Dark Energy and Dark Matter, Mirror World and E_6 Unification
aa r X i v : . [ h e p - ph ] D ec Dark Energy and Dark Matter,Mirror World and E Unification
C.R. Das ∗ L.V. Laperashvili † , Center for High Energy Physics, Peking University, Beijing, China The Institute of Theoretical and Experimental Physics, Moscow, Russia
A talk presented at the Conferenceof Russian Academy of Sciences:
Fundamental Interactions Physics
ITEP, Moscow, RussiaNov 26-30, 2007
Speaker - Larisa Laperashvili ∗ [email protected] † [email protected] bstract In the present talk we have developed a concept of parallel ordinary (O) andmirror (M) worlds. We have shown that in the case of a broken mirror parity (MP),the evolutions of fine structure constants in the O- and M-worlds are not identical.It is assumed that E -unification inspired by superstring theory restores the brokenMP at the scale ∼ GeV, what unavoidably leads to the different E -breakdownsat this scale: E → SO (10) × U (1) Z - in the O-world, and E ′ → SU (6) ′ × SU (2) ′ Z - in the M-world. Considering only asymptotically free theories, we have presentedthe running of all the inverse gauge constants α − i in the one-loop approximation.Then a ’quintessence’ scenario is discussed for the model of accelerating universe.Such a scenario is related with an axion (’acceleron’) of a new gauge group SU (2) ′ Z which has a coupling constant g Z extremely growing at the scale Λ Z ∼ − eV. ontents:
1. Introduction: Superstring theory and a mirror world.2. Particle content in the ordinary and mirror worlds.3. Gauge coupling constant evolutions in the ordinaryworld. -unification.
4. Mirror world with broken mirror parity. ( ) to the E -unification.
5. A new mirror gauge group SU ( ) ′ Z . ( ) ′ Z gauge group.5.2. The axion potential.5.3. A new cosmological scale Λ Z ≈ × − eV .
6. The gauge group SU ( ) ′ Z and the ’quintessence’ modelof our universe.
7. Conclusions. Introduction: Superstring theory and a mirror world.
The present investigation is based on the following corner stonesof theory: • Grand Unified Theories (GUTs) are inspired by the ulti-mate theory of superstrings, which gives the possibility of unify-ing all fundamental interactions including gravity:
M.B. Green, J.H. Schwarz and E. Witten,
Superstring the-ory, Vol. 1,2, Cambridge University Press, Cambridge, 1988. • There exists a mirror world, which is parallel to our ordi-nary world:
T.D. Lee and C.N. Yang,
Phys.Rev. 104, 254 (1956);
I.Yu. Kobzarev, L.B. Okun and I.Ya. Pomeranchuk,
Yad.Fiz.3, 1154 (1966) [Sov.J.Nucl.Phys. 3, 837 (1966)]. • The mirror parity MP is broken: ”The only good parity ... is a broken parity!”
Z. Berezhiani, A. Dolgov and R.N. Mohapatra,
Phys.Lett.B 375, 26 (1996);
Z. Berezhiani,
Acta Phys.Pol. B 27, 1503 (1996);
Z.G. Berezhiani and R.N. Mohapatra,
Phys.Rev. D 52,6607 (1997). ntroduction: Superstring theory and a mirror world. Superstring theory is a paramount candidate for the unificationof all fundamental gauge interactions with gravity.Superstrings are free of gravitational and Yang-Millsanomalies if a gauge group of symmetry isSO ( ) or E × E . The ’heterotic’ superstring theory E × E ′ was suggested asa more realistic model for unification: D.J. Gross, J.A. Harvey, E. Martinec and R. Rohm,
Phys.Rev.Lett. 54, 502 (1985); Nucl.Phys. B256, 253 (1985).
M.B. Green, J.H. Schwarz and E. Witten,
Superstring theory, Vol. 1,2, Cambridge University Press,Cambridge, 1988.This ten-dimensional Yang-Mills theory can undergo spontaneouscompactification:
The integration over 6 compactified dimensions of the E su-perstring theory leads to the effective theory with the E -unificationin four-dimensional space. ntroduction: Superstring theory and a mirror world. In the present investigation:See:
C.R. Das and L.V. Laperashvili,
Mirror World with BrokenMirror Parity, E Unification and Cosmology,to be published in Phys.Rev. D.we consider the old concept: there exists in Nature a ’mirror’ (M) world (hidden sector)parallel to our ordinary (O) world.
This M-world is a mirror copy of the O-world and contains thesame particles and their interactions as our visible world.Observable elementary particles of our O-world have left-handed(V-A) weak interactions which violate P-parity. If a hidden mir-ror M-world exists, then mirror particles participate in the right-handed (V+A) weak interactions and have an opposite chirality.Lee and Yang were first who suggested such a duplication of theworlds which restores the left-right symmetry of Nature:
T.D. Lee and C.N. Yang,
Phys.Rev. 104, 254 (1956);The term ’Mirror World’ was introduced by Kobzarev, Okun andPomeranchuk:
I.Yu. Kobzarev, L.B. Okun and I.Ya. Pomeranchuk,
Yad.Fiz.3, 1154 (1966) [Sov.J.Nucl.Phys. 3, 837 (1966)].They have investigated a lot of phenomenological implications ofsuch parallel worlds.The idea of the existence of visible and mirror worlds became veryattractive in connection with a superstring theory described byE × E ′ . Particle content in the ordinary and mirror worlds.
