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Familon Model of Dark Matter

If the next fundamental level of matter occurs (preons) then dark matter must consist of familons containing a"hot"component from massless particles and a"cold"component from massive particles. During evolution of the Universe this dark matter was undergone to late-time relativistic phase transitions temperatures of which were different. Fluctuations created by these phase transitions have had a fractal character. In the result the structurization of dark matter (and therefore the baryon subsystem) has taken place and in the Universe some characteristic scales which have printed this phenomenon arise naturally. Familons are collective excitations of nonperturbative preon condensates which could be produced during more early relativistic phase transition. For structurization of dark matter (and baryon component) three generations of particles are necessary. The first generation of particles has produced the observed baryon world. The second and third generations have produced dark matter from particles which have appeared when symmetry among generations was spontaneously broken.


INTRODUCTION
Using the preon structure of quarks and leptons the familon model of dark matter (DM) proposed by Hill, Schramm and Fry(1989) and Frieman et al.(1992) is reanimated. This model has more physical and cosmological consequences if the next structure level of matter is involved. Our interest to the preon model of elementary particles was also induced by the fact of possible leptoquarks resonance in HERA experiment (Adloff et al.,1997 andBreitweg et al.1997) the possibility to research a pair production of scalar leptoquarks at FERMILAB TEVATRON (Kramer et al.,1997 andAffolder et al.,2001) Chen,2001;Wu et al.,1999).
In the Universe these late phase transitions have also produced some characteristic scales.
Besides, understanding of three generations of elementary particles is become naturally. The observed baryon world and DM may be realized only then when three generations of particles occur. The first generation of particles has produced the baryon world. The second and third generations have produced dark matter. The structurization of dark matter (and the baryon component) has been produced particles appeared when the symmetry among generations was spontaneously broken.
We have studied the structure of preon nonperturbative vacuum which may arise in the result of the correlation of non-Abelian fields on two scales. Λ mc ≫ 1 T eV is the confinement scale of metacolour and Λ c ∼ 150 MeV is the quantum chromodynamics (QCD) scale. We have detected that in the spectrum of excitations of heterogenic nonperturbative preon vacuum pseudo-Goldstone modes of familon type appear. Familons are created when the symmetry of quark-lepton generations is spontaneously broken and their nonzero masses are the result of superweak interactions with quark condensates. Physics of the spontaneously broken symmetry of generations (production of familons) was considered by Feng et al.,(1998).
The distinguishing characteristic of these particles is the availability of the residual U(1) symmetry and possibility of it spontaneous breaking for temperature Λmc Λ 2 c ∼ 10 −3 eV in the result of relativistic phase transitions.
We have proposed that these relativistic phase transitions (RPT) had the direct relation to the production of primordial perturbations in DM the evolution of which leads to the fractal baryon large scale structure. Note other time that the idea of RPT in the cosmological gas of pseudo-Goldstone bosons in connection with LSS problems was early formulated in articles of Hill et al.,(1989) and Frieman et al.,(1992). Here we have investigated by quantitatively the preon-familon model of these RPT.
In the beginning the astrophysical motivation of our theory is discussed more detail.
Observational data show that some baryon objects such as the quasar on z ∼ 4.9 and the galaxy on z ∼ 6.68, CO lines on z ∼ 4.43 and z ∼ 4.69 (Omont et al.,1996;Chen et al.,1999) were produced as minimum on redshifts z ∼ 6 ÷ 8. This is the difficulty for the standard CDM and ΛCDM models to produce their (the best fit is z ∼ 2 ÷ 3 (Madau,1999) and observations provide the support of this). If early baryon cosmological structures produced on z > 10 then the key role must play DM particles with nonstandard properties.
Probably DM consists of ideal gas particles with m ≈ 0 practically noninteracting with usual matter (till now they do not detected because of their superweak interaction with baryons and leptons). In the standard cosmological model DM (here CDM) contains 25% of the total density that is: Ω 0 = Ω Λ + Ω CDM + Ω ν + Ω b = 0.7 + 0.25 + 0.02 + 0.03 = 1.
In the article (Caldwell,2004) more exact data on Ω Λ are given. Also the important point is to know the end of formation of observed baryon structures. A characteristic moment of the most of cosmological structures formation finishing remains the same (z ∼ 2 ÷ 3). The appearance of baryon structures on high red shifts (z > 4) was the result of statistical outbursts evolution of the spectrum of DM density perturbations. Therefore early cosmological baryon structures may be connected to statistical outbursts only in the sharply nonlinear physical system which is a medium after RPT (the production of inhomogeneities).
