Tuesday, May 20, 2014

Spacetime Expansion (i.e. Dark Energy) is due to the production of Quantum-Degenerate Active Neutrinos

(Note: Aug 14 2015:   I no longer find my argument regarding light neutrinos as dark energy convincing. I think that I was trying to find a connection between the fact that the energy density of dark energy is roughly (2 meV)^4, and this value is close to the value of the lightest neutrino.

Even though I don't agree with my arguments regarding dark energy, I have kept this page up to show my thinking at that time...and because there are a number of discussions about warm dark matter. As of Aug 2015, warm dark matter is still looking like a better explanation than cold dark matter.
As for light neutrinos bring dark energy. the problem is that fermi degeneracy pressure is positive. In order to explain why the Hubble expansion rate is reaching a positive, constant value. One needs to include a form of energy in which the pressure is negative, and with an equation of state of roughly the following: pressure = -1 * energy density. Instead, the equation of state for decaying dark matter into relativistic particles is the following:     pressure = 1/3 * S(a) * energy density
where S(z) is like the sigmoid function...it goes from a value of zero at small size, a, to a value of 1 at large size, a.

Also, I found a paper written in April 2015 that models dark matter decaying into relativistic matter...such as light neutrinos. http://arxiv.org/pdf/1505.05511v1.pdf
There are some tight constraints on this model. For example, the decay rate of the dark matter to relativistic species would have to be <0 .015="" an="" average="" decay="" gyr="" i.e.="" of="" time="">70 Gyr...which then makes it hard to explain why so much has happened in the first 13 Gyr.)
Original post from 5/20/2014
I'd like to summary what I've been trying to put into words over the last few years at this site. This article is still in rough draft form, and I will likely be editing it over the next few weeks as I improve the main argument.

Dark energy is not actually actual energy. Dark energy is just the expansion of spacetime because matter (mostly keV sterile neutrinos dark matter) is slowly turning into active neutrinos, which are relativistic & quantum degenerate.

Assuming that the rest mass of lightest active  neutrino is 0.001 - 0.06 eV and assuming that their temperature right now is 2 Kelvin, then their de Broglie wavelength is between 0.3 mm and 2 mm.

Also, using estimates for the electron neutrino density of 60-200 per cubic cm,  the average spacing between electron neutrinos is between 1.7 and 2.5 mm. These two numbers are extremely close to each other, which means that the lightest neutrino is quantum Fermi-degenerate, i.e. you can't pack more into a region than given by their de Broglie wavelength cubed. (Just as you can't pack more electrons into a metal than its de Broglie wavelength cubed, without increasing its temperature.)

The pressure of a relativistic Fermi quantum gas is only a function of the number density of fermions. The pressure (in units of mass per volume) is proporitonal to planck's constant divided by the speed of light, all multipled by the number density to the 4/3rd power. By starting with the density of dark matter at the recombination time (z ~ 1100), and assuming that the number of light neutrinos that can be created from a heavy neutrino is equal to the ratio of their rest masses, then I estimate a degenerate pressure of 10^-30 grams per cubic cm. This number is surprisingly close to the current mass density of dark matter (~5*10^-30 grams per cubic cm) and is only a factor of 10 less than the required dark energy pressure of 10^-29 grams per cubic cm. This means that with a few(somewhat) minor tweaks to my calculations, I could derive the dark energy "pressure" from the equations of relativistic, quantum degenerate neutrinos. (Note: here's a link to an article saying that relativistic, quantum degenerate neutrinos can't be the source of dark energy because the pressure is way too low. However, in that article, they assume a rest mass of the neutrino of 0.55 eV and don't assume that neutrinos can be generated from dark matter. When you change the rest mass to ~0.01 eV and include other sources of neutrinos from the decay of dark matter into many light neutrinos, then the quantum degeneracy pressure of neutrinos is large enough to explain dark energy. To be clear, my argument rests on a still on proven statement:  that a ~2 keV sterile neutrino can slowly convert into ~10^5 active neutrinos of ~0.02 eV rest mass. If this statement is true, then we can explain why neutrinos have mass, what is dark matter, and what is dark energy.)

So, if dark matter can slowly turn into active neutrinos over time, then dark energy might just be the quantum degeneracy pressure of relativistic, quantum degenerate neutrinos. I'll continue in the rest of this post to make this argument stronger.

During the Big Bang, there would be a large amount of active neutrinos produced, and then some more would be produced as sterile neutrinos (i.e. dark matter) slowly converts/oscillates into light active neutrinos. Spacetime expands as active neutrinos are generated because it can't be any smaller than that which would be required to keep the de Broglie wavelength cubed times the number density less than 1.