We can describe the ordinary and mirror worlds by a minimalsymmetry G SM × G ′ SM , whereG SM = SU ( ) C × SU ( ) L × U ( ) Y stands for the Standard Model (SM) of observable particles:three generations of quarks and leptons and the Higgs boson.Then G ′ SM = SU ( ) ′ C × SU ( ) ′ L × U ( ) ′ Y is its mirror gauge counterpart having three generations of mirrorquarks and leptons and the mirror Higgs boson.The M-particles are singlets of G SM and O-particles are singletsof G ′ SM . These different O- and M-worlds are coupled only by gravity(or maybe other very weak interaction).
Including Higgs bosons φ we have the following SM content ofthe O-world: L − set : ( u , d , e , ν, ˜u , ˜d , ˜e , ˜N ) L , φ u , φ d ; ˜R − set : ( ˜u , ˜d , ˜e , ˜ ν, u , d , e , N ) R , ˜ φ u , ˜ φ d ; with antiparticle fields: ˜ φ u , d = φ ∗ u , d , ˜ ψ R = C γ ψ ∗ L and ˜ ψ L = C γ ψ ∗ R . Considering the minimal symmetry G SM × G ′ SM we have thefollowing particle content in the M-sector:L ′ − set : ( u ′ , d ′ , e ′ , ν ′ , ˜u ′ , ˜d ′ , ˜e ′ , ˜N ′ ) L , φ ′ u , φ ′ d ; ˜R ′ − set : ( ˜u ′ , ˜d ′ , ˜e ′ , ˜ ν ′ , u ′ , d ′ , e ′ , N ′ ) R , ˜ φ ′ u , ˜ φ ′ d . In general, we can consider a supersymmetric theory whenG × G ′ contains grand unification groups: SU ( ) × SU ( ) ′ ,SO ( ) × SO ( ) ′ , E × E ′ , etc. Gauge coupling constant evolutions in the O-world.
In the present paper we consider the running of all the gaugecoupling constants in the SM and its extensions which is welldescribed by the one-loop approximation of the renormalizationgroup equations (RGEs) from the Electroweak (EW) scale up tothe Planck scale.For energy scale µ ≥ M ren , where M ren is the renormalizationscale, we have the following evolution for the inverse fine struc-ture constants α − given by RGE in the one-loop approximation: α − ( µ ) = α − ( M ren ) + b i π t , where α i = g π , g i are gauge coupling constants andt = ln (cid:18) µ M ren (cid:19) . We have assumed that the following chain of symmetry groupsexists in the ordinary world:SU ( ) C × SU ( ) L × U ( ) Y → [ SU ( ) C × SU ( ) L × U ( ) Y ] SUSY → SU ( ) C × SU ( ) L × SU ( ) R × U ( ) X × U ( ) Z → SU ( ) C × SU ( ) L × SU ( ) R × U ( ) Z → SO ( ) × U ( ) Z → E . .1 Standard Model and Minimal Supersymmetric Standard Model.We start with the SM in our ordinary world.In the SM for energy scale µ ≥ M t (here M t is the top quarkpole mass) we have the following evolutions (RGEs) for the in-verse fine structure constants α − (i = , , ( ) , SU ( ) L and SU ( ) C groups of the SM): C. Ford, D.R.T. Jones, P.W. Stephenson, M.B. Einhorn,
Nucl.Phys. B 395, 17 (1993),which are revised using updated experimental results:
C.R. Das, C.D. Froggatt, L.V. Laperashvili and H.B. Nielsen,
Mod.Phys.Lett. A 21, 1151 (2006)
C.D. Froggatt, L.V. Laperashvili, H.B. Nielsen,
Phys.Atom.Nucl.69, 67 (2006); Yad.Fiz. 69, 3 (2006). α − ( t ) = . ± . − π t ,α − ( t ) = . ± . + π t ,α − ( t ) = . ± . + π t , where t = ln (cid:18) µ M t (cid:19) . We have used the central value of the top quark mass:M t ≈
174 GeV . tandard Model and Minimal Supersymmetric Standard Model.The Minimal Supersymmetric Standard Model (MSSM)(which extends the conventional SM)gives the evolutions for α − (i = , , ( ) , SU ( ) , SU ( ) groups)from the supersymmetric scale M SUSY up to the seesaw scaleM R .Figs. 1,3 present by red lines the SM and MSSM evolutions,which are given by the following MSSM slopes:b = − = − . , b = − , b = . These evolutions are shown from M t up to the scale M SUSY , wherex = log µ ( GeV ) , t = x · ln10 − lnM t . In Figs. 1-4 we have presented examples with the followingscales:Fig. 1,2 – 10 TeV , Fig. 3,4 – 1 TeV , and M R ∼ or GeV . Here and below red lines correspond to the ordinary world. .2 Left-right symmetry, SO(10) and E -unification.At the seesaw scale M R the heavy right-handed neutrinos appear,and the following supersymmetric left-right symmetry originates:SU ( ) C × SU ( ) L × SU ( ) R × U ( ) X × U ( ) Z . Considering the running of coupling constants we have thefollowing slopes:b X = b = − . , b Z = − , b = . Also the running for SU ( ) L × SU ( ) R is given by the slope:b = − . Then we have the following evolution: α − ( µ ) = α − ( M R ) + π ln µ M R , with the following relation: α − ( M R ) = α − ( M R ) . The next step is an assumption that the group by Pati and Salamoriginates at the scale M giving the following extension of thegroup: SU ( ) C × SU ( ) L × SU ( ) R × U ( ) X × U ( ) Z → SU ( ) C × SU ( ) L × SU ( ) R × U ( ) Z . J. Pati and A. Salam,
