Does a field's vacuum density violate conservation of energy?

  • #26
PeterDonis
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The redshift mechanism reduces the kinetic energy of a electron, too, when it moves in an expanding universe.
If the electron is moving at relativistic speed relative to comoving observers, yes. But the number of electrons that were doing that for the vast majority of the universe's history were negligible. "Cold" matter, i.e., matter that is at rest relative to comoving observers, does not redshift as the universe expands.

What about a scalar field which some people claim, is causing the acceleration of the expansion right now?
We don't know that it is a scalar field. A cosmological constant, which is the simplest explanation for accelerating expansion, is not a scalar field; it's just a constant.

a field whose energy increases in an expanding universe is "exotic matter"
Correct.

It is highly speculative to assume that such matter could exist.
No, it isn't. We already know of one scalar field: the Higgs field. We also know that quantum vacuum fluctuations are exotic. And we know that only something with the characteristics of exotic matter (which includes a cosmological constant--that is also exotic) can account for accelerating expansion. So given that we observe accelerating expansion, we have no choice but to believe that something exotic exists.

What about the energy content in the hypothetical scalar field? Is that energy contained in quanta of some kind? If yes, does the number of such quanta increase as the universe expands?
Not as long as there are no interactions, which was the condition you imposed on the other fields. In the absence of interactions, the number of quanta is constant for any field.

The question is harder in a strongly interacting system
In a strongly interacting system, the number of quanta does not have to be constant. But you said earlier you wanted to ignore interactions. Which is it? And if you don't want to ignore interactions, what interactions do you think are happening in the vast empty regions of our expanding universe?

The hypothesis that a scalar field can grow its energy in an expanding universe is highly speculative.
No, it isn't. It's an obvious consequence of the stress-energy tensor for scalar fields plus the absence of interactions.

Literature seems to ignore the fact that the hypothetical scalar fields in inflation and dark energy would be exotic matter
You really should read the literature before making such a claim.
 
  • #27
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https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model
The Higgs lagrangian contains the term which is quartic (fourth power) on the Higgs field strength. I would say the Higgs field interacts strongly with itself.

The question which I posed in my previous post: how does such a field behave in an expanding universe? Is it possible that the energy of the field might grow?

Specifically for the Higgs field: assume that we have excited the field so that it is no longer in the lowest energy point. Would the energy of the field grow when space expands? If yes, then there is a huge negative pressure present. Can that negative pressure accelerate the expansion of space locally? Can it even create a new "bubble universe"?
 
  • #28
PeterDonis
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I would say the Higgs field interacts strongly with itself.
"Strongly" is subjective; the quartic term is simply the lowest order interaction term possible for a scalar field, and how "strong" the interaction is depends on the coupling constant, not the order of the term.

assume that we have excited the field so that it is no longer in the lowest energy point
Doing that in a brief experiment in the LHC is not at all the same as doing it throughout the entire universe. Averaged over the universe, any field will be very, very close to its ground state, and how far it departs from the ground state will be measured by a temperature. For example, the temperature of the CMBR is 2.7 K.

Would the energy of the field grow when space expands?
You can read off the answer to this from the stress-energy tensor, as I said in my previous post. Basically, if you have a stress-energy tensor of perfect fluid form, and there is a positive energy density ##\rho## and a pressure ##p \le - \rho / 3##, then the field will cause accelerated expansion and the "energy" of the field will grow as the universe expands. A scalar field has ##p = - \rho##, just as a cosmological constant does; the only difference is that a cosmological constant means ##\rho## and ##p## are the same everywhere in spacetime, whereas for a scalar field ##\rho## and ##p## can vary.

Can that negative pressure accelerate the expansion of space locally?
See above.

Can it even create a new "bubble universe"?
I don't know where you're getting this from; accelerated expansion has nothing whatever to do with "bubble universes".
 
  • #29
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The logic goes like this:

Suppose that we have a box full of a matter field.

If the energy of the field inside the box grows as the box expands,

THEN

we say that there is negative pressure in the box.

For positive pressure, the field energy inside decreases as the box expands.

The question is if there can exist a matter field whose energy grows as space expands. That is the question I am looking at. Cosmologists seem to take for granted that a scalar field can grow its energy as space expands.
 
  • #30
PeterDonis
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The logic goes like this:

Suppose that we have a box full of a matter field.

If the energy of the field inside the box grows as the box expands,

THEN

we say that there is negative pressure in the box.

For positive pressure, the field energy inside decreases as the box expands.
Applying this to an expanding universe is based on a heuristic (and often misleading) analogy between "space expanding" and the expansion of a fluid in a box in flat spacetime.

Cosmologists seem to take for granted that a scalar field can grow its energy as space expands.
No, they don't "take it for granted". As I said, they look at the stress-energy tensor of the scalar field and read off the (positive) energy density and (negative, with equal absolute value) pressure from it.
 

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