# What is the energy density of spacetime?

• I
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## Main Question or Discussion Point

Vacuum or dark energy have energy densities. (Markus, a science advisor at Physics Forums in 2003, estimated that dark energy has an energy density of about 0.5 Joule per cubic km.) I assume that the structure of space-time has an energy density, that it was measured and that it can be calculated. How is it calculated? (I am not referring to the kinetic and potential energy of an asteroid moving in space-time.) The geometry of space-time functions like a field, but is not a field as the electro-magnetic field is. Is space-time energy density higher near a star than in deep space? (I am not referring to the strength of the gravitational force at these locations.) Is dark energy just an average of space-time energy? Space-time is a proven mathematical model for our universe, but there must be a physical reality an the quantum level.

• Kevin the Crackpot

PeterDonis
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I assume that the structure of space-time has an energy density, that it was measured and that it can be calculated.
You assume incorrectly.

As far as classical GR is concerned, spacetime has no energy density other than the cosmological constant aka dark energy.

Quantum mechanically, we don't know because we don't have a quantum theory of gravity, so we don't know how to quantize spacetime, or even if that idea makes sense.

You assume incorrectly.

As far as classical GR is concerned, spacetime has no energy density other than the cosmological constant aka dark energy.

Quantum mechanically, we don't know because we don't have a quantum theory of gravity, so we don't know how to quantize spacetime, or even if that idea makes sense.
I am probably misunderstanding the question, but I might have answered differently.

There is a 2.7° temperature left over from the Big Bang, and a certian amount of radio noise that reverberates through the Universe from the same event.

So, I answer the question as "How much energy from radio static from the Big Bang is there per cubic kilometer of space?

PeterDonis
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There is a 2.7° temperature left over from the Big Bang, and a certian amount of radio noise that reverberates through the Universe from the same event.
These are not two different things. They are the same thing. There is a cosmic radiation background which has a temperature of about 2.7 K, which corresponds to electromagnetic radiation in the radio wave (microwave) region of the spectrum.

I answer the question as "How much energy from radio static from the Big Bang is there per cubic kilometer of space?
Yes, this is a meaningful question, but this energy density is not the "energy density of spacetime". It's the energy density of the CMB radiation. The answer to the question is easily found by Googling.

• Kevin the Crackpot
PeterDonis
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There is a 2.7° temperature left over from the Big Bang
Also, strictly speaking, the CMB radiation is not left over from the Big Bang, it's left over from the "recombination" event that took place about 300,000 years after the Big Bang, when the ionized plasma filling the universe "recombined" into neutral atoms, making the universe transparent to EM radiation.

• Kevin the Crackpot
These are not two different things. They are the same thing. There is a cosmic radiation background which has a temperature of about 2.7 K, which corresponds to electromagnetic radiation in the radio wave (microwave) region of the spectrum.

Yes, this is a meaningful question, but this energy density is not the "energy density of spacetime". It's the energy density of the CMB radiation. The answer to the question is easily found by Googling.
Thank you.

Orodruin
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There is a 2.7° temperature left over from the Big Bang
Pet peeve: There is no temperature unit called °. The temperature units using ° are °C and °F. The temperature unit typically used for the CMB temperature is K (Kelvin), no degree. ° by itself is a unit for an angle.

• davenn and Kevin the Crackpot
Pet peeve: There is no temperature unit called °. The temperature units using ° are °C and °F. The temperature unit typically used for the CMB temperature is K (Kelvin), no degree. ° by itself is a unit for an angle.
Thank you. I meant to put 2.7°K, but I was using my phone at work when I wasn't supposed to, and had to hurry before getting busted by my boss.

Orodruin
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I meant to put 2.7°K
for the CMB temperature is K (Kelvin), no degree.
The correct way of putting it would therefore be 2.7 K, not 2.7 °K or 2.7°K. There is no unit called "degrees Kelvin", it is just "Kelvin".

• Kevin the Crackpot
kimbyd
Gold Member
tl;dr: Nobody really knows. All attempts to calculate the vacuum energy so far have produced ridiculous answers.

First, I'd like to point out that the cosmological constant isn't necessarily an energy density. In general relativity, it's basically just a parameter in the theory, like G which determines the strength of the gravitational force. In GR terms, the cosmological constant can be interpreted as determining how much space-time curvature exists when there is no matter or energy anywhere.

However that parameter is peculiar in that if you massage the equations to place the cosmological constant next to the matter part, it looks like a perfect fluid with constant energy density.

So, is it an energy density? There no way to know just yet. Maybe quantum gravity will make the answer more clear.

As for calculating the energy density, the simplest calculations give a value that's around ##10^{120}## times larger than the observed value of the cosmological constant. No satisfactory solutions to this have yet been produced.