Phys.Rev. D 10, 275 (1974).The scale M is given by the intersection of SU ( ) C with U ( ) X : α − ( M ) = α − ( M ) . eft-right symmetry, SO(10) and E -unification.Considering only the minimal content of the scalar Higgs fields,we obtain the following slope for the running of α − ( µ ) :b = . The intersection of α − ( µ ) with the running of α − ( µ ) leads to thescale M GUT of the SO(10)-unification:SU ( ) C × SU ( ) L × SU ( ) R → SO ( ) ,α − ( M GUT ) = α − ( M GUT ) . Then we deal with the running of the SO(10) inverse gauge con-stant α − ( µ ) , which runs from the scale M GUT up to the scaleM
SGUT of the super-unification E :SO ( ) × U ( ) Z → E . The slope of this running is: b = . Then we have the following running: α − ( µ ) = α − ( M GUT ) + π ln µ M GUT , which is valid up to the M SGUT = M E6 ∼ GeV.All evolutions of the corresponding fine structure constantsare given in Figs. 1-4:(O-world – red lines; M-world – blue lines).Here Figs. 2 and 4 show the running of gauge coupling con-stants near the scale of the E -unification (for x ≥ Mirror world with broken mirror parity.
In general case the mirror parity MP is not conserved,and the ordinary and mirror worlds are not identical:
Z. Berezhiani, A. Dolgov and R.N. Mohapatra,
Phys.Lett.B 375, 26 (1996);
Z. Berezhiani,
Acta Phys.Pol. B 27, 1503 (1996);
Z.G. Berezhiani and R.N. Mohapatra,
Phys.Rev. D 52,6607 (1997).If O- and M-sectors are described by the minimal symmetrygroup G SM × G ′ SM with the Higgs doublets φ and φ ′ , respectively,then in the case of non-conserved MP the VEVs of φ and φ ′ arenot identical: v = v ′ .Following Berezhiani-Dolgov-Mohapatra, we assume thatv ′ >> vand introduce the parameter characterizing the violation of MP: ζ = v ′ v >> . Then the masses of fermions and massive bosons in the mirrorworld are scaled up by the factor ζ :m ′ q ′ , l ′ = ζ m q , l , M ′ W ′ , Z ′ ,φ ′ = ζ M W , Z ,φ , but photons and gluons remain massless in both worlds. irror world with broken mirror parity. Let us consider now the following expressions: α − ( µ ) = b i π ln µ Λ i — in the O-world, and α ′− ( µ ) = b ′ i π ln µ Λ ′ i — in the M-world.A big difference between the Electroweak scales v and v ′ willnot cause a big difference between scales Λ i and Λ ′ i : Λ ′ i = ξ Λ i with ξ > . The values of ζ and ξ were estimated by astrophysical implica-tions (by Berezhiani-Dolgov-Mohapatra),which gave: ζ ≈ and ξ ≈ . . As for the neutrino masses, the same authors have shown that thetheory with broken mirror parity leads to the following relations:m ′ ν = ζ m ν , M ′ ν = ζ M ν , where m ν are light left-handed and M ν are heavy right-handedneutrino masses in the O-world, and m ′ ν , M ′ ν are the correspond-ing neutrino masses in the M-world.The last relation gives the following relation for seesaw scales:M ′ R = ζ M R . .1 Gauge coupling constant evolutions in the mirror SM and MSSM.In the SM of the M-sector we have the following evolutions: ( α ′ ) − ( µ ) = ( α ′ ) − ( M ′ t ) + b i π t ′ = b i π ln µ Λ ′ i , where ( α ′ ) − ( M t ) = α − ( M t ) − b i π ln ξ, or ( α ′ ) − ( M ′ t ) = α − ( M t ) . In the M-world the scales Λ ′ i are different with Λ i , but O- andM-slopes are identical: b ′ i = b i . Finally, we obtain the following SM running of gauge couplingconstants in the mirror world:1) ( α ′ ) − ( µ ) = . ± . − π t ′ , ( α ′ ) − ( µ ) = . ± . + π t ′ , ( α ′ ) − ( µ ) = . ± . + π t ′ , where t ′ = ln (cid:18) µ M ′ t (cid:19) . The pole mass of the mirror top quark isM ′ t = ζ M t . auge coupling constant evolutions in the