Quark (Anti)Nugget Dark Matter

Kyle Lawson and Ariel R. ZhitnitskyDepartment of Physics & Astronomy, University of British Columbia, Vancouver, B.C. V6T 1Z1, Canada

We review a testable dark matter model outside of the standard WIMP paradigm in which theobserved ratio Ωdark ' 5·Ωvisible for visible and dark matter densities finds its natural explanation asa result of their common QCD origin. Special emphasis is placed on the observational consequencesof this model and on the detection prospects for present or planned experiments. In particular, weargue that the relative intensities for a number of observed excesses of emission (covering more than11 orders of magnitude) can be explained by this model without any new fundamental parameters asall relative intensities for these emissions are determined by standard and well established physics.

I. QCD AS A SINGLE SOURCE FOR DARKMATTER AND VISIBLE BARYONS

In this proposal we argue that two of the largestopen questions in cosmology, the origin of the mat-ter/antimatter asymmetry and the nature of the darkmatter (DM), may have their origin within a single the-oretical framework. Furthermore, both effects may orig-inate at the same cosmological epoch from one and thesame QCD physics.

It is generally assumed that the universe began in asymmetric state with zero global baryonic charge andlater, through some baryon number violating process,evolved into a state with a net positive baryon number.As an alternative to this scenario we advocate a model inwhich “baryogenesis” is actually a charge separation pro-cess in which the global baryon number of the universeremains zero. In this model the unobserved antibaryonscome to comprise the dark matter. A connection betweendark matter and baryogenesis is made particularly com-pelling by the similar energy densities of the visible anddark matter with Ωdark ' 5 · Ωvisible. If these processesare not fundamentally related the two components couldexist at vastly different scales.

In this model baryogenesis occurs at the QCD phasetransition. Both quarks and antiquarks are thermallyabundant in the primordial plasma but, in addition toforming conventional baryons, some fraction of them arebound into heavy nuggets of quark matter in a coloursuperconducting phase. Nuggets of both matter and an-timatter are formed as a result of the dynamics of theaxion domain walls [1, 2], some details of this processwill be discussed in section II. Were CP symmetry to beexactly preserved an equal number of matter and anti-matter nuggets would form resulting in no net “baryoge-nesis”. However, CP violating processes associated withthe axion θ term in QCD result in the preferential forma-tion of antinuggets 1. At the phase transition θ ∼ 1 and

1 This preference is essentially determined by the sign of θ. Note,that the idea of a charge separation mechanism resulting fromlocal violation of CP invariance through an induced θind canbe experimentally tested at the Relativistic Heavy Ion Collider(RHIC) and the LHC. We include a few comments and relevant

One part: visible matter

Two parts: matter nuggets

Three parts: anti-matter nuggets

Btot = 0 = Bnugget + Bvisible − Bantinugget

BDM = Bnugget + Bantinugget 5 Bvisible

The ratio is determined by CP violating parameter

Bnugget/Bantinaget 2/3

θ ∼ 1

FIG. 1. Matter in the Universe. A model which explainsboth the matter -antimatter asymmetry and the observed ra-tio of visible matter and DM

all asymmetry effects would have been order one whileduring the present epoch, long after the phase transition,this source of CP violation is no longer available. The re-maining antibaryons in the plasma then annihilate awayleaving only the baryons whose antimatter counterpartsare bound in the excess of antinuggets and thus unavail-able to annihilate. The observed matter to dark matterratio results if the number of antinuggets is larger thannumber of nuggets by a factor of ∼ 3/2 at the end ofnugget formation. This would result in a matter contentwith baryons, quark nuggets and antiquark nuggets in anapproximate ratio

Bvisible : Bnuggets : Bantinuggets ' 1 : 2 : 3, (1)

and no net baryonic charge, as sketched on Fig.1.Unlike conventional dark matter candidates, dark-

matter/antimatter nuggets are strongly interacting but

references, including some references to recent experimental re-sults supporting the basic idea, in section V.

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macroscopically large. They do not contradict the manyknown observational constraints on dark matter or anti-matter for three main reasons [3]:

• They carry a huge (anti)baryon charge |B| & 1025,and so have an extremely tiny number density;

• The nuggets have nuclear densities, so their effec-tive interaction is small σ/M ∼ 10−10 cm2/g, wellbelow the typical astrophysical and cosmologicallimits which are on the order of σ/M < 1 cm2/g;

• They have a large binding energy such that thebaryon charge in the nuggets is not available toparticipate in big bang nucleosynthesis (bbn) atT ≈ 1 MeV.