Note again that we have investigated the idea in which the baryon component of matter repeats the structure of DM owing to gravitation. That is relativistic phase transitions have produced DM fractal fluctuations in which baryons have subsequently clustered. The fractal structure of the baryon component was studied by Bak and Chen (2001) and Wu et al.,(1999) starting from the article of Coleman et al.,(1988) in which authors have suggested that the Universe up to some Mpc has the fractal structure (the fractal structure was observed up to 50 Mpc by Martinez and Coles (1994) and the sharp transition to homogeneity was predicted at 300 Mpc also by these authors. Only the critical phenomenon like to a phase transition creates fractal structures.
A new theory of DM must combine the properties of superweak interaction of DM particles with baryons and leptons and intensive interaction of these particles each other. Such interactions are provided by nonlinear properties of DM medium. This is the condition for realization of RPT.

THE BASIC ARGUMENTS
The familon symmetry is experimentally observed (the different generations of quarks and leptons participate in gauge interactions the same way). Breaking of this symmetry gives masses of particles in different generations. A hypothesis about spontaneous breaking of familon symmetry is natural and the creation of Goldstone bosons is inevitably. The properties of any pseudo-Goldstone bosons as and pseudo-Goldstone bosons of familon type depend on the physical realization of Goldstone modes. These modes may be arisen from fundamental Higgs fields or from collective excitations of a heterogenic nonperturbative vacuum condensate more complex than a quark-gluon one in QCD. The second possibility can realize the theory in which quarks and leptons are composite particles that is the preon model of elementary particles. If leptoquarks will be detected then two variants of explanations may be. If a leptoquarks resonance will be narrow and high then these leptoquarks come from GUT or SUSY theories. The low and wide resonance can be explained by composite particles only.
The simplest boson-fermion preon model consists of left-handed fermion preons U α L , D α L and scalar preons of quark (Φ iα a ) and lepton (χ α l ) types. In this model the interior structure of elementary particles is: In the case of leptoquarks our model gives: here and in the following i is color index of QCD, a, b, c = 1, 2, 3; l, m, r = 1, 2, 3 are numbers of quark and lepton generations, α is metacolor index corresponding to a new metachromodynamics interaction linking preons in quarks and leptons.
Inside quarks and leptons metagluon fields G ω µν and scalar preon fields are in the confinement state like to the confinement of quarks and gluons inside hadrons. This effect is provided by the existence of nonperturbative metagluon and preon condensates: here Λ mc is the energetic scale of preon confinement, V ab , V lm are the condensate matrixes.
Condensates (3) and (4) together with gluon and quark condensates ( 0 | αs π G a µν G µν a | 0 ; 0 |q L q R +q R q L | 0 ) provide the mechanism of mass quarks production of all third generations. It is shown on the diagram 1: in which G ik µν = λ ik n G in µν , λ ik n is Gell-Mann matrices; G αβ µν = λ αβ ω G ω µν , λ αβ ω is an analogue of Gell-Mann matrices for metacolour. As it can see from this diagram (1) the main contribution in the effect of familon symmetry vacuum breaking is formed by the preon condensates (4).
The theory of preons predicts the complex structure of a heterogenic nonperturbative vacuum and familons are collective excitations of these condensates. These excitations are the result of local processes of weakening and rebuilding of correlations among fields entering in condensates: Also it is necessary to note the peculiar properties of the first generation of quarks. Their masses are exclusively produced by the interaction with the quark-gluon condensate. The production of second and third generations of quark masses is outside limits of QCD. But this fact may be natural in preon model. Scalar preon condensates of the first generation are efficiently suppressed and they do not carry contribution in (6-8). This situation may be explained in the model containing composite scalar preons (the scale more than Λ mc ). In this preon -subpreon model (Evnin,1997) the initial familon symmetry SU F (3) → SU F (2) is broken on scale Λ smc ≫ Λ mc and then on more low scale the symmetry SU F (2) → U (1) is broken also. Therefore here we will discuss the chiral-familon symmetry of second and third generations only ( the discussion of the familon symmetry was in detail given by Feng magnitudes (Groom,2000). m astrophysical ∼ 10 −3 ÷ 10 −5 eV m laboratory ≤ 10 eV (9) The effect of familons mass production corresponds formally mathematically the appearance of mass terms in the Lagrangian of Goldstone fields. From general considerations one can propose that massive terms may arise as with "right" as and with "wrong" signs.
The sign of the massive terms predetermines the destiny of residual symmetry of Goldstone fields. In the case of "wrong" sign for low temperatures T < T c ∼ m f amilons ∼ 0.1 ÷ 10 5 K a Goldstone condensate produces and the symmetry of familon gas breaks spontaneously.