mirror SM and MSSM.If the Minimal Supersymmetric Standard Model (MSSM) ex-tends the mirror SM , then mirror sparticle masses obey thefollowing relation: f m ′ = ζ e m , and the mirror SUSY-breaking scale is larger:M ′ SUSY = ζ M SUSY . The mirror MSSM gives the evolutions for α ′− ( µ ) ( i = 1 , , )from the supersymmetric scale M ′ SUSY up to the mirror GUTscale M ′ GUT .A seesaw scale M ′ R in the M-world is given in the previousSubsection. For ζ = ′ R = ζ M R ≈ M R . Now if M R ∼ GeV, then M ′ R ∼ GeV, and a seesaw scaleis close to the superGUT scale of the E -unification.This means that mirror heavy right-handed neutrinos appear atthe scale ∼ GeV.Figs. 1-4 present by blue lines the mirror MSSM evolutionsof α ′− ( µ ) (i = , , ′ SUSY =
10 TeV and 300 TeV , and M ′ R ∼ GeV; ζ =
10 – for M
SUSY = ζ =
30 – for M
SUSY =
10 TeV. .2 Mirror gauge coupling constant evolutionsfrom SU ( ) to the E -unification.Let us consider now the extension of the MSSM in the mirrorworld.The first step of such an extension is: [ SU ( ) ′ C × SU ( ) ′ L × U ( ) ′ Y ] MSSM → [ SU ( ) ′ C × SU ( ) ′ L × U ( ) ′ X × U ( ) ′ Z ] MSSM , and then [ SU ( ) ′ C × SU ( ) ′ L × U ( ) ′ X ] MSSM → SU ( ) ′ C × SU ( ) ′ L . Assuming that the supersymmetric group SU ( ) ′ C × SU ( ) ′ L originates at the scale M ′ , we find the intersection of SU ( ) ′ C with U ( ) ′ X : α ′− ( M ′ ) = α − ( M ′ ) . The gauge symmetry group SU ( ) ′ C starts from the scale M ′ andruns up to the intersection with the evolution ( α ′ ) − ( µ ) corre-sponding to the supersymmetric group SU ( ) ′ L .Here we have: b = − . The point of this intersection is the scale M ′ GUT . irror gauge coupling constant evolutionsfrom SU ( ) to the E -unification.The scale M ′ GUT is given by the following relation: ( α ′ ) − ( M ′ GUT ) = ( α ′ ) − ( M ′ GUT ) . At the mirror GUTscale M ′ GUT we obtain the SU ( ) ′ -unificationif U ( ) ′ Z also meets SU ( ) ′ C and SU ( ) ′ L at the same scale:SU ( ) ′ C × SU ( ) ′ L × U ( ) ′ Z → SU ( ) ′ . Here again b Z = − . Then we consider the running of ( α ′ ) − ( µ ) up to the superGUTscale M ′ SGUT = M ′ E6 : ( α ′ ) − ( µ ) = ( α ′ ) − ( M ′ GUT ) + π ln µ M ′ GUT , where we have used the resultb = . Calculating the slope b , we assumed the existence of only min-imal number of the Higgs fields, namely h + ¯h, belonging to thefundamental representation 6 of the SU ( ) ′ group.Now it is obvious that we must find some unknown in theO-world symmetry group SU ( ) ′ Z , which must help us to get thedesirable E ′ -unification in the M-world at the superGUT scaleM ′ SGUT : SU ( ) ′ × SU ( ) ′ Z → E ′ . irror gauge coupling constant evolutionsfrom SU ( ) to the E -unification.In the present investigation we assume that at the very smalldistances the mirror parity is restored and super-unifications E and E ′ , inspired by superstring theory, are identical having thesame M SGUT : M ′ SGUT = M SGUT = M E6 ∼ GeV . By this reason, the superGUT scale M
SGUT may be fixed by theintersection of the evolutions of gauge coupling constants in both– mirror and ordinary – worlds, which from the beginning werenot identical.The scale M
SGUT of the E × E ′ -unification is given by thefollowing intersection: α − ( M SGUT ) = ( α ′ ) − ( M SGUT ) . Finally, one can envision the following symmetry breaking chainin the M-world: E ′ → SU ( ) ′ × SU ( ) ′ Z → SU (4) ′ C × SU (2) ′ L × SU (2) ′ Z × U (1) ′ Z → SU ( ) ′ C × SU ( ) ′ L × SU ( ) ′ Z × U ( ) ′ X × U ( ) ′ Z → [ SU ( ) ′ C × SU ( ) ′ L × U ( ) ′ Y ] × SU ( ) ′ Z . Now it is quite necessary to understand if there exists the groupSU ( ) ′ Z in the mirror world. What it could be? A new mirror gauge group SU ( ) ′ Z . The reason of our choice of the gauge group SU ( ) ′ Z :See: C.R. Das and L.V. Laperashvili,
Mirror World with Bro-ken Mirror Parity, E Unification and Cosmology, submitted toPhys.Rev. D; ArXiv:was to obtain the correct running of ( α ′ ) − ( µ ) , which: • leads to the new scale Λ Z ∼ − eV at extremelylow energies; See:
H. Goldberg,
Phys.Lett. B 492, 153 (2000).