To reiterate: the weakness of the visible-dark matterinteraction in this model due to the small geometri-cal parameter σ/M ∼ B−1/3 rather than due to theweak coupling of a new fundamental field to standardmodel particles. It is this small effective interaction∼ σ/M ∼ B−1/3 which replaces the conventional require-ment of sufficiently weak interactions for WIMPs.

An fundamental measure of the scale of baryogenesisis the baryon to entropy ratio at the present time

η ≡ nB − nBnγ

' nBnγ∼ 10−10. (2)

If the nuggets were not present after the phase transi-tion the conventional baryons and anti-baryons wouldcontinue to annihilate each other until the temperaturereaches T ' 22 MeV when density would be 9 ordersof magnitude smaller than observed. This annihilationcatastrophe, normally thought to be resolved as a re-sult of “baryogenesis,” is avoided in our proposal becausemore anti-baryons than baryons are hidden in the formof the macroscopical nuggets and thus no longer avail-able for annihilation. Only the visible baryons (not anti-baryons) remain in the system after nugget formation isfully completed.

In our proposal (in contrast with conventional models)the ratio η is determined by the formation temperatureTform at which the nuggets and anti-nuggets basicallyhave competed their formation and below which annihi-lation with surrounding matter becomes negligible. Thistemperature is determined by many factors: transmis-sion/reflection coefficients, evolution of the nuggets, ex-pansion of the universe, cooling rates, evaporation rates,the dynamics of the axion domain wall network, etc.In general, all of these effects will contribute contributeequally to determining Tform at the QCD scale. Tech-nically, the corresponding effects are hard to computeas even basic properties of the QCD phase diagram atnonzero θ are still unknown. However, an approximateestimate of Tform is quite simple as it must be expressedin terms of the gap ∆ ∼ 100 MeV when the colour su-perconducting phase sets in inside the nuggets. The ob-served ratio (2) corresponds to Tform ' 41 MeV whichis indeed a typical QCD scale slightly below the critical

temperature Tc ' 0.6∆ when colour superconductivitysets in.

In different words, in this proposal the ratio (2)emerges as a result of the QCD dynamics when processof charge separation stops at Tform ' 41 MeV, ratherthan a result of baryogenesis when a net baryonic chargeis produced.

II. QUARK (ANTI)NUGGETS AS DARKMATTER

The majority of dark matter models assume the exis-tence of a new fundamental field coupled only weakly tothe standard model particles, these models may then betuned to match the observed dark matter properties. Wetake a different perspective and consider the possibilitythat the dark matter is in fact composed of well knownquarks and antiquarks but in a new high density phase,similar to the Witten’s strangelets [4]. The only new cru-cial element in comparison with previous studies basedon Witten’s droplets [4] is that the nuggets could bemade of matter as well as antimatter in our framework,and the stability of the DM nuggets is provided by theaxion domain walls [1].

Though the QCD phase diagram at θ 6= 0 is not known,it is well understood that θ is in fact the angular vari-able, and therefore supports various types of the domainwalls, including the so-called N = 1 domain walls when θinterpolates between one and the same physical vacuumstate θ → θ + 2π. While such domain walls are formallyunstable, their life time could be much longer than lifetime of the universe. Furthermore, it is expected thatclosed bubbles made of these N = 1 axion domain wallsare also produced during the QCD phase transition witha typical correlation length ∼ m−1

a where ma is the ax-ion mass. The N = 1 axion domain walls are unique ina sense that they might be formed even in case of infla-tion which normally prevents the generation of any othertypes of topological defects.

The collapse of these closed bubbles is halted due tothe fermi pressure acting inside of the bubbles as sketchedon Fig. 2. The equilibrium of the obtained system hasbeen analyzed in [1] for a specific axion domain wall withtension σa ' 1.8 · 108GeV3 which corresponds to ma ∼10−6 eV. For these axion parameters it has been foundthat a typical baryon charge of the nugget is B ∼ 1032

while a typical size of the nugget is R ∼ 10−3cm. Usingthe dimensional arguments one can easily infer that theseparameters scale with the axion mass as follows

σa ∼ m−1a , R ∼ σa, B ∼ σ3

a. (3)

Therefore, when the axion mass ma varies within the ob-servationally allowed window 10−6eV ≤ ma ≤ 10−3eV,see e.g. reviews [6, 7], the corresponding nuggets param-eters also vary as follows

