Wednesday, July 18, 2018

Conjectures, Thoughts and Questions To Explore

This post is just a rambling stream of consciousness and should provoke thought but not be considered a reliable source of information.

The energy density of dark energy is about four times the energy density of the cosmic microwave background radiation.

In a quantum gravity theory, what would be the average energy density of gravitons in the universe? How would that compare to dark energy?

Numerically, how would Alexander Deur's conception of dark energy as at least partially due to diversion of gravitons excessively towards places where dark matter effects are observed work out?

Does a calculation of the Schwarzschild radius of the universe include dark energy?

The Schwarzschild radius of the universe is slightly smaller than the size of the universe (13.7 billion light years v. 13.8 billion light years). Does that mean that we are inside a black hole? The 0.7% discrepancy is not statistically significant, could they be an exact match. What would that imply?

I considered the notion that dark energy is a soup of energy outside the universe that is gobbled up as it expands. But this doesn't address the pull of gravity from outside the universe that we would feel if that was the case. On the other hand, if the soup of energy outside the universe were spherically symmetric, would we observe it at all?

If gravity is the curvature of space-time, why is a non-vacuum universe almost perfectly flat?

The only baryon number violating and lepton violating interaction in the Standard Model is the sphaleron. But, the energy scale where it should be possible for sphaleron events to take place is ca. 10 TeV. This is a temperature 100,000 times greater than the 100 MeV = 2 trillion degrees kelvin temperature at which quark-gluon plasma would occur (i.e. 2*10^20 K). It corresponds to a conventional cosmology time after the Big Bang time of 10^-14 seconds (considerably after "inflation" but prior to everything else in the standard cosmology). This isn't long enough to reach modern matter-antimatter asymmetry levels in baryons and charged leptons from pure energy and maybe didn't happen at all. Rather than devising ways to reach a pure energy starting point, we have to assume that the starting part was not pure energy.

Also, renormalization of all of the Standard Model constants cannot be ignored at this energy scale, and more importantly, the impact of quantum gravity on the renormalization of the Standard Model constants probably cannot be safely ignored at that energy scale. What direction does including a graviton in the model have on the other Standard Model constant renormalizations? How material is the tweak? Could it lead to gauge unification within the Standard Model?

If the timeline of the Big Bang prior to 10^-12 seconds (where the "quark era" of quark-gluon plasma  starts), is unreliable, then maybe this never happens.

Whose frame of reference is being used in the standard cosmology chronology? Everything is moving at relativistic speeds at this point so the time frame of the moving particles is very different from a hypothetical outside observer.

We know that the ratio of particles in the universe is 15 up quarks per 9 down quarks per 1 electron per 10^9 photons. But what about other particles?

We know that there are about 10^80 baryons in the universe, and we know that about 49% of the mass of a proton or neutron comes from gluons (49% comes from the kinetic energy of the quarks and 2% comes from the Higgs field derived mass of the quarks). There are also quite precise gluon density measurements, but I don't know how to convert that to how many gluons at present at any given time in an average proton or neutron. But, with that you could get the number of gluons on the universe at any given time.

We think that there are a much higher number of neutrinos in the universe, but don't know the neutrino-antineutrino ratio, and have only weak support for the lamdaCDM assumption that the number of electron neutrinos is approximately equal to the number of muon neutrinos is approximately equal to the number of tau neutrinos as a result of neutrino oscillation.

We know that in addition to these components that there are a relatively negligible number of top quarks, bottom quarks, charm quarks, strange quarks, W+ bosons, W- bosons, and Z bosons at any given time. This is because all of these particles have very short mean lifetimes and only emerge "on shell" in high energy environments which are relatively rare. But, nonetheless, this isn't zero. My intuition is that the frequency of each depends upon the amount of ordinary matter that it is at the requisite temperature at any given time adjusted by the creation rate and decay rate of these particles.

We have extremely precise figures on all of these factors except the temperature mix of the matter in the universe and actually can do pretty well even with the temperature mix because we have a pretty good census of stars (which are pretty much the only places in the universe hot enough) and we know quite a bit about the temperature of stars.

