics)
holds, I think, the supreme position among the laws of nature. If someone points
out to you that your pet theory of the universe is in disagreement with Maxwell's
equations, then so much the worse for Maxwell's equations... But if your theory
is found to be against the Second Law of Thermodynamics, I can give you no
hope; There is nothing for it but to collapse in deepest humiliation."
The reason for this strong worded criticism of the theory is that for the Universe to have gone through infinite numbers of oscillations the entropy must be periodically reduced, and there is no known system that can do this. However I think it is naive to think in this way - because all through scientific history man has questioned the accepted wisdom. In experimental science there is no proof, only a cycle of theories and experiment.