Lorentz symmetry violation, dark matter and dark energy
aa r X i v : . [ a s t r o - ph . C O ] J u l Lorentz symmetry violation, dark matter and dark energy
Luis Gonzalez-Mestres aa LAPP, Universit´e de Savoie, CNRS/IN2P3, B.P. 110, 74941 Annecy-le-Vieux Cedex, France
Taking into account the experimental results of the HiRes and AUGER collaborations, the present status ofbounds on Lorentz symmetry violation (LSV) patterns is discussed. Although significant constraints will emerge,a wide range of models and values of parameters will still be left open. Cosmological implications of allowedLSV patterns are discussed focusing on the origin of our Universe, the cosmological constant, dark matter anddark energy. Superbradyons (superluminal preons) may be the actual constituents of vacuum and of standardparticles, and form equally a cosmological sea leading to new forms of dark matter and dark energy.
1. Patterns of Lorentz symmetry violation
A formulation of Planck-scale Lorentz symme-try violation (LSV) testable in ultra-high energycosmic-ray (UHECR) experiments was proposedin [1,2]. It involves two basic ingredients: i)the existence of a privileged local reference frame(the vacuum rest frame, VRF) ; ii) an energy-dependent parameter driving LSV and possiblymaking it observable in the ultra-high energy(UHE) region. Then, standard special relativ-ity can remain a low-energy limit in the VRF,contrary to approaches where the critical speedin vacuum is not the same for all standard parti-cles. A simple LSV pattern of the type proposedin [1,2] is quadratically deformed relativistic kine-matics (QDRK), where the effective LSV parame-ter varies quadratically with energy. In the VRF,we can write: E = (2 π ) − h c a − e ( k a ) (1) E being the particle energy, h the Planck con-stant, c the speed of light, k the wave vector, a the fundamental length and [ e ( k a )] a convexfunction of ( k a ) . a can correspond to the Planckscale or to a smaller length scale. Expanding (1)for k a ≪ e ( k a ) ≃ [( k a ) − α ( k a ) + (2 π a ) h − m c ] / (2)where p is the particle momentum, α a positivemodel-dependent constant and m the mass of the particle. For p ≫ mc , one has: E ≃ p c + m c (2 p ) − − p c α ( k a ) / E trans where the deformation term − p c α ( k a ) / m c (2 p ) − . For this comparisonto make sense, the existence on an absolute localrest frame is a fundamental requirement, even ifthe ansatz (1)-(3) can be a limit of many differentbasic theories.Assuming exact energy and momentum conser-vation, two important implications of QDRK forUHE particles were already emphasized in [1] : i)QDRK can lead to a suppression of the Greisen-Zatsepin-Kuzmin (GZK) cutoff [3,4] ; ii) unstableparticles live longer at UHE than in standard spe-cial relativity, and some of them can even becomestable at these energies. For such phenomenolog-ical applications, the Earth is assumed to moveslowly with respect to the VRF.Subsequent papers [2,5,6] further discussedthese issues and that of the universality of the α parameter. Particles with negative values of α could not be stable at UHE, or even at lowerenergies. Assuming α to be positive, particleswith lower values of α would decay into thosewith larger α . There would be at least one sta-ble UHE particle, with the highest value of α .A recent paper by Mattingly et al. [7] studies aparticular application of this discussion to neu-trinos. More obvious possibilities can be consid-1ered [2,5,6], taking different families of particles.Spontaneous decays of protons and nuclei by pho-ton emission due to LSV can fake the GZK cutoff[8]. Similarly, spontaneous decays of UHE pho-tons into e + e − pairs, or the converse effect, mayoccur at UHE with a moderate difference in α between electrons and photons [5,8].The model previously proposed by Kirzhnitsand Chechin [9] does not lead to such predictionsand is unable to produce the suppression of theGZK cutoff [10]. The situation is similar for stan-dard Doubly Special Relativity (SDSR) patterns[11]. In both cases, the laws of Physics are as-sumed to be the same in all inertial frames. Thus,a symmetry transformation can turn the UHEparticle into a less energetic one, leading to a situ-ation where LSV is weaker. We call Weak DoublySpecial Relativity (WDSR) our approach that, in-stead, assumes the existence of a local privilegedVRF where special relativity is a low-energy limit.In this case, the laws of Physics are not exactlyidentical in all inertial frames. The QDRK dis-cussed here is a