Given that QGP is almost entirely absent in Nature because the universe hasn't been at 100 MeV temperatures for about 13.8 billion years, it seems likely that while there may be some places hot enough for muon and strange quark formation (and we do see muons in nature), that almost no place is hot enough for top quarks, bottom quarks, charm quarks and tau leptons to be created and that W and Z bosons and Higgs bosons that are on shell should likewise be very rare.

In quantum gravity, we also don't know how many gravitons there are in the universe, on average. This could be appreciable and at least on the same order of magnitude as the CMB.

In quantum gravity, gravitational energy is localized and is a source of gravitons.

I think that mass-energy is conserved in quantum gravity and the cheat that denies this is general relativity is a serious chink in the armor of general relativity as a theory.

I think that it is plausible that the Big Bang never had a density greater than the black hole-neutron star threshold density (about 10^20 g/m^3), and that there are no primordial black holes, hence that there is a maximum density in the universe which may be, or may be a consequence of, an ultraviolet fixed point. What is the mass of the universe? 10^55 grams. What is its volume of the mass of the universe at this density? 10^35 m^3. What is the radius of this volume if it is spherical? About 3*10^12 meters. This is 3*10^9 km and is 0.000317107023 light years (about 167 light minutes) and is 20.0537614 Astronomical Units. This is about 5% larger than the size of a sphere centered in the Sun and extending to the orbit of the planet Uranus. This would be quite different from standard theory however and might screw up Big Bang nucleosynthesis, although it is hard to be clear how. If you cut it to 4% of the mass (removing dark matter and dark energy), this cuts the radius by roughly one-third to about 6.5 AU and about 56 light minutes (about 15% farther than the orbit of Jupiter).

I remain deeply skeptical of cosmological inflation as a theory.

The temperature of the universe is proportionate to 1/t^3 where t is time. The estimated age of the universe is 13.8 +/0.21 billion years. The estimated temperature at ca. 10^-12 to 10^-6 seconds is 100 MeV.

Suppose that there is no dark energy or dark matter, then the Schwartzchild radius is 548 million light years because only about 4% of the mass-energy of the universe in lambda CDM is ordinary matter. So, this would be a black hole from the inception. Are we inside a black hole?

Do black holes have an internal shell structure of density with black hole's interior mass always containing sufficient mass to form a black hole at every radius?

Big Bang nucleosynthesis, which is more precisely confirmed than ever, is a tight constraint on alternatives to the Standard Model of Cosmology and other BSM theories.

The precision with which we know the up and down quarks recently significantly improved and strongly rules out the otherwise attractive zero mass up quark.

We know that the Schwarzschild radius establishes a minimum density to form a black hole. Is it possible that there is another upper boundary threshold of some sort (density, mass, who knows) at which a black hole explodes or leaks? How could that be tested?

How different would the universe be if it had two generations of fermions instead of three? I don't think it would be very different. What kind of mathematical structure or mechanism would require three and exactly three generations of fermions?


neo said...

if gravitons don't exist, how would this impact Deur's theories?

andrew said...

Conceptually, it would be a huge problem. But, in principle you would recast it as it a self-interaction of a non-Abelian field.

Mitchell said...

"The energy density of dark energy is about four times the energy density of the cosmic microwave background radiation"

Dark energy density is more like 100,000 times CMB energy density, I think.

andrew said...

I looked up references on that and could certainly be wrong, but I will have to confirm. I was even thinking of making it a Physics.SE question to confirm it. Still, I think it is a good comparison to have in hand.

andrew said...

If I'm wrong, I'm totally blaming it on still getting used to bifocals and misreading an exponent somewhere.

Mitchell said...

The ratio might be what you said, in the very early universe.

Mitchell said...

I mean, the ratio between dark energy density and radiation energy density. It wouldn't have been CMB.

neo said...

How different would the universe be if it had two generations of fermions instead of three? I don't think it would be very different. What kind of mathematical structure or mechanism would require three and exactly three generations of fermions?"

why are there 3 color charges? maybe the 3 generations is related to 3 color charges in the strong force, or they have same mathematical formalism

Ryan said...

Do we know there aren't more generations at high energy levels?

andrew said...


"Do we know there aren't more generations at high energy levels?"

