It's been a while since I've posted. It's been a while since I talked cosmology. And meanwhile BICEP2 came out with what may be the big measurement of the decade, along with LHC's 2012 determination of the Higgs boson mass.

Specifically, BICEP2 has estimated the cosmological "r" parameter, which quantifies the relative magnitude of tensor perturbations and scalar perturbations of the cosmic microwave background, as 0.2. I'll confess that I'm still working out the basic meaning of this quantity. It seems to be a ratio of energies-squared - the square of the energy in the tensor perturbations, divided by the square of the energy in the scalar perturbations. And the physical meaning of squaring the energy may be, that it corresponds to the "work done" by that type of perturbation. So perhaps it would mean that the fluctuations of the inflaton field (which supposedly caused the scalar perturbations) did five times as much work on the CMB photons, as was done by the fluctuations of the gravitational field (which supposedly caused the tensor perturbations). But you should probably ask someone better informed, before believing me about this.

Now there are all sorts of complicated models out there - Higgs inflation... axion monodromy inflation from string theory... - in which people are trying to get an "r" near 0.2. Meanwhile, what are physics numerologists saying? So far, I have spotted two examples of BICEP2 numerology.

First was a vixra paper by Tony Smith, in which Tony estimates "r" as 7/28 = 0.25. 7 and 28 are the dimensions of different algebras which he associates with the tensor and scalar perturbations, respectively, in the context of an octonionic theory of inflation. Of course I don't understand Tony's logic, but an important part is probably the proposition, a few pages along, that "Cl(64) is the smallest Real Clifford algebra for which we can reflexively identify each component Cl(8) with a vector in the Cl(8) vector space". So it all has something to do with space-time qubits and Bott periodicity and self-embeddings.

Then there was a characteristically laconic post by Marni Sheppeard, in which the idea is that "r" is about 1/5, and that this would be a ratio of... dimensions of certain Hilbert spaces, I think, that are relevant for her theory of mass generation in quantum gravity. In her paradigm, space-time is something like a big concatenation of morphisms between these vector spaces. For more, see her papers at vixra.

My "contribution" to BICEP2 numerology is not going to be based on advanced math - though it does build on the observation that 0.2 = 1/5. My thought is just that this is also the ratio of baryonic matter to dark matter densities in the present-day universe. (I'd also like to acknowledge that work by A. Hattawi helped to fix this fact in my mind - that the OM/DM ratio is about 1/5.) So my question is, is there some theory in which this is not just a coincidence?

"My "contribution" to BICEP2 numerology is not going to be based on advanced math - though it does build on the observation that 0.2 = 1/5. My thought is just that this is also the ratio of baryonic matter to dark matter densities in the present-day universe. (I'd also like to acknowledge that work by A. Hattawi helped to fix this fact in my mind - that the OM/DM ratio is about 1/5.) So my question is, is there some theory in which this is not just a coincidence?"

ReplyDeleteFWIW, I'd say that your observation is really just that, an observation, and not really numerology at all.

I have almost on confidence that the 0.2 value reported by BICEP-2 is accurate even to two significant digits, and the official MOE of +0.07/-0.05 in the result is quite large. More wisdom would probably be imparted by quoting the BICEP result as a 0.15-0.27 confidence interval than as a central value that seems more precise than it actually is in reality. I am also troubled by the discrepancies between Plank and BICEP on the value of r which are not quite consistent with each other at the two sigma level. The Plank result was 0<r<0.11 at the two sigma level with a best fit value of r=0.01.

As result on the high end of the Plank allowed range and low end of the BICEP-2 allowed range ca. r=0.10-0.11 (approximately equal to 1/9th which is equal to 1/(3*3)), gives an ever tempting result that is topologically flat, rather implying an inflation era with a topology that is clearly concave or convex, which is consistent with a universe that is very nearly flat in global topology at a large scale level in the post-inflation era.

Still, the notion that tensor modes might be connected in some deep way to ordinary matter, while scalar modes might be connected in some deep way to dark matter is quite plausible, and does provide a good motive for your efforts to better articulate what "r" is in a physical sense.

@Mitchell: "(I'd also like to acknowledge that work by A. Hattawi helped to fix this fact in my mind - that the OM/DM ratio is about 1/5.)"

DeleteAbout this OM/DM ratio, there is a detailed description at (http://profmattstrassler.com/2013/07/31/a-few-stories-worth-a-comment/#comment-71962 ), and the following is the quote.

“For the 48 SM particle-land-patches, 40 of them are dark-lands. Electron-neutrino is also dark. So, the total dark-lands are 41, that is, the dark/visible ratio is [(41/7 = 5.8571428) – w].

Boy: Why “-w”?

Grandmother: The playing of these visible-kids is often getting out-of-the-bound into the dark-lands, and it causes some sparks there. According to the AMS-2 data, the out-of-the-bound sparks account about (8 to 10%) of the dark-landmass. Thus, [41 x (100 – 9)% /7 = 5.33] is almost identical to the Planck data [(25.8/4.82) = 5.3526].”

With your view that r = OM/DM = (8 -1)/(40 + 1) = .17, or

It can be r = OM/DM = 8/40 = .2

Depending on how you define the OM and DM.

Looks like the data is flawed anyway, per rumors via Jester.

ReplyDelete@andrew: "Looks like the data is flawed anyway, per rumors via Jester."

ReplyDeleteTheoretical calculation is much more creditable then those rumors. BICEP2 data could be flawed but it will not change the theoretical calculation which is available at http://blog.vixra.org/2014/03/20/how-certain-are-the-bicep2-findings/#comment-36510 .

Then, as the dark energy can also produce the E-mode in addition to the B-mode, the r ration can be rewritten as r = (64 -48)/64 = 0.25

Very soon I am to published a paper who proof, more other things, that the tensor-scalar ratio B modes is: 2/(Pi)^2= 0.202642367..

ReplyDeletehttp://vixra.org/abs/1407.0217

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