Monday April 5th 1999
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Lecture notes:

Class 34
 

Lecture Title -- Will the Universe End with Ice or Fire?

Review the three main pieces of evidence for the Big Bang
1. The expansion of the Universe
2. The Cosmic Microwave Background
3. Primordial Nucleosynthesis

We have now extended our understanding of the Universe back to about three minutes after the Big Bang. Scientists think
they understand things pretty reliably back to about three minutes after the Big Bang. At earlier times however things are less certain.

We really don't have a totally satisfactory answer for example about why the Universe came into being. We have some good ideas but nothing totally compelling.

Also we don't know know what happened before the Big Bang if anything at all. It is possible that there was simply nothing
before the Big Bang since time and space had not yet come into being.

We have already learned that a long time ago the Universe started expanding. By observing the redshifts of distant galaxies we know that it is still expanding today.

A natural question to ponder is the distant future of the Universe.  What will happen to the Universe on a very long timescale? Will it keep expanding like it is now forever? Or will it start to contract someday and shrink back down to a very small size?

The Universe basically has 3 possible fates
1. It will keep expanding forever
2. It will ultimately stop expanding and contract again
3. It will expand forever but more and more slowly so that it essentially reaches a standstill

To understand this in more detail we must first ask ourselves what  might halt the expansion of the Universe? GRAVITY.

To understand this better let's draw an analogy.
Consider a rocket being launched from a planet.

If we start the rocket with a huge velocity it will escape the planet's gravitational pull because the planet's gravity is not enough to hold onto it. It will then keep going forever. This is like the Universe that keeps expanding forever.

On the other hand if the rocket launch velocity is small it will slow down stop and fall back to the planet. This is like the Universe that collapses.

Now how fast the rocket must be launched depends on the mass of the planet (assuming the planet has a fixed size).
On a very massive planet the rocket will need more velocity to escape. On a low mass planet it will be easier for the rocket to
escape.

This is how mass enters the picture and determines the fate of the spacecraft.

Now we can draw a loose analogy between this situation and the Universe in which we live. Just like the mass of a planet will
determine whether a rocket launched at a certain velocity escapes to infinity the amount of mass in the Universe determines whether the Universe will stop expanding.

However we don't know the precise mass of the Universe so it is hard to predict whether the Universe will expand forever or whether it will start contracting.

Actually the DENSITY of the Universe is what matters rather than its mass. As we learned before density = mass/volume.

So there are three ranges of density the Universe can have
1. above the critical density
2. below the critical density
3. the exact critical density
 
 
 

Possible Fate	Density	Name
Expand forever	Less than critical	Open
Stop expanding and contract	More than critical	Closed
In between	Equal to critical	Flat

Astronomers can theoretically calculate the critical density of the Universe. The critical density is about
3 hydrogen atoms/cubic meter = 4 x 10^-30 gm/cubic centimeter.

This is an amazingly small number! Compare it to anything on Earth and it is very small. Far lower density than air.
Far lower density than the best manmade "vacuum" on Earth.

Now astronomers don't know if the density of the Universe is more or less than this critical value. What matters here is the average density of the Universe on a very large scale. Clearly the density of small bits of the Universe such as Earth are much more dense than this. But there is also a lot of intergalactic space that could be less dense than this. So the overall density depends on how these things average out.

Averaged over the very largest scales the Universe is thought to be quite homogeneous.

So to measure the density of the Universe we would have to study a huge volume of it and measure the amount of mass
in stars gas and dark matter. We can measure the stars and gas not too badly but the dark matter is very hard to measure
well mainly because we can't see it.

So if the Universe is closed it will start to collapse again and we will start to observe galaxy blueshifts. Space itself will be
contracting carrying the galaxies with it.

The Universe will get hotter and denser. This is then the end of  the Universe by fire. Everything is consumed as the Universe shrinks back down into a fiery furnace.

An open Universe on the other hand expands forever. Stars will go through their life cycles and die. Some will explode to
eject their elements to make yet more stars. However in the end the matter will get locked up in compact objects as all
the stars burn out. There are no stars to make light and heat so all planets around stars freeze. So this is death by ice.

Also this will be our fate if we live in a flat Universe.
 

Which form of death will the Universe in which we live undergo?  Fire or ice?

Astronomers are working very hard to try to answer this question.  As we have learned it basically depends on the density of the Universe on very large scales. If on average we have more than 3 hydrogen atoms per cubic meter = 4 x 10^^-30 gm/cubic centimeter then we die by fire. Otherwise we die by ice.

Astronomers actually have a pretty good guess what the answer might be although the case is not yet closed. If we add up all
the stars and gas we can see we only get about 0.02 hydrogen atoms/cubic meter.

But as we discussed before we also need to include the dark matter. We know there is a lot of dark matter but it is hard
to estimate precisely how much there is.

Our best studies suggest that in galaxies we have about 10 x as much dark matter as mass in gas and stars. In
clusters we see about 10--30 x as much dark matter as  mass in gas and stars.

Thus our best estimates suggest about 0.4 atoms per cubic meter on the average.

So our best estimates suggest that we only have 10--20 per cent of the closure density. So it looks like our Universe will die by
ice.

However it's hard to be certain at this stage because there could still be a lot of dark matter out there in intergalactic
space. This is a fundamental problem that astronomers work to solve every day.

Of course this will take many billions of years so don't worry about it now!