P.Q. Hung,
Nucl.Phys. B 747, 55 (2006); J.Phys. A 40, 6871(2007); arXiv: hep-ph/0707.2791.
P.Q. Hung and P. Mosconi,
ArXiv: hep-ph/0611001. • is consistent with the running of all inverse gaugecoupling constants in the O- and M-worlds with bro-ken mirror parity, considered in this investigation. Only the following slopes are consistent with our aims:b = ≈ .
33 and b
SUSY2Z = . ( ) ′ Z gauge group.The particle content of SU ( ) ′ Z is as follows:1. two doublets of fermions ψ ( Z ) i and two doublets of the ’mes-senger’ scalar fields φ ( Z ) i with i = ,
2, or2. one triplet of fermions ψ ( Z ) f with f = , ,
3, which are singletsunder the SM, and two doublets of the ’messenger’ scalarfields φ ( Z ) i with i = , ϕ Z = ( , , , ) under the symmetry groupG ′ = [ SU ( ) ′ C × SU ( ) ′ L × U ( ) ′ Y ] × SU ( ) ′ Z . article content of the SU ( ) ′ Z gauge group.The so called ’messenger’ fields φ ( Z ) carry quantum numbers ofboth the SM’ and SU ( ) ′ Z groups. They have Yukawa couplingswith SM’ leptons and fermions ψ ( Z ) .All the SM’ and SM particles are assumed to be singletsunder SU ( ) ′ Z . Then we obtain the following evolutions:1. for the region M ′ t ≤ µ ≤ M ′ SUSY : α ′− ( µ ) = α ′− ( M ′ t ) + b π ln µ M ′ t ≈ b π ln µ Λ Z ,
2. and for the region M ′ SUSY ≤ µ ≤ M ′ SGUT : α ′− ( µ ) = α ′− ( M ′ SUSY ) + b SUSY2Z π ln µ M ′ SUSY . Also we have the following relation: α ′− ( M ′ SGUT = M SGUT ) = α − . In Figs. 1-4 we have shown the evolution α ′− ( µ ) given by bluelines for b = SUSY2Z = . The total picture of the evolutions in the O- and M-worldsis presented simultaneously in Figs. 1–4 for the cases:M
SUSY = R ∼ , GeV, M ′ R ∼ GeV, ζ =
10 and ζ = ′ SUSY =
10 and 300 TeV.Here M
SGUT ≈ · GeV and α − ≈ .
64– for Figs. 1,2 (M
SUSY =
10 TeV),M
SGUT ≈ . · GeV and α − ≈ .
06– for Figs. 3,4 (M
SUSY = .2 The axion potential.The Lagrangian corresponding to the group of symmetryG ′ = SU ( ) ′ C × SU ( ) ′ L × SU ( ) ′ Z × U ( ) ′ Y exhibits a U ( ) ( Z ) A global symmetry.The singlet complex scalar field ϕ Z was introduced in theory withaim to reproduce the model of Peccei-Quinn (PQ) (well-knownin QCD): R. Peccei and H. Quinn,
Phys.Rev.Lett. 38, 1440(1977).Then the potential: V = λ ( ϕ + Z ϕ Z − v ) gives the VEV for ϕ Z : < ϕ Z > = v Z . Representing the field ϕ Z as follows: ϕ Z = v Z exp( ia Z / v Z ) + σ Z , we obtain the following VEVs: < a Z > = < σ Z > = . A boson a Z (the imaginary part of a singlet scalar field ϕ Z ) is anaxion, and could be a massless Nambu-Goldstone (NG) boson ifthe U (1) ( Z ) A symmetry is not spontaneously broken.However, the spontaneous breakdown of the global U ( ) ( Z ) A by SU (2) ′ Z instantons gives masses to fermions ψ ( Z ) and inverts a Z into a pseudo Nambu-Goldstone boson (PNGB). he axion potential.Then the field ϕ Z becomes: ϕ Z = exp( ia Z / v Z )( v Z + σ ( x )) ≈ v Z + σ ( x ) + ia Z ( x ) , with the field σ is an inflaton.Our axion a Z ( x ) is just the famous PQ-axion with a masssquared m ∼ Λ / v Z ∼ − Gev , and its potential, given by PQ model, has (for small a Z ) theexpression of the following type:V axion ≈ λ ( ϕ + Z ϕ Z − v ) + K | ϕ | cos( a Z / v z ) , where K is a positive constant: K > < a Z > = < a Z > = π v Z with the potential barrierexisting between them.The minimum of the above-mentioned potential at < a Z > = < a Z > = π v Z is called the ’false’ vacuum.Such properties of the present axion leads to the ’quintessense’model of our expanding universe and the axion a Z could be calledan acceleron. .3 A new cosmological scale Λ Z ≈ × − eV.A new gauge group SU ( ) ′ Z introduces a new dynamical scaleΛ Z ∼ − eV, which is consistent with present measurements ofcosmological constant: A.G. Riess et al.,
Astron.J. 116, 1009 (1998); ArXiv: astro-ph/9805201.
