# Total energy of the universe

1. Jul 27, 2008

### deneve

Many texts and research papers seem to argue the case for the total energy of the universe being zero or constant. Indeed the Friedmann equation is often derived in books using KE+PE=constant, where the constant is zero for a flat universe. The sign of the constant also determines whether the universe recollapses again (or not). I know that in GR it is difficult to deal with the total energy of the universe but surely in a collapsing universe, the energy density would diverge as the universe collapsed so that even thogh there was finite energy in the form of matter and radiation the energy density would grow without bound. In Bianchi anisotropic models the shear also gives rise to a radiation temperature difference which provides an average shear term to be included in the energy density sum. (Lets forget the cosmological constant for the moment). This shear dominates the final collapse in these models and again seems to provide unlimited energy as the assymetrical collapse occurs. For the extreme kasner metric the energy from shear grows as one over the time from big crunch. I don't think I am mixing up energy with energy density here (energy density will go to infinity for even small amounts of matter as the volume decreases) - but I am a bit confused about Taub like collapse because it seems as though there is infinite available energy from the shearing weyl curvature collapse. Thus there must be an infinite energy content rather than zero in these anisotropic models. Is this the right way to interpret this? Especially since anisotropy(weyl curvature) could develop from normal symmetric(Ricci) curvature as a universe collapses - e.g. chaotic collapse.

I know that the current data fits an accelerating universe but that does not mean collapsing models are unphysical. If the CC is due to a scalar field which can decay then recollapse will occur any way so the jury is out on the final fate of the universe but the questions about energy still remain.

Can any one put my understanding on the right track with this?

2. Jul 28, 2008

### JimJast

Can you specify what you mean by energy? I'm not kidding. This is what cosmologists ask when you ask them such a question.

However if you mean what Einstein might have meant it is just $$mc^2$$ where m is the total relativistic mass of the universe and c the speed of light in vacuum, a constant according to Einstein's gravitation. Also there is no "potential energy" unless you split this $$mc^2$$ into $$m_0c^2$$, where $$m_0$$ is what used to be called "rest" mass and call it "potential energy" and $$(m-m_0)c^2$$ call "kinetic energy".

Of course the sum of them never wil be zero unless you act on Newtonian prejudice and expect that potential energy is "negative" and equal to all the kinetic energy in the universe. Which is only the way some folks do the math but in physics no energy can be negative since neither mass nor speed of light (squared) can be negative and every real energy has its (relativistic) mass.

Does it help?

3. Jul 28, 2008

### C Rob

I thought negative energy was a possibility , and if found, would be the key to stabilizing worm-holes...

4. Jul 28, 2008

### JimJast

A difference of two energies may be negative, but to remain exact you should say e.g. "the differance between energy E1 and E2 is negative" which means only that energy E1 is smaller than E2. But any energy by itself has physical sense as energy only being positive since it has inertial mass that is also only a positive quantity.

5. Jul 28, 2008

### LURCH

Correct me if I'm mistaken, but aren't you asking two different questions here? Yes, the energy density in the universe changes as the volume changes, and yes, the total energy in the universe remains the same. In fact, the reason the energy density changes is specifically because the total energy remains the same while the voluum changes.

6. Jul 28, 2008

### C Rob

I'm not sure. I was reading a peice by Michio Kaku about wormholes and I'm positive he postulated that negative energy could be the key to keeping wormholes open and stable as they try to pinch off. Not negative in the sense of an arithmetic problem, but actual negative energy. Kind-of like anti-matter.

7. Jul 28, 2008

### George Jones

Staff Emeritus
Yes, negative energy, as measured by at least some observers, is needed to hold wormholes open. See

No, this isn't anti-matter. An anti-electron has the same positive mass as an electron.

8. Jul 28, 2008

### deneve

By energy I mean the energy due to particles, radiation and if they exist, scalar fields like the inflaton or a quintessence component. Thus for particles, this means the sum of sqrt(m^2+p^2c^2) for all particles in the universe where m = rest mass and p is the momemtum of the particles as seen by an observer at the particles location, who sees the universe (currently) expanding around them. Any motion that a particle has, in addition to that associated with the expansion or contraction of the universe, is usually called the particle's peculiar motion(meaning "private" property from the latin generic) and is the motion which belongs to the particle alone and not to the global expansion or contraction of the universe. Thus if the universe contained only slowly moving massive particles then the energy would be mc^2 plus the small correction (1/2)mv^2). More importantly though, photons (and other massles particles) have energy = pc = hf which also contribute to the energy density. In the mixmaster cosmology the shearing gives rise to a radiation temperature diference between antipodes which would then generate the massless photons which would increase the energy density as the universe contracts. It is the fact that the shear gives rise to a seemingly infinite source of energy (via the mixmaster collapse) that is confusing. according to Tipler (in his book The Anthropic Cosmological Principle co authored with Barrow) positive energy like photons can be obtained from the negative gravitational shear energy of a collapsing mixmaster universe without bound - since the gravitational energy of a system is inversely proportional to the size of the system, then if the system collapses to zero size then unlimited negative energy (i.e. energy which can do work) can be available from the collapse. Tipler's ideas (on the so called Omega Point theory) have often been criticised but this aside I have to say that over twenty years ago when I was a post grad I used some of his theorems from global general relativity for my thesis and whatever anyone says, I think that he is a very accomplished theoretician and he does have a very remarkable grasp of cosmology so I don't want to dispel his work too quickly.

Has anyone else studied these cosmologies.