particular form of WDSR.In 1971, Sato and Tati [12] suggested that thepossible absence of the GZK cutoff be explainedby an ad hoc suppression of hadron production inUHE collisions related to a cutoff in the Lorentzfactor below ≈ . Pion production would thenbe precluded above ≈ eV. Our proposal doesnot involve such a hypothesis. UHE protons canrelease a substantial part of their energy in theform of pions when colliding with a photon, pro-vided the photon energy is larger than both theproton mass term and the LSV deformation termof proton kinematics. In QDRK, contrary tothe Sato-Tati scenario, the possibility to suppressthe GZK cutoff is linked to the exceptionally lowenergy of cosmic microwave background (CMB)photons and not to an intrinsic cutoff on UHEhadron production.From a cosmological point of view, it seems rea-sonable in WDSR patterns to associate to Plancktime, or to a smaller time scale, the arisal of LSVin the structure of the physical vacuum. Thistime scale can be ≈ a c − , or ≈ a c − s if acritical superluminal speed c s exists as in the su-perbradyon hypothesis. In all cases, the inter-nal structure of the physical vacuum and the his- tory of the Universe may contain strong remnantsof their early, Lorentz violating, formation thatare not incorporated in standard particle physicsand cosmology. Such remnants can also exist asfree particles in the present Universe or have in-fluenced structure formation. Issues such as thecosmological constant, inflation, dark matter anddark energy may crucially depend on the role ofthis new physics.
2. Superbradyons
Standard preon models [13] assumed that pre-ons feel the same minkowskian space-time asquarks, leptons and gauge bosons, and carry thesame kind of charges and quantum numbers. Butthere is no fundamental reason for this assump-tion.Superbradyons [1,8,14] would have a criticalspeed in vacuum c s ≫ c possibly correspond-ing to a superluminal Lorentz invariance (a sym-metry of the Lorentz type with c s instead of c ).They may be the ultimate constituents of mat-ter, generate LSV for ”ordinary” particles (thosewith critical speed equal to c ) and even obey anew mechanics different from standard quantummechanics [15,16].After Planck time, superbradyons and ”ordi-nary” particles may coexist in our Universe. Inthis case, contrary to tachyons, superbradyonswould have positive mass and energy, explicitlyviolate standard Lorentz invariance and be ableto spontaneously emit ”Cherenkov” radiation invacuum in the form of ”ordinary” particles. Sin-gle superbradyons would in general have veryweak direct couplings to the conventional inter-actions of standard particles. In particular, theywould not obey the standard relation between in-ertial and gravitational mass. Then, the vacuumitself may present a similar behavior leading toimportant effects. We do not consider here : i)the possible existence of several superbradyonicsectors of matter ; ii) the possible differences be-tween the critical speed of superbradyons in theiroriginal dynamics without conventional matter,and the actual superbradyon critical speed in ourUniverse.In the VRF, the energy E and momentum p of a free superbradyon with inertial mass m andspeed v would be : E = c s ( p + m c s ) / (4) p = m v (1 − v c − s ) − / (5)and, for v ≪ c s , we get : E ≃ m c s + m v / p ≃ m v (7)The kinetic energy E kin is then E kin ≃ m v /
2, and E kin ≫ p c for v ≫ c .Superbradyons with v > c are kinematicallyallowed to decay by emitting standard particles.As lifetimes for such processes can be very longbecause of the weak couplings expected, the de-cays may still exist in the present Universe andplay a cosmological role. A superbradyon de-cay would emit a set of conventional particleswith total momentum p T ≪ E T c − where E T is the total energy of the emitted particles.Such an event may fake the decay of a conven-tional heavy particle or the annihilation of twoheavy particles, or contain pairs of heavy parti-cles of all kinds. The situation would be similarif the superbradyon decays into one or severallighter superbradyons plus a set of conventionalparticles, or if two superbradyons annihilate orinteract emitting ”ordinary” particles.Superbradyons can thus provide an unconven-tional form of dark matter in our Universe, andeven produce observable signatures at compara-tively low energies. Those with v ≃ c would forma stable sea, except for annihilations. The possi-bility that superbradyons be a source of standardUHECR was also considered in [17].