10−6cm . R . 10−3cm, 1023 . B . 1032. (4)

3

Antiquark nugget structure. Source of emission

e-

e+

e+e+

e+

511 keV

~ 100 MeV - 1 GeV

e+Antimattercolor superconductor

e+

e+

e

e+

e+

p,n

electrosphere

e

1-20 MeV

X rays ~10 keV

thermalization

(10−4− 1)eV

bremsstrahlung radiation( largest fraction)

qq → 2 GeV

energy

γ

(rare events)

(finite fraction)

axion domain wall pressure

Fermi PressureR ∼ 10−5cm, B ∼ 1025

FIG. 2. (Anti)nugget internal structure and sources of emis-sion from the core of the galaxy.

The corresponding allowed region is essentially uncoveredby present experiments, see Fig.5 from section IV.

While the observable consequences of this model arestrongly suppressed by the low number density of thequark nuggets the interaction of these objects with thevisible matter of the galaxy will necessarily produce ob-servable effects. Any such consequences will be largestwhere the densities of both visible and dark matter arelargest such as in the core of galaxies or the early uni-verse. The nuggets essentially behave as conventionalcold DM in an environment where the surrounding den-sity is small, while in environments of sufficiently largedensity they begin interacting and emitting radiation (i.e.effectively become visible matter) when they are placedin an environment of sufficiently large density 2.

We emphasize that the phenomenologically relevantfeatures of the nuggets are determined by properties ofthe surface layer of electrons (or positrons in the caseof an antimatter nugget) known as the electrosphere assketched on lower right corner of Fig.2. These proper-

2 In this short review we concentrate on the phenomenological con-sequences of anti-nuggets which can act as additional radiationsources as a result of rare annihilation events, see sections III, IVfor some details. Matter nuggets may also be phenomenologicallyinteresting as they will occasionally be captured by astronomi-cal objects. Captured matter nuggets will behave very differentlyfrom strangelets [4] because the nuggets do not convert the entiresurrounding object into strange matter. Rather, the high den-sity regions inside any object will remain a finite size (4) withthe quark matter extending to eventually become normal nuclearmatter at lower densities, as in studies of possible colour super-conducting cores of neutron stars. The possibility that standardastronomical objects may have a small quark matter core impliesthat some objects may bebe observer to have a much higher den-sity than typically assumed, see e.g. [5] and the many referencestherein on some observational consequences of high density ob-jects dressed by a normal matter.

ties are in principle, calculable from first principles usingonly the well established rules of QCD and QED. As suchthe model contains no tunable fundamental parameters,except for a single mean baryon number < B > which ishard to compute theoretically as it depends on all com-plications mentioned above such as QCD phase diagramat θ 6= 0, formation and evolution of the nuggets, etc.This parameter < B >∼ 1025 is fixed in our proposal as-suming that anti-nuggets saturate the observed 511 keVline from the centre of galaxy, see next section III.

III. ASTROPHYSICAL OBSERVATIONS

A comparison between different observations of emis-sion from the centre of galaxy is possible becausethe rate of annihilation events is proportional tonvisible(r)nDM (r)-the product of the local visible and DMdistributions at the annihilation site. The observed fluxesfor different emissions thus depend on one and the sameline-of-sight integral

Φ ∝ R2

∫dΩdl[nvisible(l) · nDM (l)], (5)

where R ∼ B1/3 is a typical size of the nugget which de-termines the effective cross section of interaction betweenDM and visible matter. As nDM ∼ B−1 the effective in-teraction is strongly suppressed ∼ B−1/3 as we alreadymention in section I. The average baryonic charge B ofthe nuggets is the only unknown parameter of the model.It is determined by the properties of the axion as reviewedin section II. In what follows we fix Φ from (5) for allgalactic emissions considered below by assuming that ourmechanism saturates 511 keV line as discussed below. Itcorresponds to an average baryon charge B ∼ 1025 for atypical density distributions nvisible(r), nDM (r) entering(5). Other emissions from different bands are expressedin terms of the same integral (5), and therefore, the rela-tives intensities are completely determined by the inter-nal structure of the nuggets which is described by con-ventional nuclear physics and basic QED.

