[jeffreyH (OP)]

The vacuum contains energy and presumably can have a density. Maybe not I don't know. Could the vacuum density have dropped dramatically during inflation and been relaxing into a lower density state ever since? Could this be the reason for expanding space? This would not require dark energy. Where is this idea wrong?

[PhysBang]

The idea is wrong because if the vacuum has a density, then that is dark energy.

Whether or not there has been a change in the energy density associated with the vacuum is an open question. Current cosmological projects are attempting to measure possible change in vacuum energy density.

[jeffreyH (OP)]

Thanks for the reply. It is much more than I expected. I had not considered the vacuum energy density as dark energy. It is something I have not investigated. Can you point me to any links on current hypotheses?

[jeffreyH (OP)]

This link is from 5 years ago but an interesting read.

http://www.astro.ucla.edu/~wright/cosmo_constant.html

[PhysBang]

This link is from 5 years ago but an interesting read.

http://www.astro.ucla.edu/~wright/cosmo_constant.html

That's pretty much where I would have pointed you.

[jeffreyH (OP)]

I'm posting a Baez page because I will be discussing parts of it later.

http://math.ucr.edu/home/baez/vacuum.html

[JohnDuffield]

The vacuum contains energy and presumably can have a density. Maybe not I don't know. Could the vacuum density have dropped dramatically during inflation and been relaxing into a lower density state ever since? Could this be the reason for expanding space? This would not require dark energy. Where is this idea wrong?

I think this is more or less right Jeffrey. It's like the balloon analogy, but with a bubble-gum balloon. I've written about this in various locations, see for example this. I said this:

...take a look at page 5 of http://arxiv.org/abs/0912.2678 where Milgrom mentions the strength of space. Think in terms of the tensile strength of space, and it's something like our balloon analogy, but for a 3D bulk. Then go back to Einstein, who introduced the cosmological constant to stop his universe collapsing. That was akin to a pressure, but the cosmological constant is described as a negative pressure. And negative pressure is tension. So in my humble opinion the cosmological constant is described as a tension, rather like the tension of the bag model. The tension is reducing, along with the energy density. And because the cosmological constant is "the value of the energy density of the vacuum of space", it isn't constant after all.

[jeffreyH (OP)]

On the page in the link above Baez gives 5 methods of attempting to calculate vacuum energy density. His choice is number one as is mine since it is backed up by observations and based on general relativity. So then there are still 4 other methods to consider. The four remaining methods give the following answers.

2 Infinity
3 Enormous but finite
4 zero
5 Not determined

The conclusion Baez reaches is that 2, 3 and 4 be rejected and to reconcile quantum field theory and general relativity we need to reconcile methods 1 and 5. This is where I believe he is wrong. It should be numbers 1 and 3 that we should be reconciling. Both are finite but the scales are radically different. More on this later.

[jeffreyH (OP)]

To start to see why I think baez is wrong I need to propose an upper limit on mass density. In his article for method 3 Baez assumed units of Planck mass per Planck length cubed. Instead we need to consider the density of the planck mass as its volume approaches its own event horizon. The radius of the horizon is 2 Planck lengths. In units of Planck lengths we have for the volume contained within the horizon 4/3*pi*rs^3. For rs we get a value of 2 in Planck units so that the expression becomes 4/3*pi*8.

Now read Sean Carroll on the role of pi in general relativity.

http://www.preposterousuniverse.com/blog/2014/03/13/einstein-and-pi/

[jeffreyH (OP)]

Since the point is to find the density as the volume approaches that of the horizon the radius will need to be set at 3 Planck lengths. This then gives 4/3*pi*27. It is this expression that should be used to calculate maximum mass/energy density. Once this is established then point 3 of the Baez article can be re-examined.

[jeffreyH (OP)]

In calculation method 3 in the Baez article the energy density of the vacuum equates to a value of the order of 10^96 kg m^-3. For a spherical volume with radius of 3 Planck lengths and the Planck mass our maximum density is 1.27*10^96. This means that the energy density of the vacuum calculated by quantum field theory describes the maximum vacuum energy density just after the big bang. The missing piece of the puzzle is how to go from that to the density we see in current observation.

[jeffreyH (OP)]

I have corrected an order of magnitude typo in the above post for maximum density. Now we can work backwards by plugging in the value for vacuum energy density found by observation and then calculate the radius needed for the Planck mass to have this density. We end up with a radius of 7.42*10^17 metres. That is a large radius. The next step would be to find the mass of a black hole whose density just before collapse into its event horizon equals the observed vacuum density.

[jeffreyH (OP)]

Looking at both the Carroll and Baez articles they are concerned with densities and fields in both quantum field theory and general relativity. There should be some mechanism to connect both to the vacuum energy density. Using mass density as illustrated above doesn't solve the problem. We can derive correct values for mass that equate to the vacuum values but there is a missing piece to the puzzle.