S.J. Perlmutter et al.,
Nature 39, 51 (1998); Astrophys.J. 517,565 (1999).
C. Bennett et al.,
ArXiv: astro-ph/0302207.
D. Spergel et al.,
ArXiv: astro-ph/0302209.
P. Astier et al.,
ArXiv: astro-ph/0510447.
D. Spergel et al.,
ArXiv: astro-ph/0603449.A total vacuum energy density of our universe (named cosmolog-ical constant) is equal to the following value: ρ vac ≈ ( × − eV) . A new asymptotically free gauge group SU ( ) ′ Z gives the run-ning of its inverse fine structure constant ( α ′ ) − ( µ ) , which growsfrom the extremely low energy scale Λ Z ∼ − eV up to thesupersymmetric scale M SUSY and then continues to run (in ourmodel – does not change, see Figs. 1,2) up to the superGUTscale M ′ SGUT = M E6 ∼ GeV.Near the scale Λ Z ∼ − eV the coupling constant of the gaugegroup SU ( ) ′ Z infinitely grows. At this scale we have a minimumof the effective potential (the first vacuum in the mirror world).Now it is worth the reader’s attention to observe that in themirror world we have three scales (presumably corresponding tothe three vacua of the universe):Λ = Λ Z ∼ − GeV , Λ = Λ EW ∼ GeV , Λ = Λ SGUT ∼ GeV . They obey the following interesting relation:Λ · Λ ≈ Λ . The gauge group SU ( ) ′ Z and the ’quintessence’ modelof our universe. Recent models of the Dark Energy (DE) and Dark Matter(DM) are based on measurements in contemporary cosmology.Supernovae observations at redshifts (1 . ≤ z ≤ .
7) by the Su-pernovae Legacy Survey (SNLS), cosmic microwave background(CMB), cluster data and baryon acoustic oscillations by the SloanDigital Sky Survey (SDSS) fit the equation of state for DE:w = p /ρ with a constant w:w = − . ± . ± . . which is given by P. Astier et al.,
ArXiv: astro-ph/0510447.The value w = − P.J.E. Peebles and A. Vilenkin,
Phys.Rev. D 59, 063505 (1999),
C. Wetterich,
Nucl.Phys. B 302, 668 (1998),
L.J. Hall, Y. Nomura, S.J. Oliver,
Phys.Rev.Lett. 95, 141302(2005); ArXiv: astro-ph/0503706.Here we present the quintessence scenario, which was developedin connection with the existence of a new gauge group SU ( ) ′ Z .In our model a Z plays the role of the ’acceleron’, and a scalarboson σ Z , partner of the acceleron, plays the role of the ’inflaton’in the low scale inflationary scenario. .1 Dark energy and cosmological constant.For the ratios of densities Ω X = ρ X /ρ c , cosmological measurementsgave: Ω B ∼ % for baryons (visible and dark),Ω DM ∼ % for non-baryonic DM, and Ω DE ∼ % for the mysterious DE, which is responsible for the accelerationof our universe.We have considered that a cosmological constant (CC) is givenby the value CC = ρ vac ≈ ( × − eV) . The main assumption is the following idea:the universe is trapped in the false vacuum with
C C = 0 , but atthe end it must decay into the true vacuum with vanishing CC.The true Electroweak vacuum would have its vacuum energy den-sity CC = ρ vac = . Such a scenario exists in the model with Multiple Point Principle(MPP):
D.L. Bennett, H.B. Nielsen,
Int.J.Mod.Phys. A 9, 5155 (1994);ibid., A 14, 3313 (1999).See review:
C.R. Das, L.V. Laperashvili,
Int.J.Mod.Phys. A20, 5911 (2005).A non-zero (nevertheless tiny) CC would be associated only witha false vacuum.
Why CC is zero in a true vacuum? ark energy and cosmological constant.People try to give a solution of this non-trivial problem: C.D. Froggatt, L.V. Laperashvili, R.B. Nevzorov, H.B. Nielsen, in: Proceedings of 7th Workshop on ’What Comes Beyond theStandard Model’, Bled, Slovenia, 19-30 Jul 2004 (DMFA, Za-loznistvo, Ljubljana, 2003), p.17; ArXiv: hep-ph/0411273.