3. Experimental considerations
As emphasized in [2,5,6], a LSV ≈ − atthe Planck scale in QDRK for the highest-energyparticles would be enough to suppress the GZKcutoff. Thus, such an approach to LSV is cur-rently being tested by ultra-high energy cosmic-ray (UHECR) experiments. Data and analysesfrom the AUGER [18] and HiRes [19] collabora-tions possibly confirm the existence of the GZKcutoff. Significant bounds on LSV scenarios will emerge from these data. However, a large domainof LSV patterns and values of parameters will stillremain allowed, even for QDRK models [8,20].A crucial issue is that of the composition ofthe UHECR spectrum. The AUGER Collabora-tion has recently reported [22] a systematic incon-sistency of available hadronic interaction modelswhen attempting to simultaneously describe theobservations of the X max parameter and the num-ber N µ of produced muons. Data on X max sug-gest UHECR masses to lie in the range betweenproton and iron, while N µ data hint to heaviernuclei.If the highest-energy particles are nuclei, theAUGER and HiRes results can still be compatiblewith a LSV ≈ α a ≈ a P l ,where a P l is the Planck length) for quarks andgluons. But even assuming that a significant partof the highest-energy particles are protons, theactual bounds on LSV for quarks and gluons willdepend on the internal structure of the protonat UHE. Possible spontaneous decays of UHECRprotons and nuclei, but also of photons, mustequally be considered [8]. Further explorationswill thus be required, including satellite experi-ments [21].Other LSV patterns (e.g. LDRK, linearly de-formed relativistic kinematics, where the parame-ter driving LSV varies linearly with energy) werediscarded in [1] and [2,5,6], as they lead to toostrong effects at low energy if the parameters arechosen to produce observable effects at UHECRenergies. Hybrid models with high-energy thresh-olds can still be considered [21], but will not bedealt with here. Inhibition of synchrotron radi-ation in LSV patterns was predicted and stud-ied in our 1997-2001 papers for QDRK at UHE[2,5,6], leading also to tests like that presented in[23] for 100 MeV synchrotron radiation from theCrab nebula with the same kind of calculation ina version of LDRK.The energy balances used here involve ener-gies that are very small as compared to those ofthe particle interactions considered. Therefore,UHECR experiments can also be viewed as testsof energy and momentum conservation and of thevalidity of quantum mechanics at UHE [15,16].These phenomenological aspects deserve furtherstudy.As an alternative to standard dark matter, cos-mic superbradyons can potentially provide [15] anexplanation to the electron and positron abun-dances reported by PAMELA [24], ATIC [25],Fermi LAT [26], HESS [27] and PPB-BETS [28].A cosmological sea of superbradyons would stillbe decaying through the emission of ”Cherenkov”radiation in vacuum or releasing conventionalparticles for some other reason. Whether or notdata on electrons do exhibit a bump between 300GeV and 600 GeV [30] does not change this con-clusion. To date, the interpretation of such exper-imental results in terms of standard dark matterremains unclear [31]. More conventional astro-physical interpretations of these data have beenconsidered in [26,32].The possible experimental consequences of asuperbradyon era in the early Universe deservefurther investigation [15,16], as well as the roleof superbradyons in the present vacuum, its con-nection to dark energy effects and the possibilitythat superbradyonic matter replaces some of thescalar field condensates of standard physics andcosmology.
