Monday, October 3, 2016

Baryogenesis And The Matter-Energy Balance Of The Universe

Estimating A Mass-Energy Mix From Rest Mass Loss In The Decay Of Democratically Created Quarks

One of the main focuses of scientists researching cosmology and fundamental physics is the matter-antimatter asymmetry of the quarks and charged leptons of the universe, almost all of which are matter rather than antimatter.

But, put that issue aside for a moment and assume that we know how the baryon number of the universe came to be something on the order of 10^54 when the laws of physics at every scale we have been able to measure them provide that baryon number is conserved.

Let's think about another issue: the relative amounts of ordinary matter and other stuff in the total mass-energy budget of the universe, which according to the standard model of cosmology is roughly 5% ordinary matter, 26% dark matter and 69% dark energy, give or take a little depending upon which set of experimental data you use to determine its parameters.

Now, there are several boson interactions in the Standard Model that can produce quarks. They can be produced in W and Z boson decays, in which case the products a "democratic" between quark flavors (although quarks are favored over leptons 3-1 because each color of quark is treated as distinct in this "democracy"), subject to conservation of mass-energy concerns. They can be produced by pairs of photons, also democratically, subject to conservation of mass-energy concerns. They can be produced by gluon fusion, again democratically, subject to conservation of mass-energy concerns. Or, they can be produced by Higgs boson decays, proportionate to rest mass and subject to conservation of mass-energy concerns.

The early universe is widely assumed to have been essentially maximal in terms of available mass-energy, so a large share of the quarks that were not cancelled out in matter-antimatter annihilations would be top, bottom, charm or strange quarks, but would swiftly decay to a mix of up and down quarks.

In those decays, the vast majority of the rest masses of these second and third generation quarks would be converted into something other than quarks, since no new net quarks could be created. And, it is straight forward to model the amount of energy emitted in this fashion relative to the current count of up and down quarks in the universe today, with a variety of assumptions about the mix of quark production methods and the amount of time elapsed during periods when some but not all quark flavors could be generated consistent with mass-energy conservation.

For example, using the assumption that all quarks were initially created in equal proportions, calculating their rest masses, and subtracting the mass (from quarks and gluons) of all baryons in existence today, you end up with a back of napkin estimate that baryons should make up about 1% of the mass-energy of the universe today. (I'll leave this straight forward naive calculation using PDG values as an exercise for the reader.)

Other Implications

Reconciling this to the 5% of mass-energy in the standard model of cosmology today takes a couple of steps.  First, you would have to add in adjustments for radiation (i.e. photons) and neutrinos, both of which are numerically small and don't make a lot of difference.  Second, you would have to make an adjustment for the aggregate kinetic energy and energy from angular momentum of the universe, for which the standard model of cosmology also makes no adjustment which might be fairly significant.

Suppose, for sake of argument, that this gives baryons 3% of the mass-energy of the universe, which is still three times our naive estimate of 1%.  This would imply that one-third of the initial mass-energy of the universe as of the time that conservation of mass-energy began to apply, went into creating quarks, while the balance went into leptogenesis (to which a similar analysis could be applied if we knew the ratio of neutrinos to antineutrinos in the universe, which we don't) and to the creation of fermion-antifermion pairs that annhilated and to the creation of bosons which lack baryon or lepton number.

This one-third fraction would also let us know how strongly CP would have to be violated in the early universe to create the existing baryon number of the universe.

Some Other Caveats

Now, one problem with this is that general relativity does not conserve mass-energy, for example, creating it with the cosmological constant as the universe expands, and destroying it via the gravitational red shifting of photons, unless there is a quantity of gravitational potential energy which is conserved and balances gravitational changes in mass-energy. Physicists differ regarding whether this is a proper thing to consider.