• nnunn, Nik_2213 and KurtLudwig
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Is dark energy more dense near a star and towards the center of a galaxy?

PeterDonis
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Is dark energy more dense near a star and towards the center of a galaxy?
If it's a cosmological constant, no, it's the same everywhere. That's the simplest hypothesis right now given the data we have.

Orodruin
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First, I'd like to point out that the cosmological constant isn't necessarily an energy density.
However that parameter is peculiar in that if you massage the equations to place the cosmological constant next to the matter part, it looks like a perfect fluid with constant energy density.
I am curious what meaning you give to the term ”energy density”. If you call whatever appears in the RHS of the EFEs ”energy density”, then certainly the CC walks and talks like a duck if you place it on the RHS. Enough so that I would call it energy density.

• Lindsayforbes
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Since there is more "concentrated gravitational activity" near a star or near the center of a galaxy, I thought that there was also more vacuum energy in these volumes. I thought that energy content of space was an average, not necessarily the same at all locations. However, PeterDonis stated that it is a cosmological constant. I accept his answer.

Orodruin
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However, PeterDonis stated that it is a cosmological constant.
No he did not. Please do not misrepresent what people have said. He said that if it is a cosmological constant then the corresponding energy density is the same everywhere, and that it is the simplest hypothesis based on current data.

PeterDonis
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Since there is more "concentrated gravitational activity" near a star or near the center of a galaxy, I thought that there was also more vacuum energy in these volumes. I thought that energy content of space was an average, not necessarily the same at all locations.
You are conflating different concepts here.

Earlier, you asked if dark energy density was the same everywhere. But "dark energy" does not mean "cosmological constant", nor does it mean "vacuum energy" or "the energy content of space". "Dark energy" means "whatever it is that is causing the accelerated expansion of the universe". As I said, the simplest hypothesis based on our current data is that what is causing the accelerated expansion of the universe is a cosmological constant, i.e., "vacuum energy" or "the energy content of space". Any such thing must be a constant, the same everywhere, because the vacuum is the same everywhere. "Concentrated gravitational activity" due to the presence of a lot of mass doesn't change the nature of the vacuum; that would violate the equivalence principle, because any change in the nature of the vacuum would be detectable locally, i.e., on scales too small to detect any spacetime curvature due to the presence of matter.

However, there are other kinds of energy density which are not vacuum energy or "the energy content of space" which can also produce an accelerated expansion of the universe. An example often used for pedagogy is a scalar field. Such an energy density, since it is not "energy denstiy of the vacuum", does not have to be constant everywhere--for example, it could change in response to the presence of matter or "concentrated gravitational activity", and logically speaking, something like this could be causing the accelerated expansion of the universe and the energy density of the vacuum itself could be zero. We don't currently have any evidence for anything like this, but it's a perfectly consistent theoretical possibility.

• Bandersnatch and Ibix
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Thank you for your detailed explanations. Excuse me for mixing up words and concepts. I need to learn the precise meanings of cosmological terms.
I am about half way through reading "An Introduction to Modern Cosmology" by Andrew Liddle. It is the most interesting book which I have ever read. I working on clearly understanding the math presented in the book, which will take me sometime.

PeterDonis
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I am about half way through reading "An Introduction to Modern Cosmology" by Andrew Liddle.
I think this is a very good choice of textbook.

An example often used for pedagogy is a scalar field. Such an energy density, since it is not "energy denstiy of the vacuum", does not have to be constant everywhere--for example, it could change in response to the presence of matter or "concentrated gravitational activity", and logically speaking, something like this could be causing the accelerated expansion of the universe and the energy density of the vacuum itself could be zero. We don't currently have any evidence for anything like this, but it's a perfectly consistent theoretical possibility.
First, can you explain "pedagogy, is a scalar field". I have Wikipedia'd it but would ask you to expand.
Second, could you expand on what you meant when you said that it's a perfectly consistent theoretical possibility.

PeterDonis
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can you explain "pedagogy, is a scalar field".
I said a scalar field is an example often used for pedagogy, i.e., as a teaching aid.

could you expand on what you meant when you said that it's a perfectly consistent theoretical possibility.
I mean that, theoretically speaking, our observation that the expansion of the universe is accelerating could be explained by a scalar field as well as by a cosmological constant (aka "energy density of the vacuum"). The reason this theoretical possibility is not part of our current best-fit model of the universe is that we have no evidence that whatever is driving the accelerated expansion is different in different parts of the universe; as far as we can tell it is constant everywhere, meaning that a cosmological constant is the simplest possibility consistent with the data.

• nnunn