Edward Witten is frequently painted equally a "basically mathematician".
In fact, it's a description that you lot may receive got heard non exclusively from the postmodern critics of scientific discipline but perchance fifty-fifty from your humble correspondent (especially whenever I constitute the publish of homotopies as well as other things excessive for a given physical role inwards a newspaper he wrote). But I receive got e'er appreciated how much he understands both mathematics as well as physics – including physics that is real unopen to experiments. I was amazed yesteryear his cognition of deeply technical, experiment-oriented particle physics phenomenology to a greater extent than than once.
Well, a calendar week ago, along amongst Lam Hui (Columbia), Jeremiah P. Ostriker (Columbia + Princeton U.), as well as Scott Tremaine (Princeton IAS), Witten co-wrote a newspaper on cosmology (astro-ph.CO) which was submitted to PRD (the acronym agency FART inwards Czech)
On the hypothesis that cosmological night affair is composed of ultra-light bosonsI don't follow astro-ph abstracts on a daily ground hence I had to acquire nearly the newspaper from a large fan of Edward Witten who religiously digests every missive of the alphabet that Witten writes anywhere as well as who went to a opor-garai – as well as declared a hiatus inwards his blogging – because he needs to read the newspaper inwards detail. Well, this fan is also a large fan of supersymmetry as well as string theory whenever he's non drunk. His cry is Tommaso Dorigo. Well, the Italian vino is skillful – I hateful skillful plenty for the Italians.
The WIMP, or the "weakly interacting massive particle", has been the #1 pop candidate for the composition of the night matter. It was in all likelihood my #1 pick equally good although I receive got never been a warrior inwards this particular battle.
By definition, a WIMP is a particle amongst a similar volume as well as a similar interaction strength equally the "lightest superpartner" (LSP) inwards supersymmetric theories. The masses were supposed to endure merely about or beneath \(1\TeV\) as well as the values of the coupling constants are dictated yesteryear the supersymmetry – inwards some cardinal counting, they are equal to those of their known superpartners inwards the Standard Model. The "number of LSPs" is typically conserved modulo ii – because of the R-parity – hence these particles may annihilate inwards pairs as well as that's frequently assumed to endure the belongings of the WIMP, too.
Exactly amongst these natural masses as well as couplings, cosmological models including the enhanced particle physics range you lot a realistic cosmological development including a pretty successful prediction of the amount of night affair for today. This a priori unexpected success is known equally the "cosmic coincidence" as well as it was – as well as it however generally is – an of import argue to accept the theory that night affair is made of WIMPs seriously.
(But it's merely generally an order-of-magnitude understanding inwards a unmarried publish hence you lot shouldn't overstate the certainty that this "consistency checks" offers you.)
WIMP is however a probable plenty possibility but it has never been a near-certain possibility. Its competitors were e'er comparably likely. Because the LHC equally good equally the remove search experiments – which move nether the ground – could receive got constitute a WIMP inwards recent years but haven't (despite the preliminary hopes that several experiments receive got ignited), the odds receive got shifted.
There are at to the lowest degree v subtypes of axions. Concerning the commencement one, don't overlook the claims that all these antibacterial ones are in all likelihood more dangerous than helpful for your health. Picture via David Saltzberg of UCLA, the scientific discipline advisor behind Sheldon Cooper as well as pals, as well as the sentiment non exclusively behind the cry is due to Frank Wilczek.
If you lot were assigning the probability 70% to the WIMP as well as 25% to the 2d most probable explanation for night matter's beef, an axion (you're 95% sure enough that it's i of those), some 5 years ago, it's rather probable that yesteryear now, you lot already retrieve that the axion is to a greater extent than probable than a WIMP. Why? Because over 2/3 of the "reasonable parameter space" of the WIMP's parameter. So 70% got reduced to some 23% as well as the axions' 25% already shell the WIMPs' 23%. Note that you lot necessitate to renormalize the percentages if you lot trim one. (The numerical values of the probabilities are arbitrary – perchance my subjective ones – but I am confident that most cosmologists as well as particle physicists would okay them equally "vaguely compatible amongst their guesses".)
(In the remaining 5%, I could say that 3% is "dark affair is made of dark holes similar to the LIGO-detected ones", 1% is some MOND-like modified gravity without zillions of excitations of novel particle species, as well as 1% is something else including the possibility that the people volition determine that "nothing similar night affair or corresponding novel physical phenomena exists at all" for some reasons I don't sympathise now. Also banknote that if you lot replaced 70% yesteryear 99.999%, similar I practice amongst the validity of SUSY equally a principle, the publish would remain way higher upwardly 99% fifty-fifty after the reduction of 2/3 of the parameter space.)
