Recently, as part of the boomerang project, scientists have found that the universe is flat. How is this possible unless the universe has no mass? I saw this in a Nature article.

I think it means that overall structure of the universe is flat as opposed to being, say, a 4D hypersphere (i.e. it is open rather than closed). On top of this flatness there will be deviations due to the presence of mass (Stars etc.) but these will not be enough to cause the universe itself to 'curl up'.

Sean

On another note, I thought that recent observational evidence showed that the universe was not flat, but open (contradicting inflation). According to a Horizon program around a year ago observations involving the red-shift of supernovae show that the universe is not only expanding but the rate at which it is expanding is increasing . This means that over long distances gravitation acts as a repulsive rather than attractive force. This can be explained by setting the newly revived cosmological constant not equal to zero (implying in this case that the vacuum has a negative energy density).

So - how come Nature are claiming that the universe has the critical mass?

Michael

Just a couple of days ago the results of a very important experiment were announced that measured the cosmic background radiation to very high accuracy, in particular in measured small fluctautions. This is what the Nature article is about.

Sean

Does this mean that the universe will never meet death by either big crunch or by all work being stopped because of thermodynamiks?

Brad

it means no big crunch, I think. I don't think it means says anything about heat death, this will still happen.

But, if the universe is flat, how could it be a finite area. The area which is occupied by stars would be finite, but it would still take infinite time for the space to reach equilibrium in temperature. maybe I misunderstand this law though.

Brad

good point. I'm not completely sure, but I guess it could get very very near to equilibrium, which would be effectively the same thing.

The universe cannot be flat!!! f the whole universe is flat, then earth must be too, else the universe would have to have some volume. Can anyone explain this to me SIMPLY because I am only 13 and I don't get what half of these words mean!?!

Rachel

By saying that the universe is flat, we are talking in a relativistic sense. I don't know how much you know about relativity, so I'll try to explain this.Near a body emiting gravitation, the distance to the body becomes much farther. This is analogous to a rubber sheet bending when an object is placed upon it. Also, if the whole universe has a positive mass, then the area of the universe would be enlarged as well. The equations of relativity show that this enlargement takes place in the form of the universe curling into a sphere. If you don't understand any of this, do not worry; i have probably done a poor job explaining it- it might be wise to get a book on relativity in your local library that has a few diagrams.Otherwise simply ask a few questions. Basically saying that the universe is flat, we are saying that overall, the universe is not curved at all and that the overall mass is 0.Sorry if this still doesn't make sense. Someone else may be able to explain this better.

Brad

I don't think that having zero overall curvature implies that the universe has zero mass. Apparently, to be flat, the universe needs about the equivalent of 2-3 hydrogen atoms in each cubic metre of space. Which is actually quite a lot, considering how much (nearly) empty space there is between galaxies. I think that somehow the fact the universe is expanding gives it a reverse curvature - but I don't know why exactly. If the universe is open (i.e. its density is below the critical density, so it expands forever) then it is curved in the reverse sense to the way in which matter curves space. I don?t know the details, but I may be able to find them out.

Flat doesn't mean that the universe is 2-D, so it isn't a normal usage of the word. What happens is - the universe started off expanding, but the expansion is gradually slowing down due to gravitation. (This was the conventional model.) If the density of the universe was quite low, then gravity would not be enough to halt the expansion. The universe would expand to an infinite size. This is the open universe. If the universe was dense, the gravity could pull all the galaxies back together again - eventually all matter would meet at the big crunch, or omega point. This would be the end of the universe. This model is called the closed universe. There is a third alternative where the mass of the universe is just enough to halt the expansion. This is the flat universe.

Incidentally does anyone know if the flat universe grows to an infinite size? (It will certainly expand forever, but this doesn't imply its radius isn't bounded.) If Newton's law of gravitation is correct (which it isn't) the answer is unequivocally yes - there is absolutely no way the universe can hang around at a finite size for eternity, without orbiting its centre of mass. General relativity may disagree.

Anyway, what is really confusing me is the question: is the universe open, closed or flat? According to Horizon, the universe is open. It is currently expanding, and will accelerate in its expansion forever, until the relative speed of galaxies approaches the speed of light. According to Nature it is flat. Has one result superseded the other?

Yours,

Michael

The Nature result is certainly the latest, which doens't necessarily mean definate I suppose.

A flat universe will tend towards a limit. It will continue expanding, in the same way that a function may continue to increase, but it will never pass a certain value. For an idea of how this works, try plotting the graph y = 2 - 1/x for positive x. The line you draw will always be increasing, but it will never be more than 2. This is how a flat universe would expand.

Basically no-one can be certain what the universe will do at the moment. The main problem is that the amount of mass in the universe is believed to be fairly near the borderline and we don't know how much mass there is that we can't see at the moment. Results like the one in Nature will keep refining the overall picture that we have.

OK, I was just wondering about this because nothing like this could ever happen under Newtonian physics. Suppose we claim that the limiting distance of the galaxies is r. Now the attraction between galaxies is always larger than:

GMm / r²

Now decrease in velocity = force/mass xtime > GM / r² xtime. In other words the velocity would decrease linearly or faster. Eventually the speed of the galaxies would be reversed and they would all collide. As I say this is only the Newtonian universe.

In general relativity, what constants do you get? Do you still use the gravitational constant? I'm just trying to work out how we're going to pull out a limiting distance, using the quantities we have, and yet still get a dimensionally correct formula.

Yours,

Michael

the GR calculation would be a mess. Just a few thoughts though:

even in Newtonian Mechanics your picture is not really correct, suppose I launch a rocket from the earth with a velocity greater than the escape velocity, it will go to infinity, it will not be attracted back to the earth. This is analogous to the cosmological situation. The question is whether the explosion of the big bang gave an initial expansion velocity that was greater or less than the "escape velocity" of the universe in some sense.

Aside (not really relevant for cosmology), if you include rotation in a Newtonian model, it doesn't necessarily collapse, e.g. the solar system.

Also (and I've just made this up so I don0t know if it is relevant to anything), imagine the universe was sphere, the galaxies would be attracting each other on both sides, so to speak, so you could probably have a configuration that wouldn't collapse, although the universe itself might, which is the question for cosmology.

Sean

Hi Sean,

For the Newtonian calculation what I was trying to show was that if two galaxies are travelling apart then their distance cannot tend to r. They can either fall towards each other resulting in an almighty crash, or they can travel to infinity. What cannot happen is that they hover at close to a distance r for eternity. Except if they are orbitting their mutual centre of mass, as you said. But I was thinking of what would happen if the galaxies are travelling directly away from each other. So one fundamental difference that GR results in is that the distance between galaxies can tend to r, which will happen when the universe is flat.

Yours,

Michael

Point taken, but I think it is possible you might be able to get a static universe in Newtonian mechanics by considering it to be a sphere etc., but I really don't have time to do calculation now as exams are close.