Pretty definitively. The structure of the Standard Model requires on up-type quark, one down-type quark, one charged lepton, and one neutrino type in each generation for consistency.

There isn't any direct evidence ruling out the t', b' and tau' at energies high enough to be utterly implausible not to be discovered yet, and cosmology data doesn't rule out a fourth generation neutrino heavier than 10 eV.

But, the close match to unitarity of the current CKM matrix and PMNS matrixes strongly disfavor SM4. So does the fact that an SM4 v(tau)' would have to be more than 62.5 GeV (half the Higgs boson mass) to have evaded detection so far, while the Mv3 is about 58 meV, Mv2 is about 8 meV and Mv1 is probably less than 1 meV. The exclusion of SM4 v(tau)' less than 45 GeV (based on W and Z boson decays) which strongly bounds the number of active neutrinos to 3 and not 4 in that mass range is even more strict to many, many sigma.

This would make the fourth to third neutrino mass ratio 6*10^10/(6*10^-3) = 10^13, when the runners up are on the order of 2*10^2. There is just no plausible theoretical reason that this could be so.

I think that there are also some more subtle clues as well.

andrew said...

"why are there 3 color charges? maybe the 3 generations is related to 3 color charges in the strong force, or they have same mathematical formalism"

At least we have solid empirical reasons for 3 color charges. I don't think that this makes much sense to have a connection with 3 generations given that leptons don't interact via color charge. But, there are probably worse hypotheses. Many theories that integrate leptons into the color charge system have leptons as a fourth color charge, which contradicts the three colors to three generations connection.

neo said...


if there's a fourth neutrino, sterile or otherwise, would that imply a fourth generation

"At least we have solid empirical reasons for 3 color charges. I don't think that this makes much sense to have a connection with 3 generations given that leptons don't interact via color charge. But, there are probably worse hypotheses"

there's also solid empirical reasons for 3 generations.

why are there 3 color charges and not 4 or 2 or 1?

what ever theory that can explain why there are 3 color charges could, perhaps also explain why there are 3 generations

and leptons don't carry color charge, a more fundamental theory might link the 3 color charges of quarks to the 3 "higgs charges" of fermions

what i have in mind is there is this fundamental entity, this entity has the ability to give rise to fermions and acquire one specific set of color charge, electric charge, spin, higgs charge that can vary, and in its variation it gives rise to SM particles and their attributes, and there are specific rules as to how these particles properties follow

Graham Dungworth said...

Why not? A coherent ramble is a fine thing. Aristotle would be proud; he made some good discoveries that fell by the wayside once we recognised how limited his scientific approach was.

The physics of big numbers was awesome two generations ago. Eddington's,Dirac's,Peebles', Hoyle's et al numbers 10^80, 10^54, 10^22 10^9-10^10. In their times several thousand galaxies were recorded. Since SDSS and then the Hubble deep field and ultra deep fields the galaxy estimate soared from ca one million classified galaxies to possibly 10^11 galaxies. Last year Nasa mentioned that we had underestimated the number of galaxies by tenfold. Thirty years ago the apparent thinning of galaxies with distance represented an additional nail in the Steady State Model although I'm not attempting to resurrect it.

The baryon/ photon number of 1/10^9 -1/10^10 comes from the numerosity of those low energy cmb photons at 2.725 Kelvin and the measured abundance of baryons to the critical density derived from the Hubble constant at that epoch. Neutrinos are considered as equally abundant as photons in the cmb. Why?

Mitchel's estimate is out by two orders of magnitude. Let's address

Andrew- saved note way exceeds your charcter limit

Graham Dungworth said...

Let's address two accepted conventional models that are hot models. There's the old Peebles/Weinberg models in which the hot start evolves from an earlier phase constrained within let's say a a glowing orb ca. 1 light year diameter, much less than the distance to our nearest star. The energy equivalent in this regime is much greater than 100meV. Each proton or equivalent eg. baryon packages >1GeV restmass. The particles are not just relativistic they are hyper super relativistic. That Ice Cube neutrino with meV rest mass had ca. 40GeV kinetic energy.

