# Expanding universe

Could the accelerating rate of the expansion of the universe be due to the conversion of potential energy to kinetic energy?
At the early stages of the big bang there would be tremendous amounts of potential energy (because it was so compressed). As it expanded, the universe, by the conservation of energy, would convert from mainly potential energy to kinetic energy.
Because energy is the ability to work and work is a force quantity, if there was potential energy being constantly converted into kinetic energy force would be added. Forces accelerate, thus the universe would accelerate as it is being acted upon by the constantly additional kinetic energy.

Chalnoth
Nope. At least, not in this way.

For the most part, potential energy is not used at all in General Relativity. It isn't all that useful of a concept, because there is no unique way to define total energy. And if you can't define total energy, how can you conserve total energy?

That said, while it is true that there is no unique way to define total energy, there are ways to do it in certain, special cases. Such as a uniformly expanding closed universe. And what you get in such a universe is that the total energy is zero: the potential energy is equal to the energy in the matter fields, but has a negative sign. What happens with the accelerated expansion is you always get a negative gravitational potential energy to balance out the dark energy. This is known as the Hamiltonian formalism of General Relativity, and it isn't commonly used. It's one way to think about the universe.

But it's just as valid (in some ways more valid) to simply point out that energy is not conserved in General Relativity. It can't be, because General Relativity blurs the line between space and time, and you can only get energy conservation if your system does not change in time (in a particular mathematical sense). But since time is no longer just a parameter, but an active participant in how General Relativity operates, it's just not possible to always conserve energy.

• julcab12 and J7H18
ChrisVer
Gold Member
I think the expansion of the universe is a result of isotropy and homogeniety ...
It's those two assumptions that lead to the FRW metric which contains the scaling factor and so the expansion of the universe. Also it can explain why the expansion itself, and the acceleration, occurs at a cosmological scale [humans are not expanding].
The acceleration occurs because of the energy density the universe contains. The universe could be as well decelerating without a "problem" (except for observational ones )...

What you are saying might just be correct,but it could be that the universe is not expanding at all!!! It could be that the space between us is shifting by itself.

Doug Huffman
Gold Member
Do you understand that normative and prescriptive statements, characterized by would, should and could, have no inherent truth value? Further, that a universally true statement, A=A, a tautology, conveys no information. A good error is more informative than a bad question.

• progyan
That's true.:s

PeterDonis
Mentor
I think the expansion of the universe is a result of isotropy and homogeniety ...
It's those two assumptions that lead to the FRW metric which contains the scaling factor and so the expansion of the universe.

Isotropy and homogeneity by themselves aren't enough to derive expansion. The FRW metric itself does not tell you whether the scale factor is increasing or decreasing with time. (It can even be constant in time if you have a cosmological constant with just the right value--that's the Einstein static universe, which is a particular FRW solution. It's unstable, like a pencil balanced on its point, but it's still a valid solution.) We use an expanding FRW solution in cosmology because we observe the universe to be expanding.

Also it can explain why the expansion itself, and the acceleration, occurs at a cosmological scale [humans are not expanding].

The FRW metric doesn't really explain this either, because it doesn't describe objects on the scale of humans, or even on the scale of individual galaxies. In the FRW metric, the universe is filled with a continuous fluid. This is obviously an idealization and is not intended to be an exact description, but the fact remains that in this model, every individual parcel of the fluid is expanding; there is no description of small-scale objects that do not expand. To explain why humans (and planets and stars and solar systems and galaxies) are not expanding, you have to use a different model, one that includes the local physics of these systems.

ChrisVer
Gold Member
Isotropy and homogeneity by themselves aren't enough to derive expansion. The FRW metric itself does not tell you whether the scale factor is increasing or decreasing with time. (It can even be constant in time if you have a cosmological constant with just the right value--that's the Einstein static universe, which is a particular FRW solution. It's unstable, like a pencil balanced on its point, but it's still a valid solution.) We use an expanding FRW solution in cosmology because we observe the universe to be expanding.