4. Post Scriptum after publication in AIPConference Proceedings
The version v1 of this paper [33] (December2009), that we have reproduced here, correspondsto the text published in the Proceedings of the2009 Invisible Universe Conference [34]. In whatfollows, we add some comments and references onmore recent information and new ideas.Recent LHC data on the quark-gluon plasma[35], confirming previous RHIC results at lowerenergies [36], seem to suggest that some aspectsof standard cosmology may have to be reconsid-ered. In this respect, it seems worth further em-phasizing the potential role of vacuum in issuesconcerning cosmology and the structure and be-haviour of matter at very small distances [37,38].This is particularly relevant for tests of the valid-ity of fundamental laws (relativity, quantum me-chanics, energy and momentum conservation...)but it also applies generally to other basic ques-tions in particle physics and astrophysics. To date, essential issues remain unsettled concern-ing the vacuum structure, dynamics and evolu-tion between the beginning of our Universe andthe present epoch.Thus, caution is required when inferring conse-quences from LHC and other accelerator resultsfor cosmological eras (f.i. concerning the possi-ble properties of a quark-gluon plasma), as thepresent physical vacuum is not the same and weare living in a much colder Universe.Energy thresholds in LSV were considered in[21], but a more radical version has been recentlysuggested by Anchordoqui et al. [39] where thenumber of effective space dimensions decreaseswith the energy scale through scale thresholds.This new LSV pattern may be a candidate toexplain the jet alignement possibly observed byPamir and other experiments above ∼ eV[40,41]. Actually, as shown in [37], missing trans-verse energy in cosmic-ray interaction jets abovesome energy scale ( ∼ eV to fit Pamir data)can be due to the production of superbradyonicobjects (waves, particles...) involving a small por-tion of the total energy and a negligible fractionof momentum. Such a phenomenon, that can berelated to energy capture by vacuum, would nat-urally lead to elongated jets. Subsequent polar-ization effects inside vacuum and secondaries canthen contribute to planar jet alignment [38].Similar phenomena can also be present athigher energies than those considered by the anal-yses of the Pamir data. Furthermore, at a scaleabove the highest observed cosmic-ray energies, afall of the cross-sections of cosmic rays with theatmosphere is also expected [5].As previously foreseen for LSV with QDRK[14,21] considering the role of the deformationand the new approach to vacuum structure, therecent suggestion by Anchordoqui et al. is alsoclaimed to potentially cure ultraviolet divergencesin field theory [39] or solve the cosmological con-stant problem [51]. More generally, a new ap-proach to quantum field theory seems necessaryat the present stage for very high energy interac-tions and vacuum structure.As in other periods in the development of par-ticle physics, condensed matter physics can be auseful guide to elaborate new concepts adaptedto current open questions [1,14,38].Completing [8], reference [38] also updates ouranalysis of the present situation concerning datafrom UHECR experiments and the tests of specialrelativity in the GZK energy region.Another recent development is the publica-tion of the 7-year WMAP data and analyses[42], leading in particular to the suggestion byGurzadyan and Penrose [43] that concentric cir-cles in WMAP data exhibiting anomalously lowtemperature variance may provide evidence of vi-olent pre-Big-Bang activity. For further discus-sion on the WMAP concentric circles, see [44,45]and [46,47]. In an approach based on conformalcyclic cosmology [48,49], Gurzadyan and Penroseconsider black-hole encounters in a previous aeon,possibly producing such signals and questioningthe validity of standard inflation. Noncyclic cos-mologies based on superbradyonic dynamics anda superbradyon era replacing or preceding thestandard Big Bang have also been proposed as analternative to inflation [14,15,16,38] and can nat-urally provide explanations to this kind of obser-vations. Then, the possible WMAP signals mayhave been generated in the previous superbrady-onic universe or during the transition from su-perbradyonic to ordinary matter. More generally,LSV patterns with a fundamental length smallerthan the Planck length can also produce similarphenomena in the transition to Planck scale.Furthermore, the discussion on the WMAP cir-cles raises more globally the question of the pos-sible lack of randomness of WMAP data. Ac-cording to Gurzadyan et al. [46], the cosmologi-cal sky is a weakly random one where ”the ran-dom perturbation is a minor component of mostlyregular signal”. Such a situation, if confirmed,may open unprecedented ways for new cosmolog-ical phenomenology, including tests of all kinds ofalternatives (string-like, LSV with a new funda-mental length, superbradyons...) to the standardBig Bang and inflationary scenarios.Superbradyon patterns and LSV generated be-yond Planck scale can thus provide coherent, noncyclic, alternatives to current cyclic cosmologiesdescribing pre-Big-Bang scenarios. Strings wouldthen naturally become composite objects or be re-placed by new theoretical concepts at the Planck scale or beyond.Although the superbradyon hypothesis andQDRK do not by now provide a theory of matter,they should not be considered