Volovik has written a book ‘The Universe in a Helium Droplet ‘ (google-books) where he writes about these things. He is a condensed matter ph. and anti-GUT. p. 380 – 384.

Volovik has an inner observer (consciousness), vacuum energy density magnitude depends on (varying) Planck energy scale and the sign of the scale depends on the fermionic or bosonic content.

– without fermions (He4), only phonons we have zero point energy only for inner observer

– for bosons only (He3-A) liquid comes from Dirac vacuum of quasiparticles for inner observer.

Result: two Planck energy cutoffs, solutions very far from reality, huge disagreements with experiments.

Calculations of vacuum energy within effective field theory, results are

– dependant on cut-off procedure

– depends on the choice of the zero from which energy is counted; a shift in zero gives a shift in vacuum energy. Needs exact microscopic theory (TOE) for elimination (inkl thermodynamics).

The exact theory demonstrates that not just the low-energy degrees of freedom of the effective theory (phonons, Bogouliubov quasiparticles) must be taken into account, but all degrees of freedom of the quantum liquid, incl. Planckian and trans-Planckian domains. According to simple thermodynamic argument, the latter completely compensate the contribution for the two Planck energy cutoff from the low-energy domain.

Nullification of vacuum energy only for liquid-like states (isolated), gas-like need an external pressure, to be const. -> vacuum energy >0. But this non-zero energy is NOT GRAVITATING if the vacuum is in equilibrium.

So the vacuum STABILITY gives the solution. Vacuum stability and classic physical stability. What is needed is stationarity of vacuum energy with respect to small linear perturbations. -> the problem of cosmological constant vanish by stability in quantum vacuum, why it respect gauge invariance and Lorentz covariance + general covarians for emergent gravitons. The principles of a non-gravitating vacuum and of zero vacuum energy + Fermi point universality could be of this kind.

About the cosmic coincidence problem: why is c.c. of order of the present mass in expanding Universe? p 384

Einstein: vacuum energy density constant in time, dark matter energy density decrease; today dark matter energy = vacuum/2-3 The visible ordinary matter within this is in the fraction of simple noise.

Perturbations disturb the balance of zero value of vacuum energy in quantum liquid -> vacuum pressure and energy will respond prop. to perturbations, which can be:

-.the non-zero energy density of the matter in the Universe; Casimir effect give non-zero pressure -> surface tension gives distortion of atoms in the surface layer; cosmological horison (R) vacuum energy connected to the energy of Higgs condensate in electroweak phase transition.

– non-zero temp of the background radiation

– spacetime curvature

– time dependance caused by expansion of universe

– some long wavelength fields

– quintessence; partial pressure induced by surface tension related to the wall boundary or tangled networks.

– etc.

These all factors can be seen as dissipation, decoherence. I’m happy to see a novis like me is not wrong 🙂 But this is an anti-GUT theory.

The condition in GR was an closed universe. Is it so? No?

Another thing I realized: gravitons are only a gauge force, like gluons. No particle will be found?

This clearly says that gravity is only a part of DE?

]]>(a’/a) = 8πGρ/3

for a’ = da/dt. The solution for a constant value of density is easy to solve

a’ = sqrt{8πGρ/3}a

and so a = exp(sqrt{8πGρ/3} t}. This is the exponential expansion of the universe observed. During inflation the density of the vacuum ρ was larger than the QCD vacuum energy density inside a hadron, and so the exponential inflation was enormous. So this is the result of gravitation. It is just that the equation of state is such that the pressure p = -ρ. This can be seen from the basic equation pV = NkT = E. This leads to

V(dp/dV) = -ρ.

So the upshot is the dark energy is an aspect of gravitation. It is just a bit different from ordinary configurations seen with gravity.

]]>The superconductive state. ]]>

I wanted to point to the many unsolved questions. So this equation of yours is also very unsolved and speculative 🙂 but this discussion is still good.

You wanted to keep this discussion in GR, but now it is firmly linked into the vacuum energy and cosmological constant. And that is quantum world. In GR we have four dimensions, in quantum world we have many more (I don’t want to say how many), and they also should have some energy? Say Higgs potential, how is it seen in the dark energy as seen in gravitational lensings? Could it be only a gravitational field? The “Grid” is gravitation, also seen as the geometry of empty space? What kind of geometry has the Planck scale, and beyond? Microwave background?

How can a gravitational field bend light? By gravitation, of course. So gravitation invoke on light, but light has a constant speed? This equation is not true.

What is interesting in this is the relation of gravity to the dark energy/cosmological constant (72% today). But gravity is coming from the Planck scale and is manifest only in 4-D? That makes gravity to a very vast field of energy, can it be so, really? Or is gravity coming from a part of DE only? In that case gravity should be used as energy source (perpetum mobile?) But gravity has also a quantum aspect, and it must be holistic (information) and highly negentropic (entangled). It can’t be repellation? Because the expansion is negative adiabatic pressure without energy-input. A repellation needs energy?

This leads to your next condition. You said: “However, at the level of classical general relativity with a cosmological constant (where entropy is just about heat which is explained by the kinetic theory and black holes have no detectable temperature or entropy) the conservation of energy does not require entropy to be taken into account.”

According to what I have said entropy is not only about heat. Heat is a consequence of dissipation, and decoherence. The real axis is decoherence – coherence, and so we have again a coherent quantum world. In GR it is decoherence. Your sentence “conservation of energy does not require entropy”, may be totally false. This also explains why Ervin was wrong 🙂 I still wait for his comment.

I also come back to Sakharov. Maybe a simpler solution exist?

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