The general FRW metric contains the scale factor as being a function of the time coordinate. The thing is that this scale factor in the metric exists because of the homogeneity and isotropy of the universe - a dust cloud [these are the assumptions that let you build the FRW metric]. Now there is also a special case where the scale factor is just a constant. This is obtained by solving the Friedmann equations [which are the natural result of applying the EFE on the FRW metric]. The main differences appear only after you start taking into account the energy densities of your "dust cloud" , and where the cosmological constant comes into use.

For me humans don't expand because the expansion occurs only when FRW model is applicable, that is in cosmological scales where you can indeed use the isotropy and homogeiniety. These things are not true for the local systems [I don't know how to justify this correctly], because I guess, when I look on my left and on my right I don't see myself again.

As for the universe being a fluid, well... you can apply perturbative methods on the FRW metric, so it seems that the last is indeed a very good approximation - as good an approximation as the approximate assumption of Universe being isotropic [as measured in CMB]. If you look at an anisotropic object, such as a galaxy, the FRW is no longer good in explaining the mechanisms and so you can't apply an expansion over the galaxy...

PeterDonis
Mentor
The general FRW metric contains the scale factor as being a function of the time coordinate. The thing is that this scale factor in the metric exists because of the homogeneity and isotropy of the universe

Yes, agreed. But this by itself does not tell you how the scale factor varies with time. So you can't say that expansion is a "result of isotropy and homogeneity", because those two things together don't necessitate expansion; they tell you there's a scale factor, but they don't tell you how it changes with time.

humans don't expand because the expansion occurs only when FRW model is applicable

I think there's something true that you're trying to say here, but you're not saying it right. As you say it, it's clearly false; the FRW model is by no means the only solution to the Einstein Field Equation which shows "expansion". See below for a better way to say the true thing that I think you are trying to say.

These things are not true for the local systems [I don't know how to justify this correctly], because I guess, when I look on my left and on my right I don't see myself again.

Homogeneity and isotropy are not true for local systems because they are not the same everywhere and in all directions, yes. For example, if we idealize the Earth as a spherically symmetric isolated system, it clearly has a definite "center", a particular point in space that is different from all other points; and it clearly has a "radial" direction (toward or away from the center) which is different, physically, from the tangential directions. The model we use to describe this, which I'll call a "spherical mass" spacetime, reflects these physical facts by not being homogeneous or isotropic--it is spherically symmetric, but only about one point (the center).

So we could say that the Earth doesn't expand because it's described by the spherical mass spacetime, not FRW spacetime. This is similar to the statement you made that I quoted above. But it's backwards. What we should say is that the spherical mass spacetime describes the Earth, and FRW spacetime does not, because the Earth is not expanding. Just saying which spacetime describes the Earth does not tell us why that spacetime describes the Earth, and so doesn't tell us why the Earth is not expanding.

To see why the Earth is not expanding, we have to look at why it is well described by the spherical mass spacetime, which is static. The reason for that is that the Earth is gravitationally bound: its own self-gravity is sufficient to hold it in a static equilibrium, given the initial conditions that created it. (Those initial conditions, if we trace them back, ultimately depend on there being local fluctuations in the expansion of the universe which allowed gravitational clumping. See further comments below.) Similar remarks apply to a human, except that what holds a human together in "static" equilibrium (I put "static" in quotes here because humans, like all living things, are highly dynamic systems, but hopefully you see what I mean) is not the human's self-gravity but electromagnetic binding forces between the atoms making up the human.

The universe, by contrast, started out in an initial condition that prevented it from ever reaching a static equilibrium as a whole. (As I noted above, local fluctuations in the expansion allowed local regions to gravitationally clump into systems that could maintain a local static equilibrium.) That physical fact is why we have to use a different solution to the Einstein Field Equation, FRW spacetime, to describe the universe.

• ChrisVer