L. Mersini,
ArXiv: gr-qc/0609006.The axion potential V ( a Z ) determines the origin of DE:when the temperature of the universe T is high: T >> Λ Z , thenthe axion potential is flat because the effects of the SU ( ) ′ Z in-stantons are negligible for such temperatures.When the temperature begins to decrease, the universe getstrapped in the false vacuum.At T ∼ Λ Z the true vacuum at < a Z > = . The universe is still trapped in the false vacuum withCC = ρ vac = Λ .The first order phase transition to the true vacuum is provokedby the bubble nucleation. In fact, the universe lives in the falsevacuum for a very long time.When the universe is trapped in the false vacuum at < a Z > = π v Z , the deceleration stops and acceleration begins at ¨a Z = = ( a Z ) = − .2 Dark matter.The existence of DM (non-luminous and non-absorbing matter)in the universe is now well established.Candidates for non-baryonic DM must be particles, which arestable on cosmological time scales. They must interact veryweakly with electromagnetic radiation. Also they must have theright relic density.These candidates can be black holes, axions, and weakly inter-acting massive particles (WIMPs). In supersymmetric modelsWIMP candidates are the lightest superparticles. The mostknown WIMP is the lightest neutralino. WIMPs could be photino,higgsino, or bino.In our model fermions ψ ( Z ) i of the gauge group SU ( ) ′ Z also couldbe considered as candidates for HDM (hot dark matter), andtheir composites (”hadrons” of SU ( ) Z ) could play a role of theWIMPs in CDM.Investigating DM, it is possible to search and study various sig-nals such as: ψ ( Z ) + e → ψ ( Z ) + e, or ψ ( Z ) + N → ψ ( Z ) + N, where e isan electron and N is a nucleon.The detection of mirror particles: mirror quarks, leptons, Higgsbosons, etc., could be performed at future colliders such as LHC.Also the ’messenger’ scalar boson φ ( Z ) can be produced at LHC,and then the decay: φ ( Z ) i → ψ ( Z ) i + l , where l stands for the SMlepton, can be investigated with ψ ( Z ) as missing energies.Leptogenesis and inflationary model also can be considered asimplications of our new physics. The full investigation is beyondthis paper. Conclusions.
1. In this talk we have discussed cosmological implications of theparallel ordinary and mirror worlds with the broken mirrorparity MP.2. We have considered the parameter characterizing the break-ing of MP, which is ζ = v ′ / v, where v ′ and v are the VEVsof the Higgs bosons – Electroweak scales – in the M- andO-worlds, respectively.3. During our numerical calculations, we have used the value ζ ≈
30, in accordance with a cosmological estimate obtainedby Berezhiani, Dolgov and Mohapatra.4. We have assumed that at the very small distances there ex-ists E -unification predicted by Superstring theory. We havechosen a theory, which leads to the asymptotically free E unification, what is not always fulfilled.5. We have shown that, as a result of the MP-breaking, theevolutions of fine structure constants in O- and M-worldsare not identical, and the extensions of the Standard Modelin the ordinary and mirror worlds are quite different.6. We have assumed that the E -unification, being the same inthe O- and M-worlds, restores the broken mirror parity MP.7. We have considered the following chain of symmetry groupsin the ordinary world:SU ( ) C × SU ( ) L × U ( ) Y → SU ( ) C × SU ( ) L × SU ( ) R × U ( ) X × U ( ) Z → SU ( ) C × SU ( ) L × SU ( ) R × U ( ) Z → SO ( ) × U ( ) Z → E . onclusions.
8. We have shown that a simple logic leads to the followingchain in the mirror world:SU ( ) ′ C × SU ( ) ′ L × SU ( ) ′ Z × U ( ) ′ Y → SU ( ) ′ C × SU ( ) ′ L × SU ( ) ′ Z × U ( ) ′ X × U ( ) ′ Z → SU ( ) ′ C × SU ( ) ′ L × SU ( ) ′ Z × U ( ) ′ Z → SU ( ) ′ × SU ( ) ′ Z → E ′ .
9. The comparison of both evolutions in the ordinary and mir-ror worlds is given in Figs. 1–4, where we have presented therunning of all fine structure constants. Here the SM (SM’)is extended by MSSM (MSSM’), and we see different evolu-tions. Figs. 1,2 correspond to the SUSY breaking scalesM
SUSY =
10 TeV , M ′ SUSY =
300 TeV , while Figs. 3,4 are presented forM SUSY = , M ′ SUSY =
10 TeV , according to the MP-breaking parameter ζ ≈
30 and 10. Wehave considered the value of seesaw scale in the O-worldM R ∼ GeV , and in the M-world: M ′ R ∼ GeV .
10. It was shown that the (super)grand unification E ′ in themirror world is based on the groupE ′ ⊃ SU ( ) ′ × SU ( ) ′ Z .
11. The presence of a new gauge group SU ( ) ′ Z in the M-worldgives significant consequences for cosmology: it explains the’quintessence’ model of our accelerating universe. onclusions.
