Plot of energy against space-time

[axiomatical]

I was wondering what a plot of energy against space-time would look like going from alpha to omega, using the assumption that the universe is heading towards an omega of flat absolute zero.

I came up with a guess of this:

http://img585.imageshack.us/img585/9025/plotr.png (http://imageshack.us/photo/my-images/585/plotr.png/)

At alpha there was high energy in a small space and at omega there will be low energy in a large space. From this information it seemed natural to plot an inverse exponential curve (like that of 1/x).

Some thoughts I got from plotting this are (probably rambling nonsense but):


The actually points at alpha or omega are asymptotes, thus could never or will ever be reached in ordinary time. Unless you were to trace back or forwards in time infinitely then they would be?


When normally plotting an inverse exponential function like this you would also plot along the negative x-axis, the curve would then be a mirrored rotation when going into negative space-time. This would then seem to correlate well with the theory of an antimatter mirror of the universe.

So I am wondering what people of think of this? What should the plot of this actually look like using known data? Does plotting energy against space-time actually make any real sense?

ps I am (as you have probably assumed) not a physicist. I just like playing with ideas, relationships and analogies.

Thanks.
Axio.

[bcrowell]

Hi, axiomatical,

Welcome to PF!


At alpha there was high energy in a small space and at omega there will be low energy in a large space.
So aren't you talking about energy density rather than energy? (You actually can't even define energy on cosmological scales -- see the cosmology FAQ under "What is the total mass-energy of the universe?")


From this information it seemed natural to plot an inverse exponential curve (like that of 1/x).
1/x isn't an exponential. An exponential would be of the form ax, where a is a constant.

You have "spacetime" on your x axis, but that doesn't make sense. Spacetime isn't a number. You might want to look at the FAQ entry for "How are time and distance measured in cosmology?" You probably meant what the FAQ entry refers to as "universe standard time."

If you really mean energy density versus "universe standard time," then your graph has the right qualitative shape, but it's not really any simple function like 1/x.

-Ben

[axiomatical]

Thanks for replying Ben.

So aren't you talking about energy density rather than energy?
Yes, this is what I am trying to refer to.

1/x isn't an exponential.
I see now, I didn't know what to explicitly call the function set that produces such a curve.

If you really mean energy density versus "universe standard time," then your graph has the right qualitative shape, but it's not really any simple function like 1/x.
Can you point me to any data/research which shows that such a relationship is not a simple function like this? This is really what I am looking for. More specifically it should be 'average energy density'.

You have "spacetime" on your x axis, but that doesn't make sense. Spacetime isn't a number. You might want to look at the FAQ entry for "How are time and distance measured in cosmology?" You probably meant what the FAQ entry refers to as "universe standard time."
I see I was mixing up two concepts. I was trying to refer to the volume of space and universe standard time together since they both presumably increase proportionally.

[bcrowell]

Can you point me to any data/research which shows that such a relationship is not a simple function like this? This is really what I am looking for.


I don't know of anything that's accessible to a layperson, but for example: http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll8.html For a radiation-dominated, spatially flat universe, equation 8.53 gives the scale factor a as a function of t, and 8.28 gives the energy density in terms of a. This is just one type of simplified model. For realistic models, there are no closed-form expressions for this kind of thing.

[axiomatical]

Ah, I see I did not have anywhere near a clear model of how energy density is lost (the fact that I had not actually looked into it was clearly a pitfall).

Thank you for clarifying, I have learnt several things :)