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## Vacuum energy density and Hubble expansion

This may be a simple question but I didn’t found anything in my references: the vacuum energy density is a constant value, which depends on the virtual excitations of the quantum fields. If the universe expands, increases its volume, and the vacuum energy density remains is constant, does this mean (asuming energy conservation) that an additional input of energy is needed to maintain the vacuum energy density?

Thanks.
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 Originally posted by hellfire If the universe expands, increases its volume, and the vacuum energy density remains is constant, does this mean (asuming energy conservation) that an additional input of energy is needed to maintain the vacuum energy density?
http://nedwww.ipac.caltech.edu/level5/Guth/Guth3.html

skip down to "Physics of the False Vacuum":

 In the inflationary theory the Universe begins incredibly small, perhaps as small as 1024 cm, a hundred billion times smaller than a proton. The expansion takes place while the false vacuum maintains a nearly constant energy density, which means that the total energy increases by the cube of the linear expansion factor, or at least a factor of 1075. Although this sounds like a blatant violation of energy conservation, it is in fact consistent with physics as we know it. The resolution to the energy paradox lies in the subtle behavior of gravity. Although it has not been widely appreciated, Newtonian physics unambiguously implies that the energy of a gravitational field is always negative a fact which holds also in general relativity. The Newtonian argument closely parallels the derivation of the energy density of an electrostatic field, except that the answer has the opposite sign because the force law has the opposite sign: two positive masses attract, while two positive charges repel. The possibility that the negative energy of gravity could balance the positive energy for the matter of the Universe was suggested as early as 1932 by Richard Tolman, although a viable mechanism for the energy transfer was not known. During inflation, while the energy of matter increases by a factor of 1075 or more, the energy of the gravitational field becomes more and more negative to compensate. The total energy - matter plus gravitational - remains constant and very small, and could even be exactly zero. Conservation of energy places no limit on how much the Universe can inflate, as there is no limit to the amount of negative energy that can be stored in the gravitational field. This borrowing of energy from the gravitational field gives the inflationary paradigm an entirely different perspective from the classical Big Bang theory, in which all the particles in the Universe (or at least their precursors) were assumed to be in place from the start. Inflation provides a mechanism by which the entire Universe can develop from just a few ounces of primordial matter. Inflation is radically at odds with the old dictum of Democritus and Lucretius, "Nothing can be created from nothing" If inflation is right, everything can be created from nothing, or at least from very little. If inflation is right, the Universe can properly be called the ultimate free lunch.
 Blog Entries: 9 Recognitions: Science Advisor Does this mean that this mechanism applies also after inflation?

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## Vacuum energy density and Hubble expansion

Hm, may be the question was not so simple...?

Let me try to formulate it from another perspective.

The vacuum energy density remains constant, since it does not depend on any cosmological parameter, but only on quantum mechanical parameters. This means that, when the volume of the universe is growing, the vacuum energy grows and, therefore, there must be any kind of compensation to account with energy conservation.

If this has to be done by the gravitational potential of the masses/energy contained in the universe (as it was done during inflation), this would mean that the gravitational potential is becoming more and more negative.

But with the current cosmological model, the universe will expand forever and will end in a thermal death.

In this state there are free elementary particles in space, which are not supposed to be bound to any kind of potential and their sepparation to any other particle will tend to infinite.

This means that their gravitational potential will tend to zero.

 Originally posted by hellfire Hm, may be the question was not so simple...? Let me try to formulate it from another perspective. The vacuum energy density remains constant, since it does not depend on any cosmological parameter, but only on quantum mechanical parameters. This means that, when the volume of the universe is growing, the vacuum energy grows and, therefore, there must be any kind of compensation to account with energy conservation. If this has to be done by the gravitational potential of the masses/energy contained in the universe (as it was done during inflation), this would mean that the gravitational potential is becoming more and more negative. But with the current cosmological model, the universe will expand forever and will end in a thermal death. In this state there are free elementary particles in space, which are not supposed to be bound to any kind of potential and their sepparation to any other particle will tend to infinite. This means that their gravitational potential will tend to zero. Contradiction? Please some comments. Thanks.
The Negative Energy Density relates to Lambda. In Eiensteins original workings he tweaked the Cosmological data to fit the Steady State model. He maintained that there should have been a counteractive componant in opposite to Gravatational Atractive forces, this was quite unusual for everybody to understand at the time, even Einstein hated it!

The re-evaluation of the Cosmological Constant term which Einstein tweaked, has been fused into the 'Electromagnetic-Vacuum-Energy Density', or Gravitational Repulsive force. This has been leading to a number of great breakthroughs in the Understanding of how the dynamics of the Universe evolve.