12. We have presented in Figs. 1–4 the running of the SU ( ) ′ Z gauge coupling by the evolution α ′− ( µ ) , which takes its initialvalue at the superGUT scaleM SGUT ∼ GeVand then runs down to very low energies, giving an extremelystrong coupling constant at the scale Λ Z ∼ − eV.13. We have discussed a ’quintessence’ model of our universe: atthe scale Λ Z ∼ − eV instantons of the gauge group SU ( ) ′ Z induce a potential for an axion-like scalar boson a Z , which canbe called ”acceleron”. The acceleron gives the value w = − Z ∼ − eVexplains the value of cosmological constant:CC ≈ ( × − eV ) , which is given by astrophysical measurements. Also recentmeasurements in cosmology fit the equation of state for DE:w = p /ρ with a constant w ≈ − = Λ Z ∼ − GeV , Λ = Λ EW ∼ GeV , Λ = Λ SGUT ∼ GeV . They obey the following interesting relation:Λ · Λ ≈ Λ . onclusions.
17. In our model of the universe with broken mirror parity wehave obtained the following particle content of the groupSU ( ) ′ Z : • two doublets of fermions ψ ( Z ) i (i = , ψ ( Z ) f (f = , , • two doublets of scalar fields φ ( Z ) i (i = , ϕ Z , which produces”acceleron” a Z and ”inflaton” σ Z and gives a ’quintessence’model of our universe with the low scale inflationary scenario.19. Unfortunately, we cannot predict exactly the scales M SUSY and M R presented in our Figs. 1–4. The numerical descrip-tion of the model depends on these scales. Nevertheless,we hope that a qualitative scenario for the evolution of ouruniverse, developed in this paper, is valid.20. We have discussed a possibility to consider the fermions ψ ( Z ) i of the group SU ( ) ′ Z as candidates for HDM and composites(”hadrons” of SU ( ) ′ Z ) as WIMPs in CDM. Searching DM,it is possible to observe and study various signals of theseparticles.21. Finally, it is necessary to emphasize that this investigationopens the possibility to fix a grand unification group (E ?)from cosmology. C.R.D. deeply thanks Prof. R.N.Mohapatra for useful advices.This work was supported by the Russian Foundation for Basic Research(RFBR), project No 05-02-17642. eferences [1] T.D. Lee and C.N. Yang, Phys.Rev. 104, 254 (1956).[2] I.Yu. Kobzarev, L.B. Okun and I.Ya. Pomeranchuk, Yad.Fiz. 3, 1154(1966) [Sov.J.Nucl.Phys. 3, 837 (1966)].[3] Z. Berezhiani, Int.J.Mod.Phys. A19, 3775 (2004) [ArXiv:hep-ph/0312335].[4] Z. Berezhiani, Through the looking-glass: Alice’s adventures in mirror world , in:Ian Kogan Memorial Collection “From Fields to Strings: Circumnavi-gating Theoretical Physics”, Ed. M. Shifman et. al., World Scientific,Singapore, Vol. 3, pp.2147-2195, 2005 [ArXiv: hep-ph/0508233].[5] L.B. Okun, JETP 79, 694 (1980).[6] Ya.B. Zeldovich and M.Yu. Khlopov, Usp.Fiz.Nauk 135, 45 (1981)[Sov.Phys.Uspekhi 24, 755 (1981)].[7] S.I. Blinnikov and M.Yu. Khlopov, Yad.Fiz. 36, 809 (1982)[Sov.J.Nucl.Phys. 36, 472 (1982)]; Astron.Zh. 60, 632 (1983) [Sov.Astron.27, 371 (1983)].[8] B. Holdom, Phys.Lett. B166, 196 (1986).[9] S.L. Glashow, Phys.Lett. B167, 35 (1986).[10] E.D. Carlson and S.L. Glashow, Phys.Lett. B193, 168 (1987).[11] M. Sajin and M. Khlopov, Sov.Astron. 66, 191 (1989).[12] M.Yu. Khlopov, G.M. Beskin, N.G. Bochkarev, L.A. Pustylnik andS.A. Pustylnik, Astron.Zh. 68, 42 (1991) [Sov.Astron. 35, 21 (1991)].[13] R. Foot, H. Lew and R.R. Volkas, Phys.Lett. B272, 67 (1991);Mod.Phys.Lett. A7, 2567 (1992);R. Foot and R.R. Volkas, Phys.Rev. D52, 6595 (1995) [ArXiv:hep-ph/9505359].[14] M.Yu. Khlopov and K.I. Shibaev,
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GUT = 1.46 ⋅ GeV α X-1 α α α α α Z-1 M S G U T = . ⋅ G e V E M ′ R = 1.25 ⋅ GeVM ′ = 1.44 ⋅ GeVM ′ GUT = 2.25 ⋅ GeV α′ α′ α′ Z-1 α′ α′ α′ α′ α′ X-1 ζ = 10 (b) Fig. 4: This figure presents the same running of the inverse coupling constants α − i ( x ) inboth ordinary and mirror worlds with broken mirror parity from the scale 10 GeV up tothe E unification for SUSY breaking scales M SUSY = 1 TeV, M ′ SUSY = 10 TeV; ζ = 10;and seesaw scales M R = 1 . · GeV, M ′ R = 1 . · GeV; M SGUT ≈ . · GeVand α − SGUT ≈ ..