as a purely phe-nomenological framework. Superbradyons implya new conceptual approach to preons and to thestructure of vacuum and conventional particles.QDRK is the natural choice for the deformed rela-tivistic kinematics if the particles of the standardmodel are assumed to be composite [1,37,38]. Itremains to be determined to what extent su-perbradyons can be represented as particles, ifthey indeed obey quantum mechanics and a newLorentz symmetry with c s as the critical speed, ifor how energy and momentum are conserved atUHE scales... The study of UHE physics and ofthe possible superbradyonic domain will requirea long term experimental and phenomenologicalwork involving UHECR experiments and possiblythe study of cosmic microwave background radi-ation. LHC experiments and dark matter studiescan also be relevant in specific cases [14,38,52].A possible solution to the dark energy prob-lem may also involve geometric patterns of space-time structure like that considered in [50], whereit was suggested to replace the standard real four-dimensional space-time by a SU(2) spinorial one.Then, spin-1/2 particles would be representationsof the actual group of space-time transformations.From a space-time spinor ξ , the positive scalar | ξ | = ξ † ξ can be obtained where the daggerstands for hermitic conjugate. In a simple physi-cal interpretation of the geometry at cosmologicalscale, a positive cosmic time t = | ξ | , the spinormodulus, can be defined which leads in particu-lar to a naturally expanding Universe. To definelocal space coordinates in this approach, one canconsider a spinor ξ (the observer position) on the | ξ | = t hypersphere. Writing, for a point ξ ofthe same spatial hypersphere : ξ = U ξ (8)where U is a SU(2) transformation : U = exp ( i/ t − ~σ.~ x ) ≡ U ( ~ x ) (9)and ~σ the vector formed by the Pauli matri-ces, the vector ~ x , with 0 ≤ x (modulus of ~ x ) ≤ πt , can be interpreted as the spatial posi-tion vector at constant time t . A 2 π rotation( x = 2 πt , U = −
1) changes the signs of ξ and ξ simultaneously, and leaves ~ x invariant.Conventional local space coordinates are obtainedfor x ≪ t . More details can be found in [50].Then, the local time scale and physical lawswill be determined by physical processes and vac-uum structure in the space-time region close to ξ . The very small t region, associated in princi-ple to the Big Bang, may be deformed or alteredby superbradyon dynamics and by LSV generatedbeyond Planck scale.Reformulating general relativity, quantum fieldtheory, possible LSV and cosmology in suchspinorial coordinates can be a useful exercise, andwill be further dicussed elsewhere.
5. Note added to the Post Scriptum
Further discussion on possible signatures ofcyclic cosmologies and on the degree of random-ness of WMAP data can be found in [53,54],[55,56] and [57,58].In page 2 of this paper, the sentence : ”In 1971,Sato and Tati [12] suggested that the GZK be ex-plained by an ad hoc suppression of hadron pro-duction in UHE collisions” must be understood asreferring to an explanation of the possible absenceof the GZK cutoff suggested in [12]. According toSato and Tati, the GZK cutoff would possibly beabsent due to an impossibility to produce pionsabove ≈ eV. As stressed above, such a con-straint does not exist in QDRK. In connection with such a debate, it seemsworth emphasizing again that properties of thestandard particles and of our Universe nowadaysconsidered as fundamental principles of Physicsmay actually be of composite origin or the natu-ral result of a primordial evolution.As an example, Lorentz symmetry (even ap-proximate or as a low-energy limit) can be anatural outcome of many primordial scenariosdue to the stability of its kinematical struc-ture as compared to other space-time geometries (f.i. euclidean) that would make matter unstablethrough spontaneous particle production and arealso disfavoured by phase space considerations.A simple illustration of metrics instability canbe provided by a kinematics of the form: E + ( p c ′ ) = M c ′ (10)where c ′ is a characteristic speed and M a mass.With such a kinematics, the particle phasespace is strongly restricted as compared to aminkowskian metrics. Therefore, possible metricsfluctuations at the Big Bang scale or at some pre-vious fundamental scale can eventually favour thetransition to a space-time structure of the stan-dard Lorentz type. Furthermore, if the kinemat-ics defined by (10) applies, the vacuum can inprinciple spontaneously emit particles with mo-mentum p = M c ′ and is therefore naturallyunstable. Again, the dynamical transition to aminkowskian metrics appears as a logical phe-nomenon.Such considerations apply not only to conven-tional particles, but also to superbradyons. Theymay naturally lead to the patterns considered inour papers since 1995 [14,21] where several sectorsof matter may exist with different critical speedsin vacuum but possibly obeying in all cases sym-metries of the Lorentz type in the low-momentumlimit.Then, it is possible that effective space-timeconfigurations of a different form can only ex-ist temporarily in specific transition situations(the nucleation of our Universe in superbradyonicmatter ?). As emphasized in version 5 of [15], in a compos-ite pattern where the standard particles and ourUniverse would be generated from a superbrady-onic medium, the standard gauge bosons do notneed to be associated to local symmetries in theconventional