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What I'd like to know:

  1. The mass-energy from S.R and used in the energy tensor part of the field equation gives the source of gravity. Therefore does the vacuum energy source gravity too?

  2. Imagine a distant part of space say between our galaxy and Andromeda where the gravity is weak and theres not much matter. Suppose by chance a cubic metre was free of any matter or EM radiation by chance. Would that cubic metre be filled with the zero vacuum enegy?

  3. Given that the universe is expanding does the vacuum energy under the conditions described in (2) remain constant? and does the cubic metre of vacuum energy expand with the universe?

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If I understand your question correctly you are referring to the cosmological constant problem. Quantum field theory tells us that the vacuum state should have an energy called the zero point energy. In QFT the presence of this energy doesn't matter since we can only measure energy differences, however in general relativity the absolute value of the energy matters since that is what goes into the stress-energy tensor.

The problem is that however we calculate the zero point energy it comes out vastly greater than is compatible with observation. The naive calculation predicts a value for the cosmological constant $10^{120}$ times too high. Other calculations can reduce the discrepancy but it remains absurdly large.

The conclusion has to be that the zero point vacuum energy does not gravitate otherwise we wouldn't be here. Why it doesn't gravitate is an open question.

Re your last question: the zero point energy density does not dilute as spacetime expands i.e. the energy density remains constant. It is this behaviour that means it has a negative pressure and hence causes accelerated expansion.

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  • $\begingroup$ Does the density remain constant per cubic metre since the measurement ruler also expands with the universe OR it does not dilute because simply more energy per cubic metre comes from somewhere and the absolute (if there was such a thing say very low speed where S.R can be ignore) cubic metre there is more energy available causing the negative pressure. Is one of these two assertions correct or are they both wrong? $\endgroup$ – onepound Sep 12 '16 at 20:00
  • $\begingroup$ @onepound: The vacuum energy doesn't dilute because as the universe expands energy appears from nowhere. In an expanding universe energy isn't conserved. Well, whether or not energy is conserved is a controversial issue because it depends on how you define energy. However the vacuum energy isn't conserved - as the universe expands more vacuum energy just appears. $\endgroup$ – John Rennie Sep 13 '16 at 4:10

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