In recent years, the axions haven't been weakened (almost) equally a theory of night affair at all because the axions are difficult to straight attain or discovery because of their interaction constants. (I say "almost" because some cosmological observations practice constrain axions as well as those observations got a niggling flake better, too.) Note that axions are usually real low-cal scalar particles that play several roles inwards physics as well as may come upwardly from many sources. The key role they were designed for is to solve the strong CP-problem i.e. explicate why the coefficient of the topological term \({\rm Tr}(F\wedge F)\) inwards the QCD role of the Standard Model – a term that could contribute a lot to the violation of the CP-symmetry but contributes real niggling if non zero – is hence tiny.
Concerning the origins, string theory may commonly attain lots of axions, perchance fifty-fifty hundreds of them. It's because the 10- or 11-dimensional effective theory for string/M-theory contains \(p\)-form fields such equally \(C_{\lambda\mu\nu}\). When integrated via \(\oint_C\) over \(p\)-cycles (noncontractible or topologically nontrivial \(p\)-dimensional submanifolds) of the compactification manifold (such equally a Calabi-Yau or a \(G_2\) holonomy manifold), they trim to i of the scalars (a \(0\)-form is a way to telephone telephone a scalar inwards the \(p\)-form language). There may endure hundreds of inequivalent cycles, hence you lot may acquire hundreds of scalars. It may endure shown that their masses are naturally depression as well as "exponentially small" patch the exponents may accept real various values. General ideas similar that are known equally the "axiverse".
The recent newspaper yesteryear Witten et al. describes the stringy ancestry of the axions equally follows:
For example, all models of particle physics derived from string theory receive got at to the lowest degree several periodic scalar fields such equally \(a\), as well as typical models receive got many of them (dozens or fifty-fifty hundreds). Various possible applications of these fields receive got been considered (see for event [23]). With dissimilar assumptions nearly their masses, they receive got been proposed equally candidates for the inflaton acre of inflationary cosmology; equally potential QCD axions, whose beingness may explicate CP conservation yesteryear nuclear forces; as well as equally contributors to night loose energy or the cosmological constant and/or ingredients inwards a machinery to explicate its smallness. For our acquaint purposes, nosotros are interested inwards these fields equally candidates for FDM.A paragraph later, they also cite an gauge from heterotic string theory. I am mentioning these things to assure you lot that Witten hasn't forgotten that he is a string theorist.
OK, let's supply to the novel claims inwards the newspaper yesteryear Witten as well as co-authors.
They merely signal out – a non completely novel but nicely as well as concisely phrased as well as supplemented amongst some novel ideas that thicken the motion-picture demonstrate – that a massive but ultralight axion seems compatible amongst everything nosotros know as well as demand from night matter. In particular \[
m \gtrapprox 10^{-31}\GeV
\] seems to endure a non bad value for the axion mass. This is a tiny volume relatively to the LHC particles, indeed, which is why I used the high-energy unit, i \({\rm GeV}\). (Witten as well as pals used \({\rm eV}\) to demonstrate how much grounded to the Earth, lithium-ion batteries, as well as the Galaxy they are.) This tiny volume is equivalent to the de Broglie wavelength\[
\lambda\lessapprox 3,000\,\,\text{light years}
\] which the authors depict equally i kiloparsec, for Edward Witten to remind us that he wanted to endure an astronomer as well as
There are at to the lowest degree v subtypes of axions. Concerning the commencement one, don't overlook the claims that all these antibacterial ones are in all likelihood more dangerous than helpful for your health. Picture via David Saltzberg of UCLA, the scientific discipline advisor behind Sheldon Cooper as well as pals, as well as the sentiment non exclusively behind the cry is due to Frank Wilczek.
If you lot were assigning the probability 70% to the WIMP as well as 25% to the 2d most probable explanation for night matter's beef, an axion (you're 95% sure enough that it's i of those), some 5 years ago, it's rather probable that yesteryear now, you lot already retrieve that the axion is to a greater extent than probable than a WIMP. Why? Because over 2/3 of the "reasonable parameter space" of the WIMP's parameter. So 70% got reduced to some 23% as well as the axions' 25% already shell the WIMPs' 23%. Note that you lot necessitate to renormalize the percentages if you lot trim one. (The numerical values of the probabilities are arbitrary – perchance my subjective ones – but I am confident that most cosmologists as well as particle physicists would okay them equally "vaguely compatible amongst their guesses".)