sense.Superbradyons would not be mere buildingblocks in the usual sense of conventional preon[13] patterns. They can instead form a realnew phase of matter where conventional particleswould be collective excitations of a large medium.This may have strong implications for standardgauge theories.Then, the Big Bang may correspond to thenucleation of a new phase of matter (the ”con-ventional” one as seen by human observers) ina superbradyonic pre-Universe. The new phasesubsequently expands in superbradyonic matter.Several scenarios can then be imagined, such asfor instance :i) The Universe just expands as a nucleatedphase, the nucleation corresponding basically tothe transformation of the superbradyonic groundstate into our physical vacuum. Then, if the ex-pansion of the conventional vacuum occurs in alocally random way, the dilation of the apparentspace can be a natural consequence leading toLemaˆıtre’s relation between distances, velocitiesand redshifts [59]. The dark energy effect can berelated to the energetic balance of the phase tran-sition between the superbradyonic ground stateand the conventional vacuum.ii) Our three-dimensional Universe is similarto a new kind of three-dimensional soliton in aspace with four or more dimensions. Soliton -antisoliton pair production may then account formatter-antimatter separation and CP violation.Such solitons would have an internal structure,initially very hot and with a very small spatialsize, and expand in the superbadyonic matter.Again, Lemaˆıtre’s law can result from relaxationthrough the expansion of the conventional phys-ical vacuum from the phase transition of the su-perbradyonic matter.iii) Our Universe is generated within a spino-rial space-time structure like that described in[50], also considered in [38] and in the abovePost Scriptum. Then, the standard space coordi-nates would be defined locally and Lemaˆıtre’s lawwould correspond to conventional matter follow-ing basically straight lines along the orthogonal(cosmic time) direction. The relation between lo-cal and cosmic time would depend on the dynam-ics of the Universe expansion.Scenario iii) appears particularly well suited todescribe half-integer spin as a real angular mo-mentum and formulate a primordial version ofquantum mechanics. Incorporating a similar ge-ometry into scenarios i) and ii) is also feasible. In i), a physical privileged point or small zoneinside our Universe may correspond to its ori-gin. In ii), a similar point or small zone canexist in the superbradyonic matter. Matter andenergy exchanges between the conventional Uni-verse and outside superbradyonic matter cannotbe excluded.
Standard quantum field theory is based on lo-cal gauge symmetry, where the existence of gaugebosons is required by invariance under local sym-metry transformations. But does this concept ap-ply to Physics at Planck scale or beyond it ? Howshould it be possibly modified ? And how wouldpossible new Physics extrapolate to lower energyscales, especially if the string model is not theultimate theory [38] ?In an underlying superbradyonic picture, tak-ing for simplicity a lattice description, our con-ventional gauge interactions can at the origin beassociated to nearest-neighbour couplings (localpotentials) describing the interaction between dif-ferent local superbradyonic excitation modes. Atsuch stage and scales, quantum mechanics wouldnot necessarily apply and virtual standard parti-cles are not yet needed.Then, it is perfectly conceivable that a new dy-namics be at work where the standard vector bo-son fields carrying the conventional gauge forceswould be generated from the superbradyonic mat-ter and degrees of freedom only in specific situ-ations. Basicallly, when these nearest-neighbourcouplings turn out to depend on position, timeand direction due to the material existence ofpropagating vacuum excitations (the standardparticles) involving the same family of local ex-citation modes. In the absence of surround-ing conventional particles, the vacuum structurewould be different from that suggested by stan-dard quantum field theory.In this case, for instance, the Higgs bosonswould not need to be statically materialized as apermanent condensate in the physical vacuum ofour Universe. The Higgs mechanism can insteadbe part of a dynamical reaction of vacuum to thephysical presence of gauge bosons and of otherstandard particles, and occur at the set of fre-quencies required by the interaction between thestandard particles involved. Otherwise, the orig-inal superbradyonic matter and degrees of free-dom can fill the physical vacuum in a differentway. Similar considerations would apply to thezero modes of standard bosonic oscillators. Con-trary to conventional quantum field theory, onlythe wavelengths and frequencies excited by thepresence of standard matter would contribute tothe conventional local vacuum condensate.Such a scenario would imply that the energydifference between the superbradyonic groundstate and our vacuum is small, and that the su-perbradyonic structure does not couple to grav-ity and to other conventional interactions in thesame way standard matter (including the vac-uum) does. It does not contradict experimentalresults [60,61] on the Casimir effect [62]. It natu-rally generates new and simpler solutions to thecosmological constant problem, as well as to thedark energy and dark matter issues, and leads toa new and safer approach to the question of ul-traviolet divergencies.