But, this does not itself imply that the analysis above is pointless even if general relativity does not conserve mass-energy. If the universe does start to obey conservation of baryon number at some point, and not all quarks in the universe of up and down quarks at that point, the difference between the mass at that point and the mass of up and down quarks in the end state mere minutes later, must end up in creating mass-energy of some other type. This is true whether or not general relativity conserves mass-energy and continues to be a source for other constants of the standard model of cosmology.

There are also subtle issues with determining total kinetic energy and total energy from angular momentum in the universe, in part, from the fact that kinetic energy is usually frame of reference dependent while general relativity is background independent, and in part from the fact that gravitational lensing estimates of the mass of galaxies and galactic clusters ought to automatically include the gravitational mass equivalent attributable to the angular momentum and internal kinetic energy of those systems.  An effort to estimate it is found here. A similar March 2014 paper by the same author is found here.

Thirdly, a less naive calculation would have to consider the fact that the masses of quarks in high energy circumstances are different from the masses of quarks in today's low energy circumstances, because quark masses, like many other Standard Model of particle physics physical constants, run with energy scale. In general, if I recall correctly, the running of the quark masses tends to make them lighter at higher energy scales and heavier at lower energy scales.

Fourth, this analysis assumes that baryongenesis begins after the laws of physics start to conserve baryon number. But, it is also perfectly possible that quarks are created and have already begun to decay in earnest before conservation of baryon number holds true, in which case the analysis above will overstate the amount of energy created by quark decay after baryon number conservation applies.

For example, another interpretation of baryons making up 3% of the mass energy of the universe would be that baryon number conservation didn't begin to apply until a large share of the quarks created in the universe had already decayed, so that a disproportionate number of the quarks in existence when baryon number conservation began to apply were not heavy quarks.  Indeed, this cutoff would merely need to happen sometime between a time that was energy rich enough for top quarks to be one-sixth of all quarks created and a time when the universe was not energy rich enough to create bottom quarks.

This could be a feature rather than a flaw as well, however, because if we apply whatever assumptions we determine are necessary to get the numbers to work for baryogenesis, and then apply the same assumptions to leptogenesis, we might very well be able to make both an untestable prediction of the energy content of the universe attributable to lepton decay, and a testable prediction (in principle, at least) regarding the currently unknown total lepton number of the universe (which would not necessarily be the same as the baryon number of the universe, as most GUT models assume, in this analysis). This could be tested as soon as the ratio of neutrinos to antineutrinos in the universe could be measured to any meaningful precision (even plus or minus 10% accuracy would rule out all sorts of leptogenesis theories and favor others). 

But, the fact that a very naive back of napkin estimate of the amount of ordinary mass in the universe based upon the loss of rest mass from quark decay and the conservation of baryon number is of the right order of magnitude, and that some of the adjustments required to make that estimate less naive (such as considering the total kinetic energy and energy from angular momentum in the universe and adjusting quark masses for energy scale) suggest that this kind of analysis isn't entirely off the mark as a useful line of inquiry about the cosmology of the very early universe.


This analysis, other than the general principles of it, are my personal conjecture and are not supported by any literature in the field done by professionals considering the question in this manner that I have read. So, please do not take these conjectures as established scientific facts.

But, on the other hand, I do not claim to be the first person to come up with this analysis which is fairly obvious to anyone in the field, and due to the caveats I mention or some other reason, it could be that there is good cause why this doesn't work that is more obvious to professionals in the field which is why it isn't considered.  But, I have not reviewed the literature sufficiently to know if this idea is original or not (only that it is not the subject of much active publishing and investigation in the last few years) and honestly, I don't know that I would have the competence to do such a comprehensive literature search in a manner well calculated to find previous articulations of this idea as a previous investigator might have used different terminology to describe the key concepts than I do.

1 comment:

Mitchell said...

At energy scales above the electroweak symmetry-breaking scale, the masses of the quarks are zero (except for an effective "thermal mass"), because there's no Higgs vev. The yukawa coupling constants do run, but in that regime they describe the amplitude for a quark to emit a Higgs boson particle (and change flavor, if it is an offdiagonal element of the yukawa coupling matrix).