SU(2) U(1) and the nature of light

1. COSMO 2005 31 August 2005 Bonn SU(2) U(1) and the nature of light Ralf Hofmann Universitäten Frankfurt/Heidelberg hep-th/0504064 [Int. J. Mod. Phys. A 20, 4123 (2005)], hep-th/0507033 hep hep-th/0507122, hep-ph/0508176, hep-th/0508212

2. motivation • nonperturbative SU(2) Yang-Mills thermodynamics: • A very brief introduction • electric-magnetic coincidence and U(1) • CMB fluctuations at large angles as radiative corrections • Summary and Outlook Outline

3. Motivation for SU(2) U(1)

4. WMAP 1-year release of temperature map

5. temperature-polarization cross correlation at large angles ? power spectrum of TE cross correlation: excess compared to primordial prediction ! (reionization versus mobile electric monopoles at )

6. more motivation • Universe´s equation of state: • (slowly rolling Planck-scale axion) • nontrivial ground state physics related to • physics of photon propagation? • (invisible ether) • intergalactic magnetic fields ? • (condensed, electrically charged monopoles)

7. SU(2) Yang-Mills thermodynamics, nonperturbatively

8. SU(2) Yang-Mills thermodynamics at large temperatures: spatial coarse-graining over both topological fluctuations (large, topology changing quantum fluctuations, calorons) plane-wave fluctuations (small quantum fluctuations, perturbation theory) • induce magnetic monopole constituents in calorons • induce interactions between monopoles • after coarse-graining: • pure-gauge configuration • provide spatial correlations to resolve the infrared catastrophe • after coarse-graining: • inert adjoint scalar with dependent modulus • quasiparticle masses by Higgs mechanism [Polyakov 1974,Nahm 1980, Lee & Lu 1998, Kraan & van Baal 1998, Brower et al. 1998, Diakonov et a. 2004, Ilgenfritz et al. 2005,]

9. SU(2) Yang-Mills thermodynamics: phase diagram confining preconfining deconfining ground state: CVL condensate (spin-1/2) excitation: single and self-intersecting CVLs ground state: monopole condensate plus collapsing, closed magnetic flux lines (CVL) (spin-1) excitation: massive, dual mode apparent gauge-symmetry breaking: ground state: short-lived (attracting) BPS monopoles and antimonopoles ( ) plus dilute, screened BPS monopoles and antimonopoles (spin-1) excitations: two massive modes one massless mode apparent gauge-symmetry breaking: Hage-dorn 2nd order

10. microscopics of ground-state dynamics: deconfining phase inert adjoint scalar after spatial coarse-graining pure gauge after spatial coarse-graining

11. quasiparticle excitations after spatial coarse-graining Yang-Mills scale quasiparticle mass: effective gauge coupling

12. one-loop evolution of with temperature monopole condensation, decoupling of magnetic-charge conserving atrractor SU(2) SU(3) magnetic charge of isolated monopole after screening: monopoles mobile close to phase transition CMB gets polarized at large angles ! mass of isolated monopole after screening: quasiparticle mass:

13. pressure at one-loop

14. energy density at one-loop today small correction to dark-energy content of the Universe (Planck-scale axion)

15. electric-magnetic coincidence at : electric coupling , magnetic coupling (dynamically stabilized) • free photon gas (no screening, decoupled ) • 2. (i) not yet a coupling of the photon to the monopole condensate: • (ii) photon massless, • (iii) rest-frame of heat bath not visible in single photon propagation (invisible ether), • (iv) superconductivity of ground state (intergalactic magnetic fields ?) barely visible coincide! (neither dynamical magnetic charges (screening) nor condensed electric charges (photon mass) measureable)

16. CMB fluctuations at large angles as radiative corrections dominant diagram subject to compositeness constraints (plane-wave quantum fluctuations softer than , harder fluctuations integrated out into ) radiative corrections to pressure at most 0.2% [Herbst, RH, Rohrer 2004]

17. dominant correction for dipole contribution in temperature map of CMB: (computed with upper bound for modulus when ! )

18. kinematical plus dynamical generation of dipole anisotropy ? • solar system moves w.r.t. CMB rest frame • km/s [Peebles & Wilkinson 1968] • horizon-volume of solar system moves into regions which, • formerly, were causally disconnected: kin < kin+dyn kin kin+dyn

19. Summary and Outlook Universetoday possibly dynamically stabilized at boundary between deconfining and preconfining phase of SU(2) Yang-Mills theory of scale invisible ether: structureless condensate of electric monopoles (electric-magnetic concidence) after jump to preconfining phase: Universe‘s ground state visibly superconducting monopole condensate: small correction to Universe‘s dark- energy content large-angle part of CMB power spectra: radiative corrections in deconfining phase of (mobile and dilute monopoles)

20. Summary and Outlook future work: • computation of two-loop correction to pressure in an FRW background • at low • computation of various thermal two-point correlators in Minkowski • space and FRW background with or without axion background • polarization power spectra and CP violation • rate of axion rolling necessary for jump to preconfining phase • (violation of thermal equilibrium)

22. Typical situation in thermal perturbation theory taken from Kajantie et al. 2002

23. SU(2) taken from van Baal & Kraan 1998

24. Does fluctuate? quantum mechanically: No ! compositeness scale thermodynamically: No !

25. Thermodynamical self-consistency: pressure (one-loop): however: Higgs-induced masses and ground-state pressure both - dependent - derivatives involve also implicit dependences relations between thermod.quantities violated: .

26. Relaxation to the minima