We emphasize that this proposal makes a very non-trivial prediction: the morphology of all the differentdiffuse emission sources discussed below must be verystrongly correlated. Furthermore, in this frameworkall emissions from different bands are proportional to∫dl[nvisible(l) ·nDM (l)], which should be contrasted with

many other DM models in which the intensities of pre-dicted emissions are proportional to

∫dln2

DM (l) for an-nihilating DM models or

∫dlnDM (l) for decaying DM

models.There are a number of frequency bands in which an

excess of emission, not easily explained by conventionalastrophysical sources has been observed. These include:

a) The Spi/Integral observatory detects a strongerthan expected 511 keV line associated with the galacticcentre [8].

4

FIG. 3. γ ray spectrum of inner galaxy. Green verticalbars: COMPTEL data. Solid blue line: expected totalemission due to a combination of conventional astrophysicalsources. Heavy black dots: calculated emission spectrum fromelectron-nugget annihilation processes, taken from [15].

b) The Comptel satellite observes an excess in 1-30 MeV γ-rays [9], see green vertical bars on Fig.3.

c) In the x-ray range Chandra observed a ∼ 10 keVplasma associated with the galactic centre. This plasmahas no clear heating mechanism and is too energetic toremain bound to the galaxy [10].

d) In the microwave range WMAP observes a “haze”associated with the foreground galaxy [11].

e) At temperatures below the CMB peak Arcade2 hasmeasured a sharp rise in the isotropic radio backgroundsuggesting an additional source of radiation present inthe universe before the formation of large scale structure[12], see data points on Fig.4.

The interaction between the nuggets and their envi-ronment is governed by well known nuclear physics andbasic QED. As such their observable properties containrelatively few tunable parameters allowing several strongtests of the model to be made based on galactic observa-tions. It is found that the presence of quark nugget darkmatter is not merely allowed by present observations butthat the overall fit to the diffuse galactic emission spec-trum across many orders of magnitude in energy maybe improved by their inclusion. To be more specific, inour proposal the excesses of emissions are explained asfollows:

a) The galactic electrons incident on an antiquarknugget annihilate with the surrounding positron layerthrough resonance positronium (Ps) formation. This re-sults in the 511 keV line with a typical width of order∼ few keV accompanied by the conventional continuum

due to 3γ decay [13, 14], sketched on right upper corneron Fig.2. The distribution [nvisible · nDM ] from eq. (5)implies that the predicted emission will be asymmetric,with extension into the disk from the galactic center as ittracks the visible matter. There appears to be evidencefor an asymmetry of this form [8].

b) Some galactic electrons are able to penetrate to asufficiently large depth as shown on right upper corneron Fig.2. Positrons closer to the quark matter surfacecan carry energies up to the nuclear scale. These eventsno longer produce the characteristic positronium decayspectrum but a direct non-resonance e−e+ → 2γ emis-sion spectrum [15]. The transition between these tworegimes is determined by conventional physics and allowsus to compute the strength and spectrum of the MeVscale emissions relative to that of the 511 keV line [16].Observations by the Comptel satellite indeed show anexcess above the galactic background [9] consistent withour estimates, see heavy black dots on Fig. 3. We em-phasize that the ratio between these two emissions is de-termined by well established physics. This ratio is highlysensitive to the positron density in electrosphere (shownon right lower corner on Fig.2) which has highly nontriv-ial behaviour. It was was computed using Thomas-Fermiapproximation[16] to estimate the spectrum in MeV bandshown on Fig.3.

c) Galactic protons incident on the nugget will pene-trate some distance into the quark matter before anni-hilating into hadronic jets sketched on left upper cor-ner on Fig.2. This process results in the emission ofBremsstrahlung photons at x-ray energies [17]. Obser-vations by the Chandra observatory indeed indicate anexcess in x-ray emissions from the galactic centre [10]with the intensity and spectrum consistent with our es-timates [17].

d) Hadronic jets produced deeper in the nugget oremitted in the downward direction will be completely ab-sorbed. They eventually emit thermal photons with ra-dio frequencies contributing to the wmap haze sketchedon left lower corner on Fig.2. Again the relative scalesof these emissions may be estimated and is found to bein agreement with their observed levels, see [18] for thedetails.

e) The source of the emission discussed above with ra-dio frequencies contributing to the WMAP haze sketchedon left lower corner on Fig.2 is also quite active at ear-lier times at z ∼ 103 when the densities of the particlesare about the same order of magnitude as in the center ofgalaxy at present time. The analysis [19] finds that at en-ergies near the CMB peak the nugget contribution to theradio background is several orders of magnitude belowthat of the thermal CMB spectrum. However the CMBspectrum falls of at frequencies below peak much fasterthan that of the nuggets such that, at frequencies belowroughly a Ghz, they come to dominant the isotropic ra-dio background. As such the presence of dark matter inthe form of quark nuggets offers a potential explanationof the radio excess observed by ARCADE2, as shown on

