# Towards a neo-minimal synthesis for BSM physics

1. Jan 18, 2013

### mitchell porter

The standard model was created, not to conform to anyone's a-priori theoretical ideas, but just to match experiment. In the decades after that, we had the long march through unifying ideas that culminated in M-theory, and the creation of thousands of models of BSM physics, featuring supersymmetry, grand unification, extra dimensions... Those were great theoretical discoveries and they may yet be vindicated experimentally too.

However, all those models may be regarded as "baroque" in that they contain large numbers of so-far-unobserved particles and phenomena. Meanwhile, I have noticed the accumulation of ingredients for what might be called a "minimal" or "neo-minimal" alternative to the baroque mainstream of theoretical physics. Several of the regulars in this forum would undoubtedly be supporters of this new minimalism in theoretical physics.

So I thought I would list a few ingredients for a neo-minimal synthesis, just so we can see what we have to work with. The truth may be neither minimal nor baroque, but rather some hybrid of the two, but I think it would be good to distil the ideas of pure minimalism further, before trying to mix them with the baroque mainstream.

Here, therefore, are my candidate ingredients for a neo-minimal synthesis. This is absolutely not meant to be exhaustive or definitive, and I would encourage people who think there is a minimalist program implicit in certain corners of theoretical physics research today, to list further examples, clarify or dispute the definition and the philosophy, etc. What follows might be best regarded as an illustrative exercise in neo-minimalism: what if you tried to make a TOE out of these ingredients?

1) The latest version of the nuMSM, as expounded in a recent talk by Mikhail Shaposhnikov. The nuMSM is the SM plus three right-handed neutrinos with masses in the keV-GeV range. The work summarized in this talk is probably the apex of BSM minimalism right now.

2) Gauge foams and twistor networks. These are the two LQG-ish approaches to quantum geometry which sound most interesting to me; and they both draw on other alternative research programs - gauge foams employ noncommutative geometry, twistor networks use twistor variables.

3) Alexander-Marciano-Smolin's chiral graviweak model. I'm listing this one mostly because it has somehow escaped comment here, which surprises me. Also, it illustrates one type of minimalist theme, the attempt to unify without introducing the new unobserved objects characteristic of baroque unification (heavy GUT bosons, superpartners, Kaluza-Klein modes).

The usual baroque critique of this sort of neo-minimal unification is that the latter involves technical errors; it tries to jam things together in a way that isn't mathematically possible. For example, recall what was said about Garrett Lisi's E8 theory.

This list even provides a generalizable recipe for neo-minimal research: phenomenological minimalism; minimalism regarding quantum geometry or quantum gravity; and minimalist unification. Regarding the middle item, it's defined mostly in opposition to string theory, where questions of quantum gravity are resolved in a way that deeply involves the non-gravitational sector of the theory. I would also point out that some neo-minimal ideas feature a unification which develops out of ideas about quantum gravity; e.g. think of attempts to embed Bilson-Thompson's correspondence into LQG.

2. Jan 19, 2013

### marcus

I am especially intrigued by Shaposhnikov's talk. We should talk about this more. Maybe it should have a thread devoted entirely to the nuMSM. It is tempting to write it νMSM.

Here is a paper by Shapo et al which has some of the same discussion and the same FIGURES as the talk.
http://arxiv.org/abs/1205.2893
Higgs boson mass and new physics
Fedor Bezrukov, Mikhail Yu. Kalmykov, Bernd A. Kniehl, Mikhail Shaposhnikov
(Submitted on 13 May 2012)
We discuss the lower Higgs boson mass bounds which come from the absolute stability of the Standard Model (SM) vacuum and from the Higgs inflation, as well as the prediction of the Higgs boson mass coming from asymptotic safety of the SM. We account for the 3-loop renormalization group evolution of the couplings of the Standard Model and for a part of two-loop corrections that involve the QCD coupling alphas to initial conditions for their running. This is one step above the current state of the art procedure ("one-loop matching--two-loop running"). This results in reduction of the theoretical uncertainties in the Higgs boson mass bounds and predictions, associated with the Standard Model physics, to 1-2 GeV. We find that with the account of existing experimental uncertainties in the mass of the top quark and alphas (taken at 2sigma level) the bound reads MH≥Mmin (equality corresponds to the asymptotic safety prediction), where Mmin=129±6 GeV. We argue that the discovery of the SM Higgs boson in this range would be in agreement with the hypothesis of the absence of new energy scales between the Fermi and Planck scales, whereas the coincidence of MH with Mmin would suggest that the electroweak scale is determined by Planck physics. In order to clarify the relation between the Fermi and Planck scale a construction of an electron-positron or muon collider with a center of mass energy ~200+200 GeV (Higgs and t-quark factory) would be needed.