The representation about physical nature of familon excitations described above is for- the complex pseudoscalar field with the mass: and the complex scalar field the mass square of which is negative: The complex field with masses (12-13) is the nontrivial representation of residual symmetry of U(1) group but the real field (11) is the sole representation of this group. We propose that cosmological DM consists of particles with these masses and their analogies from the down-quark-familons and the lepton-familon subsystems.
The negative mass square of complex scalar field means that for pseudo-Goldstone vacuum is unstable that is when T = T c(up) in gas of pseudo-Goldstone bosons should be RPT in the state with spontaneous breaking U(1) symmetry. Two other familon subsystems can be studied by the same methods. Therefore DM consisting of pseudo-Goldstone bosons of familon type is a many component heterogenic system evolving complex thermodynamical way.
In the phase of breaking symmetry every complex field with masses (12-13) splits on two real fields with different masses. That is the familon subsystem of up-quark type consists of five kinds of particles with different masses. Analogous phenomenon takes place in the down-quark subsystem. The breaking of residual symmetry is when: In a low symmetric phase this subsystem consists also of five kinds particles with different masses. In our theory the lepton-familon subsystem can be undergone to RPT also but leptonic condensates are elements of new physics which may come in the future and probably their discussion is prematurely.

RESULTS
The relativistic phase transitions in familon subsystems must be described in the frame of temperature quantum field theory. It is important to underline that sufficiently strong interactions of familons each other provide the evolution of familon subsystem through state of local equilibrium type. Our estimates have shown that the transition in nonthermodynamical regime of evolution occurs on stage after RPT even if RPT took place for temperature ∼ 10 −3 eV . The thermodynamics of a familon system may be formulated in the approximation of a self-coordinated field. The methods of RPT theory which were be used by us are similar to ones of our article (Vereshkov and Burdyuzha,1995). The nonequilibrium Landau functional of states F (T, η, m A ) depends on the order parameter η and five effective masses of particles m A , A = 1, 2, 3, 4, 5: here J 2 is the characteristic integrals (similar integrals used for the description of RPT in article (Burdyuzha et al.,1997).
is concordant with the equation of state ∂F/∂η = 0 that allows: a) to establish the kind of RPT, b) to find the thermodynamical boundary of stability phases, c) to calculate values of observed magnitudes (energy density, pressure, thermal capacity, sound velocity et al.) in each phase. More detail the thermodynamics of the familon system has been discussed in article (Burdyuzha et al.,1998).
We have detected that RPT in familon gas is one of the first kind with wide region of phases coexistence. Therefore in epoch of RPT or more exactly in the region of phases coexistence the Universe had a block-phase structure containing domains of different phases.
The numerical modelling of this RPT has shown that average contrast of density in the block-phase structure is δǫ/ǫ ∼ 0.1. This structure is illustrated on diagram 2 in some conditional dimensionless units. The size of domains and masses of baryon and dark matter inside domains are defined by distance to horizon of events L horiz. at the moment of RPT. As it is seen from (14-15) numerical values of these magnitudes which are important for LSS theory depend on a value of the unknown today parameter of the preon confinement Λ mc .
If inhomogeneities appearing during RPT in familon gas have the relation to observable scales of LSS (10 Mpc) then Λ mc ∼ 10 5 T eV . More detail estimates today is premature but it is necessary to note that suggested theory contains as minimum two phase transitions and therefore two characteristic scales of baryon LSS. Now it would be a speculation to define exactly magnitude of these scales (probably galaxies and clusters of galaxies) since we do not know familon masses. Numerical estimates of inhomogeneities parameters arising as the result of strong interaction of domains LS and HS phases in the region of their contact show that the density contrast may increase to δǫ/ǫ ∼ 1 on the scale L ∼ 0.1L horison at the moment of the phase transition and besides effects connected with fragmentation of DM medium may be superimposed at the spectrum of the CMB radiation.
Finally note,that for structurization of DM (and baryon component of the Universe) three generations of particles are necessary obligatory. The first generation of particles has produced the baryon world which is observed. The second and third generations of particles have produced a fractal distributed DM from familons (the baryon component has repeated this distribution). Our first conclusion is that the preon structure (the next structural level of matter) must be detected since only the preon model (more exactly phase transitions) may provide a fractal distribution as DM as and baryon component. Only in the preon model some scales could be naturally produced during evolution of the Universe. Of course, the familon DM is difficult to detect owing to a superweak interaction with usual matter. Recent search of familons by CLEO collaboration gave the negative result (Ammar et al.,2001). Last publications on research of DM can be found in some last reports (Caldwell,2004;Adashe and Servant,2004;Chen,2004;Ellis,(2005); Kunz,(2007); Moffat,2004;Sahni,2004) and on site:http://www.phys.ufl.edu/ axion/welcome.html