(In the remaining 5%, I could say that 3% is "dark affair is made of dark holes similar to the LIGO-detected ones", 1% is some MOND-like modified gravity without zillions of excitations of novel particle species, as well as 1% is something else including the possibility that the people volition determine that "nothing similar night affair or corresponding novel physical phenomena exists at all" for some reasons I don't sympathise now. Also banknote that if you lot replaced 70% yesteryear 99.999%, similar I practice amongst the validity of SUSY equally a principle, the publish would remain way higher upwardly 99% fifty-fifty after the reduction of 2/3 of the parameter space.)
In recent years, the axions haven't been weakened (almost) equally a theory of night affair at all because the axions are difficult to straight attain or discovery because of their interaction constants. (I say "almost" because some cosmological observations practice constrain axions as well as those observations got a niggling flake better, too.) Note that axions are usually real low-cal scalar particles that play several roles inwards physics as well as may come upwardly from many sources. The key role they were designed for is to solve the strong CP-problem i.e. explicate why the coefficient of the topological term \({\rm Tr}(F\wedge F)\) inwards the QCD role of the Standard Model – a term that could contribute a lot to the violation of the CP-symmetry but contributes real niggling if non zero – is hence tiny.
Concerning the origins, string theory may commonly attain lots of axions, perchance fifty-fifty hundreds of them. It's because the 10- or 11-dimensional effective theory for string/M-theory contains \(p\)-form fields such equally \(C_{\lambda\mu\nu}\). When integrated via \(\oint_C\) over \(p\)-cycles (noncontractible or topologically nontrivial \(p\)-dimensional submanifolds) of the compactification manifold (such equally a Calabi-Yau or a \(G_2\) holonomy manifold), they trim to i of the scalars (a \(0\)-form is a way to telephone telephone a scalar inwards the \(p\)-form language). There may endure hundreds of inequivalent cycles, hence you lot may acquire hundreds of scalars. It may endure shown that their masses are naturally depression as well as "exponentially small" patch the exponents may accept real various values. General ideas similar that are known equally the "how frequently he looks into a existent telescope (where i may run across some angles as well as those are the exclusively possible justification for medieval units such equally i parsec which I would ban if I became an European Union commissar).
Because of this ultralong de Broglie wavelength, something is "different" when you lot attempt to squelch these particles also much. That's much similar trying to compress things to also small-scale areas inwards the stage space. And that's why this model of night affair is called "fuzzy night matter" or FDM for short. It may endure considered a competing option of the CDM or mutual frigidity night affair paradigm.
At these astronomical distances – which are however safely smaller than our galaxy – novel effects appear. The authors fighting that the FDM night affair halos cannot endure also small-scale because they e'er receive got a "minimum size object" somewhere within – which is described equally zero else than a soliton. There is an envelope merely about the soliton nitty-gritty as well as they verbalize over the relaxation procedure inwards betwixt them. They also verbalize over the evaporation of the soliton through tunneling.
Finally, they cite the Fornax dwarf galaxy – a low-luminosity satellite galaxy of our Galaxy (i.e. amongst a high ratio of night as well as visible matter; it also contains globular clusters) – equally a possible smoking gun that seems compatible amongst their preferred FDM motion-picture demonstrate patch it acre contradicts the CDM paradigm. Why does it contradict? Because it should receive got spiralled to the center, much similar the classical hydrogen atom. The fuzzy FDM motion-picture demonstrate makes the dwarf galaxy stable much similar quantum mechanics makes the atoms stable against the spiraling inwards.
It's a refreshing newspaper to read because the required scientific discipline is arguably to a greater extent than basic than (even) the scientific discipline needed to read as well as sympathise Witten's papers on condensed affair physics as well as other disciplines studied yesteryear the mortals. And the 4 authors – don't forget that in that location are 4 – merely write sufficiently clearly.
So amongst the FDM equally a possibility, in that location is clearly no "catastrophic contradiction" inwards electrical flow physics when it comes to night matter. At the same moment, if some ultralight axions similar that play such an of import role inwards cosmology, it volition exclusively deepen the thirst for the novel groundbreaking terrestrial discoveries. Just to endure sure, their ultralight FDM axion has observable consequences, specially if the axion volume is at most 10 times heavier than the lower fountain (after all, in that location is already a slight tension amongst the Lyman-\(\alpha\) forest), but all these observational consequences require astronomers as well as telescopes to endure tested rather than experimenters standing on our blue, non green, planet.
Some people may discovery it irritating as well as less scientific but Nature doesn't care. If the particle of night affair may exclusively endure studied through the telescopes, well, as well as hence it's what Nature wanted. If you're dissatisfied, apply for the political asylum inwards a dissimilar Universe (or inwards Kingdom of Saudi Arabia where the ground is however flat).
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