Here is another Shapo et al paper that talks explicitly about the NEUTRINO MINIMAL STANDARD MODEL
http://arxiv.org/abs/1208.4607
Dark Matter, Baryogenesis and Neutrino Oscillations from Right Handed Neutrinos
Laurent Canetti, Marco Drewes, Tibor Frossard, Mikhail Shaposhnikov
(Submitted on 22 Aug 2012)
We show that, leaving aside accelerated cosmic expansion, all experimental data in high energy physics that are commonly agreed to require physics beyond the Standard Model can be explained when completing it by three right handed neutrinos that can be searched for using current day experimental techniques. The model that realises this scenario is known as Neutrino Minimal Standard Model (νMSM). In this article we give a comprehensive summary of all known constraints in the νMSM, along with a pedagogical introduction to the model. We present the first complete quantitative study of the parameter space of the model where no physics beyond the νMSM is needed to simultaneously explain neutrino oscillations, dark matter and the baryon asymmetry of the universe. This requires to track the time evolution of left and right handed neutrino abundances from hot big bang initial conditions down to temperatures below the QCD scale. We find that the interplay of resonant amplifications, CP-violating flavour oscillations, scatterings and decays leads to a number of previously unknown constraints on the sterile neutrino properties. We furthermore re-analyse bounds from past collider experiments and big bang nucleosynthesis in the face of recent evidence for a non-zero neutrino mixing angle θ13. We combine all our results with existing constraints on dark matter properties from astrophysics and cosmology. Our results provide a guideline for future experimental searches for sterile neutrinos. A summary of the constraints on sterile neutrino masses and mixings has appeared in arXiv:1204.3902 [hep-ph]. In this article we provide all details of our calculations and give constraints on other model parameters.
63 pages, many figures

I think this paper could help understand the slides from the talk.

Last edited: Jan 19, 2013
3. Jan 19, 2013

### Blackforest

3) has not escaped my attention. I notice a crucial remark (citation taken in the conclusion §): "...In particular, we describe a parity symmetric theory of gravity that has a symmetry broken phase, which organizes the degrees of freedom to give rise to general relativity coupled to a SU(2) Yang-Mills theory..." The very interesting chiral graviweak model is certainly not the unique possible "coupling" scenario between gravitation and SU(2) Yang Mills theory because, at a totally theoretical level (no critic), any approach which is able to describe gravitation in terms of SU(2) can offers that opportunity. Example given: if in point 2) you add the discussion concerning C* algebra https://www.physicsforums.com/showthread.php?t=663574,
then an alternive approach would be to equipe the space of the GTR with a C* algebra in such a manner that a SO(3) structure emerge.

4. Jan 19, 2013

### Phys-excess

Here is an excellent example of a minimalist theory that jams things together and finds they fit perfectly. Namely, the author shows that Einstein's equations and the fine structure constant can be derived from one simple principle. I hesitate to post the link because I understand the mods of this forum have been handing out lifetime crackpot bans for sharing it. Hopefully, I can avoid a crackpot label by stating that I believe the information in this article is obviously wrong, but somehow relevant to a discussion of BSM minimalism. With this caveat in place, here is the link which is an update of this earlier paper.

This is very minimal, but I think it should be discounted outright. The author's prediction for α is only accurate to within half a percent which is way outside the experimental bounds found using the theory he is proposing an alternative to. The author's three-fold interpretation of the measurement process is completely divorced from reality. There is no mention of SU(3) x SU(2) x U(1) which should set off the crackpot alarm for anyone interested in a better description of reality than what we have now. One cannot simply propose a new mathematical method as the author has done with his "non-unitary basis vectors." Where is the rigor in simply stating "Let there be...?" Such a construction is preposterously non-mathematical. Finally, the introduction of that other ratio $\varphi$ is capricious and unwarranted. If $\varphi$ was a part of a complete quantum theory we would see this ratio appear everywhere in Nature as we do $\pi$. Clearly $\varphi$ makes no appearance in Nature, so any theory of natural philosophy should make no mention of it.