The current critical density of the universe is recorded at ca. 4 to 6 proton equivalents/ metre^3 (4-6 baryons)but we only observe ca. 4.5% of this normal matter. The dark energy component amounts to 75% of the critical density, let's say 3-4 baryons/m^3. The old models have many caveats, up to twelve major unsurmountable problems; flatness, horizon,matter antimatter annihilation etc. Newer inflation models attempt to solve these problems or dissolve paradoxes.
Newer models have size shrunk from light year sizes to say a basket ball through tennis ball to a size one wouldn't recognise through an electron microscope. From big number physics one has to confine a universal mass of order 10^56kg in the approach to the planck length to a wacking thermal regime equivalent to 10^32Kelvin. Since the tenfold increase of galactic numerosity last year well a 10^80 prediction becomes common sense today. There's nothing special about the enormity of this number any more. Rather than be astounded by how incredibly huge this number is , the search for a big word, the incomprehensibility which reduced Weinberg to torpor and to a anthropomorphicity worthy of Aristotle we now probe the infinitessimally minimal our origins.

All of these models pack matter-antimatter into an earlier epoch. How early? When we say the universe is 14 billion years in the making, this age isn't just based upon the Hubble Flow and lamdaCDM. There's additional independent determinations, namely cooling curves of white dwarfs, globular cluster age determinations that fall in a ball park ofsay 12-15 billion years. Sol Invictus is dated at ca. 4.5 billion years. Conditions for earthly planets appeared fine 10 billion years ago. We are quite late on in the scene of universal evolution. That's palatable. My parents were getting on in age before I was found under a gosseberry bush. Unlike an Olivia or Octavia there was no hope of becoming great great grandfolk.

Where's the antimatter in the universe? We have searched but found none. Here's where particle physics appears as an axiom for creation.That ice cube 40GeV neutrino produced many new, never ever existed before, new rest mass particles some 3.5 billion years after its creation in a far distant blazar of a galaxy. We write off some mighty bookkeeping bills but still have to pay off war debt as far back as the French Revolution-Lavoisier would give comfort to such noble treachery.

Graham Dungworth said...

We can't create a universe by cherry picking . The Standard Model of Particle Physics informs that it's all or nothing which would be great wisdom for Brexiteers. So early on, in a thermal regime far far greater than 10^Kelvin, all of these particles with or without rest mass coexisted as equals, a Utopia or Hog Heaven if so you wish. A grand coeval annihilation, all in causal contact, wiped out all of them to the accuracy of 1 part in ~10^9 leaving but a trace of what we call now call normal matter, although we only measure a small amount of these normal baryons, the stuff of stars. That's a tiny number that gave Weinberg dyspepsia for years. There's still no conventional explanation for it. Hoyle et al tried dust, iron spicules, anything to thermalise a temperature to that of the cmb radiation.
The restmass equivalent of those photons and neutrinos, some 410 million apiece per m^3 amounts to no more than a single electron's mass, about 1/2000 of baryon density per baryon. Dark energy DE amounts to 3-4 baryons/m^3. It's huge and while the unverse expands and dilutes baryon density by the inverse cube of size DE increases at constant density. It's Aristotlean logica- we all eventually dilute into non existence. We are late on in the scene in some cosmic protective haven that has existed elsewhere innumerable times and some sharpwit predicts an eventual demise with an even bigger number 10^100. Well there are even bigger numbers to creation >10^2300 possible universes! I apologise for cringeing when the numerosity of universes appears. How big does a universe need to be to satisfy fine tuning constraints? For a great range of stars we address lepton and baryon degeneracy pressures. Neutrino pressures were never addressed since they weren't expected to have rest mass. Of course a "neutrino star" doesn't exist , it would require a ~2*10^54 kg rest mass energy to create a universe.
Andrew, my time to debate all these points may exceed my endtime.

Ryan said...

"This would make the fourth to third neutrino mass ratio 6*10^10/(6*10^-3) = 10^13, when the runners up are on the order of 2*10^2. There is just no plausible theoretical reason that this could be so."

To me that sounds like it's ruled out for any reasonable energy level, but who says the universe has to be reasonable?

andrew said...


"if there's a fourth neutrino, sterile or otherwise, would that imply a fourth generation."

