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Matter cools when universe expands. Where does that energy go to? I would expect that delta E = delta V (with some clear way to represent volume in Joules). Sh

Matter cools when universe expands. Where does that energy go to? I would expect that delta E = delta V (with some clear way to represent volume in Joules). Shouldn't dark energy density also fall?

deleted 2y ago
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pdonis 2y ago
> Matter cools when universe expands. More precisely, the energy density of matter decreases as the universe expands. > Where does that energy go to? Stress-energy density is locally conserved; there is no energy being created or destroyed. In fact that local conservation of stress-energy density is what requires the energy density of matter (which in cosmology-speak means a perfect fluid with zero pressure) to decrease as the universe expands (as the cube of the scale factor). > Shouldn't dark energy density also fall? No, because dark energy, considered as a stress-energy density, includes negative pressure equal to minus the energy density, and the same local conservation of stress-energy density I referred to above requires that in this case, the energy density is constant in both space and time. Note that the new findings described in the article amount to raising the possibility that what we thought was "dark energy", i.e., a cosmological constant with pressure exactly equal to minus the energy density (that is what w = -1, mentioned in the article, means), is in fact something else whose equation of state (relationship between pressure and energy density) can change over time, with pressure becoming less negative (w less negative than -1). If that is the case, the energy density would also be decreasing over time, though much more slowly than for ordinary matter.
- thriftwy 2y ago
  > In fact that local conservation of stress-energy density is what requires the energy density of matter (which in cosmology-speak means a perfect fluid with zero pressure) to decrease as the universe expands (as the cube of the scale factor). That makes total sense! Does this meak we know how much the total density of matter has to decrease in order for universe to expand one cubic meter? What's the energy equivalent of one new cubic meter of space, in Joules? Do we know that? Does it fit the observed matter density, with and without dark matter? It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process.
  - pdonis 2y ago
    > Does this meak we know how much the total density of matter has to decrease in order for universe to expand one cubic meter? It doesn't work that way. Remember that GR is a theory of spacetime geometry. When we say "the universe is expanding", that's really shorthand for "the spacetime geometry of the universe has a particular shape". It doesn't mean that the universe "adds cubic meters" over time. There is certainly a relationship between the density of matter (or more generally stress-energy density) and the geometric property that informally we refer to as "the rate of expansion of the universe". The equations that express that relationship are the Friedmann equations, which are just the Einstein Field Equation, the central equation of GR, specialized to the kind of spacetime geometry that "expanding universe" refers to. But it's not really useful to think of those relationships as saying that if the matter density decreases by this much, it makes the universe expand that much. > It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process. No, that's not a good way to look at it. A cosmological constant aka dark energy is best thought of as just an unusual form of perfect fluid whose pressure is minus its energy density. Then you just plug that into the Friedmann equations to get predictions for what we should expect to observe, such as "accelerating expansion".
    - thriftwy 2y ago
      I don't agree with you. Between us and a redshifted galaxy, for a specific cross-section "tube", there is a dV/dt of new space and a -dE/dt of energy from the redshift. It is possible to calculate both so at least the circumstantial "cubic metres for joules" metric is possible, and interesting. But it seems I'm not geting it out of this discussion. You were talking about stress-energy tensor, and it did sound like density decrease is linked to the volume increase in a mathematical sense so that conservation happens. Now you say they are not related in that way. If the density decrease is not linked to the volume increase then you have to explain where that extra energy went. "perfect fluid whose pressure is minus its energy density" does not make sense because you said it is expanding but keeping the same density. If a fluid is expanding but not becoming less dense, it wasn't a fluid in the first place. Unfortunately what I can see is lack of understanding the mechanism and being able to productively reason about that, and stress-energy tensor is sufficiently complicated abstraction that one no longer feels the discomfort of not understanding.
deleted 2y ago
[deleted]

Matter cools when universe expands. Where does that energy go to? I would expect that delta E = delta V (with some clear way to represent volume in Joules). Shouldn't dark energy density also fall?

deleted 2y ago

[deleted]

pdonis 2y ago

> Matter cools when universe expands. More precisely, the energy density of matter decreases as the universe expands. > Where does that energy go to? Stress-energy density is locally conserved; there is no energy being created or destroyed. In fact that local conservation of stress-energy density is what requires the energy density of matter (which in cosmology-speak means a perfect fluid with zero pressure) to decrease as the universe expands (as the cube of the scale factor). > Shouldn't dark energy density also fall? No, because dark energy, considered as a stress-energy density, includes negative pressure equal to minus the energy density, and the same local conservation of stress-energy density I referred to above requires that in this case, the energy density is constant in both space and time. Note that the new findings described in the article amount to raising the possibility that what we thought was "dark energy", i.e., a cosmological constant with pressure exactly equal to minus the energy density (that is what w = -1, mentioned in the article, means), is in fact something else whose equation of state (relationship between pressure and energy density) can change over time, with pressure becoming less negative (w less negative than -1). If that is the case, the energy density would also be decreasing over time, though much more slowly than for ordinary matter.

thriftwy 2y ago
> In fact that local conservation of stress-energy density is what requires the energy density of matter (which in cosmology-speak means a perfect fluid with zero pressure) to decrease as the universe expands (as the cube of the scale factor). That makes total sense! Does this meak we know how much the total density of matter has to decrease in order for universe to expand one cubic meter? What's the energy equivalent of one new cubic meter of space, in Joules? Do we know that? Does it fit the observed matter density, with and without dark matter? It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process.
- pdonis 2y ago
  > Does this meak we know how much the total density of matter has to decrease in order for universe to expand one cubic meter? It doesn't work that way. Remember that GR is a theory of spacetime geometry. When we say "the universe is expanding", that's really shorthand for "the spacetime geometry of the universe has a particular shape". It doesn't mean that the universe "adds cubic meters" over time. There is certainly a relationship between the density of matter (or more generally stress-energy density) and the geometric property that informally we refer to as "the rate of expansion of the universe". The equations that express that relationship are the Friedmann equations, which are just the Einstein Field Equation, the central equation of GR, specialized to the kind of spacetime geometry that "expanding universe" refers to. But it's not really useful to think of those relationships as saying that if the matter density decreases by this much, it makes the universe expand that much. > It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process. No, that's not a good way to look at it. A cosmological constant aka dark energy is best thought of as just an unusual form of perfect fluid whose pressure is minus its energy density. Then you just plug that into the Friedmann equations to get predictions for what we should expect to observe, such as "accelerating expansion".
  - thriftwy 2y ago
    I don't agree with you. Between us and a redshifted galaxy, for a specific cross-section "tube", there is a dV/dt of new space and a -dE/dt of energy from the redshift. It is possible to calculate both so at least the circumstantial "cubic metres for joules" metric is possible, and interesting. But it seems I'm not geting it out of this discussion. You were talking about stress-energy tensor, and it did sound like density decrease is linked to the volume increase in a mathematical sense so that conservation happens. Now you say they are not related in that way. If the density decrease is not linked to the volume increase then you have to explain where that extra energy went. "perfect fluid whose pressure is minus its energy density" does not make sense because you said it is expanding but keeping the same density. If a fluid is expanding but not becoming less dense, it wasn't a fluid in the first place. Unfortunately what I can see is lack of understanding the mechanism and being able to productively reason about that, and stress-energy tensor is sufficiently complicated abstraction that one no longer feels the discomfort of not understanding.

deleted 2y ago

[deleted]