Please excuse my link to a non-arXiv article, I only post it because whenever we do move to a new theory BSM, it should also utilize some method to show that electrodynamics and gravity are unified.

5. Jan 19, 2013

### marcus

Phys-Ex, I don't think we have to be talking about "crackpot" here in this thread. We CAN if it interests people but I fear it will tend to derail thread. Shaposhnikov is mainstream and his idea of νMSM gets mainstream attention. A strong ally in this is the director of the Quantum Gravity and Unified Theories program at the Max Planck Institute-Potsdam, namely Herman Nicolai.

Another (not so explicit, but ally nevertheless) is Steven Weinberg. He has given reasons why it is plausible that there be no new physics between EW and Planck scale and that, with gravity asym. safety "the good old Standard Model" might be good all the way. I'm thinking particularly of a talk Weinberg gave at CERN in summer 2009.

Also of a talk Nicolai gave at the Max Born symposium in 2009 in which he outlined something that was both testable and "big desert" in that sense, or one could more precisely say MINIMAL. Just a couple of new particles and SM is good all the way to Planck.
The idea is different from the vMSM but he referred pointedly to Shaposhnikov's work in the talk. Just recently Nicolai and Meissner came out with another paper about their idea, again emphasizing the testability at LHC.

As I recall Nicolai is a central figure in the ESF and has been on the Scientific Advisory Committee of nearly all the last 15 or so annual Strings conferences. So we are talking about Minimalist ideas that have taken hold in the European physics establishment.

I think the basic idea that comes across in all of this is "hey! maybe radical inventions like String Theory AREN'T NEEDED after all! maybe with a minor modification and asymptotic safety or something the old SM is good up to Planck scale."

It's hard for me, as very much the outsider to sum this up. There must be a ton of supporting evidence that Minimalism or "big desert" unification or whatever you call it is gaining interest among key mainstream people. It is the opposite of "crackpot" in other words.

So let me recall the two Shapo papers I mentioned in post #2:

This has some of the same discussion and the same FIGURES as the talk.
http://arxiv.org/abs/1205.2893
Higgs boson mass and new physics
Fedor Bezrukov, Mikhail Yu. Kalmykov, Bernd A. Kniehl, Mikhail Shaposhnikov
(Submitted on 13 May 2012)
We discuss the lower Higgs boson mass bounds which come from the absolute stability of the Standard Model (SM) vacuum and from the Higgs inflation, as well as the prediction of the Higgs boson mass coming from asymptotic safety of the SM. ...

This is explicitly about the NEUTRINO MINIMAL STANDARD MODEL (the topic of the talk that Mitchell linked).
http://arxiv.org/abs/1208.4607
Dark Matter, Baryogenesis and Neutrino Oscillations from Right Handed Neutrinos
Laurent Canetti, Marco Drewes, Tibor Frossard, Mikhail Shaposhnikov
(Submitted on 22 Aug 2012)
We show that, leaving aside accelerated cosmic expansion, all experimental data in high energy physics that are commonly agreed to require physics beyond the Standard Model can be explained when completing it by three right handed neutrinos that can be searched for using current day experimental techniques. The model that realises this scenario is known as Neutrino Minimal Standard Model (νMSM) ...
63 pages, many figures

To have it handy, here is Mitchell's link to Shapo's talk at the Edinburgh Higgs Symposium:
http://higgs.ph.ed.ac.uk/sites/default/files/higgs_symp.pdf
=====================
Also to have it handy I'll get the link to Nicolai and Meissner's recent paper.
http://arxiv.org/abs/1208.5653
======================
About the other things Mitchell mentioned, such as the NCG gauge networks of Matilde Marcolli and Walter van Suijlekom, I can't say right now. Have to go to supper.

Last edited: Jan 20, 2013
6. Jan 20, 2013

### atyy

Last edited: Jan 20, 2013
7. Jan 20, 2013

### marcus

Mitchell I want to be sure that my proposing as additional example the Meissner Nicolai model they call "Conformal Standard Model" (nothing to do with AdS/CFT, conformal in the sense of Riemann 1851, Caratheodory 1914, Leigh Page 1936 :-)) fits in with your neo-minimal theme and your other examples. Let me know if not.