As seen in the image below, there is stringy areas and clumpy areas. It is entirely possible that the stringy areas are regions in which the dark matter is mostly light neutrinos (formed after recombination via break down of heavier, sterile dark matter) and the clumpy areas (i.e. galaxies) are regions that mostly hold the keV sterile dark matter. What is keeping the whole universe from collapsing might be the quantum degenerate pressure of the lightest active neutrino.

If quantum neutrino degeneracy holds, then this basically rules out the Big Crunch because the universe can't get any smaller than it is today...because more and more electron neutrinos are being generated as we speak. (Some are generated from the inside of stars and some from the oscillation of dark matter into active neutrinos.) It also would mean that there's no Big Rip because the universe will stop expanding when all energy has converted into active neutrinos. This is the state maximum (permutation) symmetry. This is the state of maximum entropy. You can't get any larger in entropy once all entropy is converted into light, active neutrinos. Since the bulk of the entropy of the universe would be carried by the light neutrinos, we can say that the entropy of the universe is proportional to its volume, which is increasing as the number of light neutrinos is increasing.

The reason that dark energy appears to be a constant is simply due to the fact that there are still so many sterile neutrinos, which are likely the main source of active neutrinos. Though, there are other sources of active neutrinos (such as within stars.)

This is what I mean when I've previously said that gravity (i.e. the density of mass) tells us the curvature of spacetime, whereas the weak nuclear force tells us how much the universe expands. The weak nuclear force works in one direction, which is why on average we are expanding. More and more active electron neutrinos are being generated, and they are being generated only by the weak nuclear force. (E&M, gravity, and strong nuclear force have nothing to do with the generation of neutrinos.)

Note:  it's the Fermi-constrained  (like the Pauli exclusion principle) nature of keV sterile neutrinos that is the reason why they density of dark matter is not cusped in galaxies. The density is fairly constant within the galaxy, and this can only be explain by the fact that you can't cram more sterile neutrinos into a region than given by its de Broglie wavelength cubed. The same can be said for the active neutrinos, but in this case, it's spacetime itself that has to expand into order to fit all of the neutrinos with it.

So, here's how I'd put it:   We live on the surface of a wrinkled, expanding 4D sphere. The average density of matter tells us the average curvature. Due to lumpy patches of sterile neutrinos (i.e. dark matter), the curvature is not exactly constant (more like wrinkles in a golf ball.) The weak nuclear force is responsible for the expansion of the universe because there is net generation of neutrinos from other (more massive) particles. Because neutrinos can't occupy the same state, spacetime expands to accommodate them.

That's it. It's not difficult to comprehend. The universe is a growing 4D sphere because of the weak nuclear force.

For those of you who aren't totally convinced yet and are holding on to other theories. Let me present some recent evidence against cold dark matter and for warm dark matter  (because my argument of neutrinos rests on the case that dark matter is actually ~keV sterile neutrinos that only slowly convert into active neutrinos.)

First, GeV cold dark matter is dead (see plot below).  The plot below  from Aad et al. in PRL 23 May 2014 (along with non-results from LUX and CDMS) has basically have killed off GeV Cold Dark Matter, and have likely killed Supersymmetry and superstring theory. (Sorry if you worked on these ideas, but they are dead.) The entire range of GeV dark matter is now officially dead.

Second, astrophyscists have been saying for awhile that dark matter needs to be on the order of 2 keV in order to explain why it doesn't clump in the center of galaxies. (see plots below by F.A. Kamada and J.E. Papastergis)

These results (as well as the many other plots I've shown in the past) are clear evidence that dark matter has a rest mass of approximately 2 keV.
But we also know that need at least another neutrino explain why neutrinos have any mass at all. But the PLANCK satellite has put some major constraints on the number of neutrinos species and LHC has put some major constraints on the decay products of Z, W, and Higgs Bosons. The only way out of this dilemma is to suppose that the additional neutrino is (a) sterile and (b) rest mass of ~ keV.
As PLANCK researchers state it in section 6.3.3, "In the limit in which the [sterile] neutrinos become non-relativistic well before any relevant scales enter the horizon, they will behave exactly like cold dark matter, and hence are completely unconstrained within the overall total constraint on the dark matter density." (Note that I added the word sterile because this sentence is from the section on sterile neutrinos in the document I linked to above.) So, the likely candidate for dark matter that fits all of the constraints above is a 2-7 keV sterile neutrino(s). But sterile neutrinos aren't completely sterile. There is a small probability that they will oscillate into active neutrinos, and the probably is slightly greater that they will oscillate into light active neutrinos than the opposite because of CP violation of the weak nuclear force (and because the light neutrinos are more stable.)

We are completely boxed in from all angles. But in the end, the answer was quite simple.
The universe is expanding because it has to in order to accommodate all of the active neutrinos that are been generated from keV sterile dark matter.

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