A fourth active neutrino would imply a fourth generation. A fourth sterile neutrino would not.

"To me that sounds like it's ruled out for any reasonable energy level, but who says the universe has to be reasonable?"

The universe doesn't have to be reasonable, but it is nonetheless an unlikely hypothesis unless someone can imagine a reason why a fourth generation neutrino would be profoundly more heavy than the others, all of which are quite close to each other in mass ratio.

Also, I don't think that my list of evidence disfavoring SM4 is complete, even though that was the best that I could do from memory.

andrew said...

Some other SM4 issues.

The top quark mean lifetime is 5*10^-25. The W boson mean lifetime is 1*10^-25. Given the masses of the t' and b' which we can put floors on experimentally, we can exactly determine the SM decays of the t' and b'. The only way that a top quark can decay in the SM is via a W- boson. If a t' existed at a mass not ruled out be experiment, its mean lifetime would be less than the W boson mean lifetime. This is suggestive of a reason that we can rule out SM4, even though again, one could imagine an unreasonable universe in which t' quarks produce W- bosons very, very quickly and they convert to a down-type quark as a result, after which it takes a very long time, in relative terms, for the W- boson itself to decay. This is actually one of the most powerful arguments against SM4 as it goes to internal consistency of the SM.

Also, another note about the tau-prime neutrino in SM4. One of the great things about this model is that we can predict its properties at any given mass exactly except for the unknown PMNS matrix mixing angles for the tau-prime neutrino, exactly, and we can also bound the maximum PMNS matrix mixing angles for a tau-prime neutrino by the maximum experimental deviations from unitarity in the existing PMNS matrix (i.e. the mixing angles have to be quite small). And, the PMNS mixing angles for a tau-prime neutrino would not all be independent of each other. And, as noted before, the minimum fourth neutrino mass is huge (about 10^16 or more times the heaviest known neutrino mass). This gives us a very precise target for experimental searches that can confirm or deny SM4 via the tau-prime neutrino.

Also, searches that rule out dark matter candidates in certain mass ranges at the LHC also rule out tau-prime neutrinos in those mass ranges, because they would be indistinguishable experimentally when produced from dark matter, i.e. they would look like missing traverse momentum which has been carefully studies since it is a signal of all sorts of BSM phenomena. The missing traverse momentum searches are more powerful, however, when looking for a tau-prime neutrino because we know which experiments could hypothetically produce it. So, the PDG exclusion for a tau-prime neutrino is actually far lower than it should be. And, while no mass exclusion for a tau-prime neutrino could defeat a truly unreasonable universe, it is pretty notable.

I think that a tau-prime neutrino would also meaningfully impact muon g-2 (at least at masses close to those already excluded within a couple of orders of magnitude), so that also places a practical lower bound on the tau-prime neutrino mass that is much higher than the PDG lower bound.

andrew said...

@Graham "Andrew- saved note way exceeds your charcter limit"

Sorry about that. Character limit in comments is not one of the parameters that the Blogger platform allows me to adjust.

andrew said...

While I'm thinking about it, the SM does not prohibit top quark hadrons, they're just improbable. How improbable?

The top quark mean lifetime is 5*10^-25s which is within an order of magnitude of its half life.

I saw a paper (can't find the link) that says that the mean hadronization time is 2-4*10^-23s.

So, you need a top quark to survive 65 half lives to hadronize. The probability of this is about 10^18, which is far more than the total of top quarks ever created experimentally which I think is on the order of 10^5 to 10^8. Hence, yeah, we'll probably never see it happen.

Also, that means that any t' would never hadronize, and probably a b' wouldn't either. Probably t'-b'-t-b would be the decay chain 99.8%+ of the time in SM4, with no t' or b' or t hadrons ever observable.

neo said...

for your next blog post

this paper

The dS swampland conjecture and the Higgs potential
Frederik Denef, Arthur Hebecker, Timm Wrase

suggests that using quientessnce to solve the dS problem in string theory may lead to problems with the SM

maybe its time to give up on string theory as a candidate QG and work on something else or some other approach, something that gives dS

andrew said...

300 TeV neutrinos exist and hit the Earth. If there were SM4, this would produce unexpected output.