But the problem was thought to be an inflationary problem, Guth maintained that the precise equations were so much of a precise order(I believe it is about 15 decimal places) that it had to be incorrect. The initial condition for this remarkable outcome was not the fact of observation, but the initial condition was an artifact of the numbers(mathematical input) needed to resolve the flatness problem.

This is a "correspondance paradox", if you try and create a model from the 'top down', then it will turn out completely different from a model created 'down-up'.

Quote:If this has to be done by the gravitational potential of the masses/energy contained in the universe (as it was done during inflation), this would mean that the gravitational potential is becoming more and more negative.

The Grav Pot is reversed at the moment of Big-Bang, the VSL models project that there is no 'slow-roll' from inflation, but infact quite the opposite. The Constancy of Light is currently reducing, and the Vacuum Density is Exponentionally increaseing. This has been linked to the Inflationary model(the Vacuum Expansion density IS inflation!).

The interesting thing is that from the Vacuum Potential, it can create MATTER! there is a exchange of Vacuum to Matter. As you state, the photon depletion in current models show that the the Heat-death, will not be reached, as at a certain volume, there will occur a collapse, and the conversion of Matter-Antimatter can take place(the anti-matter here is technically the potential), and a new Galaxies emerge from this area.

There is another thing that needs to be taken into account, and this relates to the early condensed state of low-energy systems, for a background of low-energy photons, the trigger mechanism for the collapse of a 'high-vacuum-density' is quite intruging!

 Originally posted by hellfire This may be a simple question but I didn¡¯t found anything in my references: the vacuum energy density is a constant value, which depends on the virtual excitations of the quantum fields. If the universe expands, increases its volume, and the vacuum energy density remains is constant, does this mean (asuming energy conservation) that an additional input of energy is needed to maintain the vacuum energy density? Thanks.
Ok I need to place this here:http://uk.arxiv.org/PS_cache/hep-th/...12/0312099.pdf

Just found this today 16th Dec.

Just an extract from the paper:For IR ¡_ H0, today¡¯s Hubble scale, we have −1 UV ¡_ 1000 km, which is much larger
than the distances to which we have probed gravity. Roughly speaking, this happens because gravity is being coupled to a sector that is sick in the limit as gravity is turned off (MPl ¡æ ¡Ä). The ¥ð¡¯s have no kinetic term in this limit, even though they
have cubic and higher order self-interactions. The theory only becomes tenuously healthy due to the coupling with gravity: mixing with gravity generates small kinetic terms for ¥ð of the correct sign (in flat space), but leads to strong coupling physics at
low energies. This does not necessarily mean that massive gravity or the DGP model cannot describe the real world, only that it appears necessary to make nontrivial assumptions about the UV completion of the theory.

I have to go over the paper again, as I am inquiring to the meaning of this quote:The ¥ð¡¯s have no kinetic term in this limit, even though they have cubic and higher order self-interactions. The theory only becomes tenuously healthy due to the coupling with gravity: mixing with gravity generates small kinetic terms for ¥ð of the correct sign (in flat space), but leads to strong coupling physics at low energies.

I do not know of the status of the Authors, but at first reading the paper seems to be a robust and very interesting paper, I am going to delve into this for some time.
 Blog Entries: 9 Recognitions: Science Advisor Ranyart, thank you for your answers, but these are too difficult for me. I’m just a beginner in cosmology as well as in GR and in QM and things like Higgs or VSL theories are rather unknown to me. I assume that the following assertion: vacuum energy density is constant and therefore the vacuum energy grows as the universe expands, is correct. So, IMHO, there are two possibilites to resolve the contradiction in my reasoning: A. there is no need for a compensation by the gravitational potential, i.e. conservation of energy does not apply for the universe as a whole. (I remember I read something like that, but my GR background is poor). In such a case I would wonder about the meaning of the text posted by Ambitwistor. B. The compensation is not done by the gravitational potential of the masses in the universe, but may be the vacuum energy itself produces a gravitational potential which compensates its energy density (may be this is senseless). Note that the vacuum energy is not negative but it has a negative pressure (i.e. a state equation rho = - P). Have a nice day.
 This quote:I assume that the following assertion: vacuum energy density is constant and therefore the vacuum energy grows as the universe expands, is correct. This is not where I stand, formally one can ascert that there is more Vacuum points than Matter points, therefore the Vacuum Energy Density is increasing when compared to the Matter density. One has to think of Matter creation within the early Universe, and Galactic formation at later times, The Vacuum Energy Density provides a background, and thus the density cannot be constant, Galactic formation is an on-going dynamical 'out-put', caused by the Dynamical increase in the Vacuum Energy density,'in-put'. The vacuum energy increase's over time, compared to the Matter Energy density which wane's over time, (actually the Vacuum Density overtakes the matter energy density, as it has a much shorter time-scale evolution, ie;accelerations).

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