A short bit of history:
Leigh Page defined and studied conformal field theories starting in 1936, with Maxwell EM. These are ones which are invariant under conformal (angle and orientation-preserving) maps.

Elementarer Beweis für den Fundamentalsatz der konformen Abbildungen. Constantin Caratheodory, Berlin 1914; Ges. Math. Schr.IV 249–275.

What Caratheodory called the "fundamental theorem of conformal mappings" was the celebrated Riemann Mapping Theorem (Riemann's thesis, 1851)​

I wish the link to Nicolai's 2009 Max Born talk was working. He was presenting the CSM model and it was very much in the "new minimalist" spirit. He interjected dry criticism of aspects of the string program, for instance as "increasingly BAROQUE if you follow the literature". He repeatedly emphasized the minimality and LHC testability of the Conformal Standard Model he has been working on with Meissner.

Atyy, one certainly does not get the impression either from listening to Nicolai or from reading the CSM papers that the CSM is "inspired by string theory".
Except in the sense that impatience with Baroque excess might inspire one to head in the opposite direction.

8. Jan 20, 2013

### marcus

Mitchell, not that my personal leanings matter but although I ADMIRE the efforts of these minimalist guys (especially asym safe nuMSM Shaposhnikov developments) my personal sentiments are certainly not 100% minimalist!

I don't see how the LQG-ish gambits you mentioned fit in to the new minimalist trend. The minimalist aim is for a UNIFIED THEORY NOW that is good to Planck scale. In that sense maybe Alain Connes spectral geometry (because it recovers the SM as something inherent engrained in the very geometry of space) might be seen as having a kind of minimalist elegance.

So although it seems a bit indirect you might think of the LQG-ish Marcolli van Suijlekom idea as minimalist because it uses networks of chunks of Alain Connes space. But although I LIKE it and find it interesting it seems comparatively roundabout. Could be a brilliant stroke of genius, might even succeed, but not as downtoearth straightforward as what Nicolai is doing, or Shaposhnikov.

And the LQG program as a whole (although I find it extremely interesting, especially as it gives more and more Big Bounce detail) is NOT A UNIFIED THEORY bid. As you well know, the idea is to get quantum geometry right (with token matter) and once that is right then build on it. So unification is postponed.

Postponement is not in the Nicolai and Shaposhnikov spirit, IMHO. That is my reservation about including your LQG-ish references. But I'll think about it, you may have it right and I wrong.

9. Jan 20, 2013

### marcus

Mitchell, since you mentioned LQG-ish research gambits at the start, even tho I don't see it as part of the current neo-minimal advance I will say what question about it occurs to me. What comes to mind is if you expect a neo-minimal synthesis to succeed, why work on LQG?
there is an increasing number of people doing LQG and LQC. What are all these people working on that for?

Here is why, I think. Suppose AsymSafe GR and a minor modification of good old SM turns out to WORK all the way to Planck scale. Then you could say it LOOKS like the end of an era for particle physics. The great goal of UNIFIED THEORY seems achieved.

But no! You have forgotten thermodynamics! Jacobson's result indicates that GR is superficial because it arises from the statistical mechanics of MICROSCOPIC GEOMETRIC degrees of freedom. If minimalism succeeds, the road is just beginning for the QG people.

What so many people seem focused on, and what seems to them to be the Big Goal, is a unification of GR and SM matter. A descriptive quantum theory of geometry with matter fields.

But this does not explain why GR equations seem to emerge from thermodynamics. So one needs a further unification, so to speak, of GR+SM+Thermo.

That may be putting it too crudely but I think you understand. Maybe you understand well enough to see a mistake in what I'm saying and correct me. What I'm saying, for instance, is that say Matilde Marcolli is working on a world which is a network of chunks of Connes spectral geometry---a bunch of quantum "chunkahedrons". And she hears that the secret neutrinos predicted by Shaposhnikov have been found at LHC---unification! Particle theory joins with asymptotic safe gravity! what does she do?

She keeps right on working on her networks of quantum chunkahedra. Or so I think anyway. Because they did not explain yet why asymptotic safe gravity has vacuum curvature, or why it probably had a big bounce, or why it looks like some kind of macro picture of some microscopic dof. Asymptotic safe GR is too arbitrary, who ordered that? Maybe I'm missing something and you can correct my misapprehension.