5

FIG. 4. Predicted antenna temperature assuming that thequark nuggets have a temperature of 0.1eV, 0.25eV and 1eVat the time of cmb formation. Also plotted are the data pointsfrom the radio band observations. Taken from [19]

Fig. 4.These apparent excess emission sources have been cited

as possible support for a number of dark matter modelsas well as other exotic astrophysical phenomenon. Atpresent however they remain open matters for investiga-tion and, given the uncertainties in the galactic spectrumand the wide variety of proposed explanations are un-likely to provide clear evidence in the near future. There-fore, we turn to direct detection prospects of such objects.

IV. DIRECT DETECTION PROSPECTS

Given the uncertainties associated with galactic back-grounds a complementary direct detection approach isnecessary. While direct searches for weakly interactingdark matter require large sensitivity a search for highmass dark matter requires large area detectors. If thedark matter consists of quark nuggets at the B ∼ 1025

scale they will have a flux of

dN

dA dt= nv ≈

(1025

B

)km−2yr−1 (6)

While this flux is far below the sensitivity of conventionaldark matter searches it is similar to the flux of cosmicrays near the GZK limit. As such present and futureexperiments investigating ultrahigh energy cosmic raysmay also serve as search platforms for dark matter ofthis type.

A nugget of dark matter impacting the earth’s atmo-sphere will annihilate the line of atmospheric moleculesin it’s path heating the nugget and depositing energy inthe atmosphere. For a nugget with a radius of 10−5cm

the annihilation of all molecules along it’s path wouldresult in the annihilation of 10−10kg of matter and gen-erate ∼ 107J substantially more than a conventionalUHECR though much of this energy is actually thermal-ized within the nugget. The majority of this energy isproduced by nuclear annihilations occurring within thenugget, the hadronic components released in these eventsremain bound to the quark matter and thermalize withinit before they are able to escape into the atmosphere.While they are less strongly bound electrons are unableto escape through the dense positron layer at the nuggetsurface and are also thermalized. As such the emissionfrom the nuggets is dominated by relativistic muons andthermal photons.

Recent work has considered the possibility that largescale cosmic ray detectors may be capable of observingquark nuggets passing through the earth’s atmosphere ei-ther through the extensive air shower such an event wouldtrigger [20] or through the geosynchrotron emission gen-erated by the large number of secondary particles [21]. Ithas also been suggested that the anita experiment maybe sensitive to the radio band thermal emission generatedby these objects as they pass through the antarctic ice[22]. These experiments may thus be capable of addingdirect detection capability to the indirect evidence dis-cussed above in section III.

On entering the earth’s crust the nugget will continueto deposit energy along its path, however this energy isdissipated in the surrounding rock and is unlikely to bedirectly observable. Generally the nuggets carry suffi-cient momentum to travel directly through the earth andemerge from the opposite side however a small fractionmay be captured and deposit all their energy. In [22]the possible contribution of energy deposited by quarknuggets to the earth’s thermal budget was estimated andfound to be consistent with observations.

The muonic component of the shower is particularlyimportant as it drives an extensive air shower surround-ing the quark nugget. This shower will be similar to thoseinitiated by an ultrahigh energy proton or nucleus, asboth arise from a large number of hadronic cascades, butwith some important distinctions. The most importantdistinction arises from the fact that the quark nugget re-mains intact as it traverses the atmosphere and continuesto produce new secondary particles all the way to the sur-face. This introduces a fundamentally new timescale intothe air shower as the nuggets move significantly slowerthan the speed of light. For nuggets with typical galac-tic scale velocities this implies a slower duration on themillisecond scale a thousand times longer than that of astandard cosmic ray event.

As with air showers initiated by a single ultra high en-ergy primary these showers may be detected through at-mospheric fluorescence, surface particle detectors or theemission of geosynchrotron radiation in the radio band.For a more extensive discussion of the phenomenologyof quark matter induced shower see [20], [21]. Both thePierre Auger Observatory and Telescope Array should, in

6

FIG. 5. Limits on quark nugget mass and density based oncurrent constraints and ANITA data currently under analysis.Taken from [22].

principle, be capable of placing significant constraints onthe flux of quark nuggets as will the JEM-EUSO experi-ment when it begins taking data. In all cases sensitivityto these events will require the analysis of data for eventswith millisecond scale durations.

