# Negative Energy in Inflation Theory (Low/Zero Energy Universe)

I've been reading Max Tegmark's book: Our Mathematical Universe. It's very interesting, but I wanted to know more about one particular thing. The book simplifies things and I know inflation theories to be varied and complex, but I will briefly describe what Max was saying and hopefully someone can pick up one what I'm talking about.

Max describes the inflation period as containing a non-diluting, inflating substance, where the energy used to inflate it causes it's mass to increase through extreme negative pressure. And gravity repulses this substance, accelerating its growth because the negative pressure causes negative gravity.

So where did this energy come from to create all this new mass? Well he says that the gravitational force provided this energy, and that to balance the energy it created negative energy in the gravitational field. Every time the gravitational field accelerates something it gains negative energy apparently.

So what does this mean? It clearly means that for all or nearly all energy in the universe there must be an equal amount of negative energy in the gravitational field (or anywhere else that can have negative energy). But what is this energy doing? Surely this means the universe could cancel out all energy and return to nothing or nearly nothing?

So can someone please explain what this negative energy actually is.

Thank you.

• In cosmological models you have to decide, if you want to keep energy conservation as a fundamental principle, or not, because it is not an experimentally tested fact. If you do want to keep energy conservation alive, then you need to identify some source of energy and sinks of it. The sources can be some nebulously characterized field, about which we know little, except that they are not stable and that they have to contain the right amount of energy to satisfy the total "energy budget" of the universe. Barring evidence, Tegmark's religious beliefs about this are as good as any other. Aug 22, 2014 at 23:25
• In these theories, this negative energy must interact somehow or it's as good as not existing. So that's what I wonder. This negative energy must do something. Aug 22, 2014 at 23:32
• I should also mention that Max Tegmark acknowledges that this (inflation in general) is one possible theory but needs more evidence, so from what I've read, I wouldn't say it's a religious-like belief. Aug 22, 2014 at 23:35
• I would point out that a theory in science is a body of work that has been validated by observation or experiment. What you are looking at aren't theories by any definition. They are mathematical models, which may or may not be true. There is no way to decide that with mathematics. Aug 22, 2014 at 23:35
• In the book he does point out that observations have so far been consistent with inflation, but the jury is still out. Aug 22, 2014 at 23:36

In Newtonian mechanics, a particle might gain kinetic energy while a corresponding gravitational potential energy decreases, thus you get that kind of conservation of energy. The total energy is the same before and after any event. However, the amount of energy depends on who's looking.

In Special Relativity a transfer of energy has to happen at an event (a specific time and specific location), so you have to have changes in kinetic energy be compensated by a loss of energy in another body or field. An example is the electromagnetic field which has an energy density, momentum density, and stress at every point in spacetime. Energy can transfer from the electromagnetic field to the particle and thus you get conservation of energy. It can be expressed by saying the energy in some region of space at some time is equal to the energy at an earlier time plus or minus the net flux of energy in or out of that region of space during that time interval. But energy conservation is just one part of a unified energy-momentum conservation, and that conservation can be expressed in a frame independent manner.

In General Relativity you generalize the kind of conservation of energy as is found in Special Relativity, but the tensor T, called the stress-energy tensor, that keeps track of the energy density, momentum density and stress at every event in spacetime is actually the same tensor from Special Relativity, and so it has no terms that correspond to gravitational potential energy. Breaking the stress-energy tensor into just an energy part is frame dependent and General Relativity is formulated in a frame independent manner. Some people try to make an energy psuedo-tensor, but that is a different tensor. And it is the stress-energy tensor T (not the psuedo-tensor) that is the source of the gravitational curvature, just as charges and currents are the source of electromagnetic waves.

So simply put, don't expect General Relativity to have something like "total energy of the universe", because that's just something that isn't naturally there. There is a stress-energy tensor, which if you pick a frame gives you an energy density at an event, but there is usually no natural frame, so no natural energy density.

But when talking about the stress-energy tensor in different epochs, there might be a sense where is has certain properties and at other times has other properties. One property a stress-energy tensor can have is whether it satisfies various so-called energy conditions. And a common consequence of many energy conditions is that the energy density (for every frame) is non-negative. So the question about whether a particular stress-energy tensor has a negative energy density is a legitimate question in General Relativity.

• Thanks for the answer, though you say this stress-energy tensor is frame-independent, but then go on to say "energy density (for every frame)". But either way, there must be a concept of a "total amount of energy" in order to show that energy is conserved? But this still doesn't explain what this negative energy hypothetically has and is doing. Aug 23, 2014 at 20:38
• @MatthewMitchell Energy density is just one of 16 components of the stress-energy tensor, and the value of that component can be different for different frames. Some tensors have that component be nonzero for every frame, so that every observer sees a non-negative energy density. The kind of conservation law (an integral law) where you have a total energy that is conserved is replaced in GR with a differential conservation law that just balances the flow of energy, so a negative energy density can flow into new regions just like a positive energy density can, but the total might not be defined Aug 24, 2014 at 5:54
• I think I clicked what you mean now. It doesn't matter what we consider energy as being negative or positive, because all that matters is the flow of energy, not the absolute value we choose to put on it. So objects close together could be considered to have negative gravitational energy, and this gets closer to zero as they move apart. But it also works if you consider the energy of close objects to have 0 energy and that energy goes up as they move apart? So the idea of absolute (negative or positive) energy doesn't matter, only the flow of energy matters. Am I right? Sep 2, 2014 at 20:54
• @MatthewMitchell In Newtonian Mechanics or in non-relativisitic Quantum Mechanics I might agree with you there. But in General Relativity it matters. It's more like how you can break spacetime into space and time, but a different person might break it up differently, or how you can talk about the x,y, and z components of momentum, but someone else might choose their axi in different directions and get different numbers. Everyone can agree that momentum flows into and out of regions and that the net flow of momentum in (versus out) increases the total momentum but the #s depend on your frame. Sep 4, 2014 at 2:32