10. Jan 20, 2013

### atyy

In considering whether the theory is plausible from the point of view of needing to eventually incorporate gravity, in http://arxiv.org/abs/0907.3298 they sketch a possibility which is (p2) "inspired by a recent re-derivation from gauged supergravities in three dimensions [20, 21] of the conformally invariant and globally supersymmetric (N ≤ 8) models thought to describe multiple M2 branes." Also, while it is unclear whether a realistic version of their sketch can be eventually realised within string theory, they do say (p14) "It is therefore clear that ‘something extra’ beyond quantum ﬁeld theory is required to avoid this impasse, and that we must invoke an as yet unknown mechanism operating at the Planck scale to make this idea work."

11. Jan 20, 2013

### mitchell porter

Marcus - in making my list, I was collecting in one place a few ideas that interest me, but that lie at the opposite pole from mainstream unification philosophy, which is based on getting a supersymmetric GUT from string theory. I suppose I was exploring my dark side :-) by seeing what ingredients I might draw upon, if I wanted to engage in a completely non-string research program. Thus nuMSM supplied the empirical framework, foams and networks an approach to quantum gravity, and "chiral graviweak unification" an idea about how everything fits together.

So it's certainly a minimal program when compared to what happens at the baroque pole, but I wouldn't claim it is the "most minimal". nuMSM + asymptotic safety might deserve that title. And you're probably right that asymptotic safety is somehow "more minimal" than LQG.

I also agree that the "conformal standard model" definitely belongs at the minimal pole. btw, apart from this business of classifying research programs as minimal or baroque... in the original CSM paper I ran across the observation that the standard model would have exact conformal symmetry, if the Higgs had no VEV. That seems a very striking fact and I'm not sure what to make of it. I suppose the CSM is Nicolai and Meissner's answer - they propose that the SM arises precisely in this way, through the breaking of an underlying conformal symmetry.

12. Jan 20, 2013

### marcus

Yes! That is exactly what Nicolai said in his 2009 talk at the Max Born symposium "On the Planck Scale". The SM arises thru breaking an underlying conformal symmetry.

Great talk. The video used to be online. I'll get the link in case it gets fixed and the talk is again available.

One link to the video was here:
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php
I just tried it and it does not work. There is also a link to Nicolai's SLIDES which might work and they are very complete, so it could be useful.
YES! The slides PDF is still there, much is self-explanatory!
http://www.ift.uni.wroc.pl/~planckscale/lectures/1-Monday/3-Nicolai.pdf

Here is another website that has the slides PDF but where the videos do not seem to be online.

Last edited: Jan 20, 2013
13. Jan 22, 2013

### marcus

Mitchell, to what extent would you say that this recent paper by Sakellariadou fits into the new minimalist category?
http://arxiv.org/abs/1301.4687
Noncommutative Spectral Geometry: A Short Review
(Submitted on 20 Jan 2013)
We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong interactions. Despite the phenomenological successes of the model, the discrepancy between the predicted Higgs mass and the current experimental data indicate that one may have to go beyond the simple model considered at first. We review the current status of the phenomenological consequences and their implications. Since this model lives by construction at high energy scales, namely at the Grand Unified Theories scale, it provides a natural framework to investigate early universe cosmology. We briefly review some of its cosmological consequences.
11 pages. Invited talk in the Sixth International Workshop DICE2012, Castello Pasquini/Castiglioncello (Tuscany), September 17-21, 2012

Correct me if I'm wrong but I think Sakellariadou considers spectral geometry as a simplification--a more direct (less Baroque) bid to unify gravity and the Standard Model of matter--a more direct approach to modeling the early universe. Or at least she is presenting spectral geometry in that light.*

This is the impression I get from looking at the paper she just posted. I'm interested to know how it strikes you.
*Remains to be seen if it lives up to promise.