A second important differentiating feature of the airshower innitiated by a quark nugget is the fact that it willcontain a thermal component emitted from the nuggetsurface. This temperature will rise with the surroundingdensity and be emitted uniformly in all directions. Thisdistinctly contrasts with the highly beamed Cherenkovand geosynchrotron radiation associated with traditionalcosmic ray showers and extending over a much wider fre-quency range than atmospheric fluorescence. At largesurrounding densities the nugget temperature can easilyreach the keV scale and contribute significantly to thetotal emission. In particular the signal from a nuggetmoving through the radio transparrent antarctic ice willbe dominantly thermal. The Anita experiment is sensi-tive to this radio component and the analysis of presentlycollected data should be able to constrain the presenceof quark nugget dark matter across a significant sectionof parameter space [22] as shown in Fig.5.

V. CONCLUSION

The model which is advocated in the present reviewwas originally invented as a simple and natural expla-

nation of the observed relation: Ωdark ' 5 · Ωvisible bypostulating that both elements originated from one andthe same QCD scale. The immediate consequence of thisproposal is the presence of antimatter in a form of macro-scopically large anti-nuggets. An equal portion of matterand antimatter in our universe does not contradict theconventional and naive arguments on the near absenceof antimatter observed in our universe as explained insection I.

It turns out that this dark matter proposal as a byprod-uct of baryogenesis may explain a number of appar-ently unrelated puzzles relating to diffuse emission ob-served in many bands as reviewed in section III. All thesepuzzles strongly suggest (independently) the presence ofsome source of excess diffuse radiation from the centreof galaxy in bands ranging over 11 orders of magnitudein frequency. Furthermore, the same dark matter modelcan also explain the isotropic background observed byarcade2 in the radio bands. In this case the emissionoriginates primarily from very early times with z ∼ 103

in contrast with our previous applications to the excessin galactic emissions. It should be emphasized that allrelative intensities of diffuse radiation in this proposalare fixed as they are determined by conventional physics.The absolute normalization is expressed in terms of a sin-gle unknown parameter: the average size of the nugget,or identically, the average baryon charge B ∼ 1025, whichitself is determined by the axion parameters as explainedin section II.

Observation of any morphological correlations betweenthe different excesses in diffuse emission mentioned insection III would strongly support this proposal as it isdifficult to imagine how such a correlation may emerge inany other model (which are typically designed to explainan excess of emission in a single specific frequency band).

In addition to this type of indirect observational sup-port this model is also amenable to direct observationaltests. As outlined in section IV several large scale ex-periments both, active and planned, have the ability toobserve the small but non-zero flux of antimatter throughthe earth. In particular large scale cosmic ray detectorsintended to study the cosmic rays near the GZK scale arecurrently probing a flux scale comparable to that of quarkantinuggets. The passage of an antinugget through theatmosphere will produce both electromagnetic radiationand a secondary particle shower that should be observ-able to a range of cosmic ray detectors. The detectionand identification of these event will require the analy-sis of data over the millisecond scale typical of a nuggetcrossing the atmosphere (or other large targets such asthe antarctic ice).

Finally, what is perhaps more remarkable is the factthat the key assumption of this dark matter model, thecharge separation effect reviewed in sections I and II, canbe experimentally tested in heavy ion collisions, where asimilar CP odd environment with θ ∼ 1 can be achieved,see section IV in ref.[23] for the details. In particular, thelocal violation of the CP invariance observed at RHIC

7

(Relativistic Heavy Ion Collider)[24] and LHC (LargeHadron Collider)[25] have been interpreted in [23, 26, 27]as an outcome of a charge separation mechanism in thepresence of the induced θ ∼ 1 resulting from a collision.The difference is of course that CP odd term with θ ∼ 1discussed in cosmology describes a theory on the horizonscale, while θ ∼ 1 in heavy ion collisions is correlated ona size of the colliding nuclei.

ACKNOWLEDGEMENTS

We are thankful to participants of the Cosmic FrontierWorkshop (CF3 and CF6 groups), SLAC, March 2013,

at which this proposal was presented, for their numerousquestions and useful discussions. This research was sup-ported in part by the Natural Sciences and EngineeringResearch Council of Canada.

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