Two recent papers by the AUGER collabora-tion are [63,64]. See also [65,66]. The crucialquestion of UHECR cosmic-ray composition re-mains by now to be settled.Saveliev, Maccione and Sigl [67] have recentlyused for phenomenological purposes the QDRKmodel we suggested in 1997 [1,2] and the subse-quent pattern for nuclei we worked out [68] wherethe effective LSV parameter varies basically like ∼ N − , N being the number of nucleons (seealso [8]). They also use the vacuum Cherenkoveffect from superluminal particles already consid-ered in [69,70] and more recently in [8,38]. Forpositive values of α , Saveliev et al. they get up-per bounds similar to those suggested in [8]. Con-cerning spontaneous decays in DRK patterns, seealso [71] and [72].However, Saveliev et al. also consider possiblenegative values of α and one might infer fromtheir result that, if Fe is present in the UHECRspectrum at E = 10 eV, then − α can be as large as ≃ a to bethe Planck length a P l .In this respect, it must be noticed that for α = - 4, one has a positive deformation term∆ E = − p c α ( k a ) / ≃
13 eV for E (nucleon) = 10 eV, whereas the nucleon massterm at this energy is m (2 p ) − ≃ − eV. With such a kinematics, a 10 eV protoncan spontaneously decay, for instance, into twoprotons plus an antiproton. Other spontaneousdecays will also occur, with processes dependingon the value of α for pions, protons, electrons...Massless photons with a positive value of − α would be unstable at all energies due to sponta-neous decays.As the photon cannot in principle have a neg-ative value of α , we expect all charged particleswith a negative α to spontaneously decay by emit-ting a photon above some energy. Such a decaywould be kinematically allowed for protons above ≃ eV if α (photon) = 0 and - α (proton) ≃ − which corresponds to the lowest positivebound on - α considered by Saveliev et al. As pho-tons with any energy can be spontaneously emit-ted in this case, we expect such decays to precludethe astrophysical propagation of charged particlesat energies where the positive deformation termis larger than the mass term.Furthermore, a negative α would make moredifficult particle acceleration at astrophysicalsources and increase synchrotron radiation by theconverse effect to that described in [73].As further emphasized in [38], relativity is notthe only fundamental principle of Physics thatcan be tested by UHECR experiments. If a privi-leged inertial local rest frame exists, as systemat-ically assumed in our papers, all basic principlesof our current understanding of Nature may un-dergo changes or transitions at the Planck scaleor at some other scale, possibly leading to observ-able signatures at very high energy.If quantum mechanics has been generated inour Universe at the Planck scale or somewherebetween a ”nucleation time” and the Planck time,the standard quantum mechanics is expected tobe deformed as considered above and in [16,38].A more complete analysis of possible patterns ofquantum mechanics deformation in cosmologicalscenarios with a VRF is required at that stage inview of test with UHECR.Similarly, if as suggested above the Higgs bo-son and the standard bosonic zero modes arenot permanently condensed in vacuum, and ifthe energy difference between the superbradyonicground state and our vacuum is actually small,nonstandard fluctuations of the vacuum structuremay occur in large zones of our Universe and befelt by conventional particles during intergalacticor galactic propagation. Again, UHECR exper-iments may be sensitive to such effects. Moredetails will be presented elsewhere. REFERENCES
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