======quotes from introduction and from conclusions on page 10======
Given the plethora of precise cosmological and astrophysical data and the measurements obtained by particle physics experiments reaching constantly higher energy scales, we are presently in a position to falsify early universe cosmological models. In return, by comparing the theoretical predictions against current data, we are able to constrain the fundamental theories upon which our cosmological models were based. A fruitful such example is the cosmological model based on Noncommutatitive Geometry [1, 2] and the Spectral Action principle, leading to the Noncommutative Spectral Geometry (NCSG), a theoretical framework that can provide [3] a purely geometric explanation for the Standard Model (SM) of strong and electroweak interactions. This model lives by construction in high energy scales, the Grand Unified Theories (GUTs) scale, offering a natural framework to study early universe cosmology [4]-[11]. Hence, instead of postulating a Lagrangian upon which we will build our cosmological model, we will adopt the one dictated by NCSG, with the constraints imposed by NCSG itself, and within the framework of this gravitational theory we will address some cosmological issues. Clearly, this is a solid approach, since the cosmological model is inspired and controlled from a fundamental theory. In return, by comparing the predictions of the model against high energy physics measurements and cosmological data, we will be able to constrain some of the free parameters of NCSG and/or its basic element, namely the choice of the algebra...

... In his approach, Connes combined spacetime with an internal space, composed by only 2 points, a construction that can be seen as a discrete Kaluza-Klein space where the product manifold of spacetime with extra spatial dimensions is replaced by the product of spacetime with discrete spaces represented by matrices...
==endquote==

On page 2 there is an important reference to a companion paper (also presented at the 2012 DICE conference) namely:
http://arxiv.org/abs/1301.2563
Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory
Mairi Sakellariadou, Antonio Stabile, Giuseppe Vitiello
(Submitted on 11 Jan 2013)
We report the results obtained in the study of Alain Connes noncommutative spectral geometry construction focusing on its essential ingredient of the algebra doubling. We show that such a two-sheeted structure is related with the gauge structure of the theory, its dissipative character and carries in itself the seeds of quantization. From the algebraic point of view, the algebra doubling process has the same structure of the deformed Hopf algebra structure which characterizes quantum field theory.
11 pages. Invited talk in the Sixth International Workshop DICE2012, Castello Pasquini/Castiglioncello (Tuscany), September 17-21, 2012

Last edited: Jan 22, 2013
14. Jan 23, 2013

### mitchell porter

The noncommutative standard model can be part of a minimalist program but doesn't have to be. It could be regarded as just a low-energy limit of a noncommutative GUT or super-GUT. NCG aims to get gauge forces from gravity on the noncommutative space, so that's a type of unification idea, and I would place most NCG physics research near the minimal pole, even if not directly on it.

btw Nicolai's talk posted on the arxiv today is clearly a minimalist manifesto. It might be interesting to extract its talking points and compare them with those in Shaposhnikov's recent talk - see what they have in common, whether there are any differences, and perhaps even complementary ideas.

15. Jan 23, 2013

### atyy

Why is it the Breughel scenario undesirable? In fact, isn't that the moral of Wilsonian renormalization?

I might be misinterpreting Wen's misinterpretation, but he gives a mischevous translation of the Tao Te Ching in the spirit of his textbook (p11, footnote 11): "The physical theory that can be formulated cannot be the final ultimate theory. The classification that can be implemented cannot classify everything. The unformulatable ultimate theory does exist and governs the creation of the universe. The formulated theories describe the matter we see everyday."

16. Jan 24, 2013

### atyy

Nicolai says "This renormalization prescription in essence amounts to an order by order tuning of a ﬁnite number of parameters by inﬁnite factors. Although mathematically on very shaky grounds, this procedure has produced results in stunning agreement with experimental ﬁndings, with a precision unmatched by any other scheme in the physical sciences." But isn't this at odds with the Wilsonian viewpoint? I agree the Wilsonian viewpoint is still not rigourous - but the philosophy is that any theory with the same symmetries looks renormalizable at low enough energies, so isn't it an absence of fine tuning?

Also, if the proposal by Castro and colleagues http://arxiv.org/abs/1111.1987 works out, then wouldn't pure gravity would be brought within AdS/CFT, which via Swingle's AdS/MERA proposal would unify string theory and LQG, so Babel might be some ways off. Given AdS/CFT maybe the bigger fundamental problem is the interpretation of quantum mechanics in a cosmological context, if one feels Many-Worlds to be much more baroque than string theory.

Last edited: Jan 24, 2013
17. Jan 24, 2013

### Chronos

Pardon the intrusion by a lurker from the unwashed masses. I find Shaposhnikov's proposal intriguing - largely because it affords generous wriggle room for sterile neutrinos [in the right mass range] as the elusive dark matter particle.