su(2) u(1) and the nature of light cosmo 2005 31 august 2005 bonn ralf hofmann universitäten...
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SU(2) U(1) and the nature of light
COSMO 2005
31 August 2005
Bonn
Ralf Hofmann
Universitäten Frankfurt/Heidelberg
today
CMB Y
hep-th/0504064 [Int. J. Mod. Phys. A 20, 4123 (2005)], hep-th/0507033
hep hep-th/0507122, hep-ph/0508176, hep-th/0508212
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Outline
• 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
Y
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Motivation
for
SU(2) U(1)today
CMB Y
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WMAP 1-year release of temperature map
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power spectrum of TE cross correlation:
excess compared to primordial prediction !
(reionization versus mobile electric monopoles at )
temperature-polarization cross correlation at large angles
20...10z
?
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• 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)
critDMcritcrit 3.0,7.0,
more motivation
GB 910
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SU(2) Yang-Mills
thermodynamics,
nonperturbatively
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SU(2) Yang-Mills thermodynamics
at large temperatures:
spatial coarse-graining over both
plane-wave fluctuations
(small quantum fluctuations,
perturbation theory)
topological fluctuations
(large, topology changing quantum fluctuations,
calorons)
1. induce magnetic monopole constituents in calorons
2. induce interactions between monopoles
3. after coarse-graining:
pure-gauge configuration
[Polyakov 1974,Nahm 1980, Lee & Lu 1998, Kraan & van Baal 1998, Brower et al. 1998, Diakonov et a. 2004, Ilgenfritz et al. 2005,]
1. provide spatial correlations to resolve the infrared catastrophe
2. after coarse-graining:
inert adjoint scalar with dependent modulus
quasiparticle masses by Higgs mechanism
T
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SU(2) Yang-Mills thermodynamics: phase diagram
T
deconfiningpreconfiningconfining
2nd order
Hage-dorn
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:
Mgs TP 3
Tem
E
w 22
3
)1()2( USU
ground state:
monopole condensate
plus collapsing,
closed magnetic
flux lines (CVL)
(spin-1) excitation:
massive, dual mode
apparent gauge-symmetry breaking:
Egs TP 34
1)1( DU
ground state:
CVL condensate
(spin-1/2) excitation:
single and self-intersecting CVLs
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microscopics of ground-state dynamics: deconfining phase
inert adjoint scalar after spatial coarse-graining
pure gauge after spatial coarse-graining bga
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quasiparticle excitations after spatial coarse-graining
quasiparticle mass:T
emE
w 22
3
effective gauge coupling
Yang-Mills scale
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one-loop evolution of with temperature e
magnetic charge of isolated monopole after screening: e
g4
mass of isolated monopole after screening: e
TM 22
Tem
E
w 22
3
quasiparticle mass:
SU(2)
SU(3)
monopole condensation,
decoupling of W
magnetic-charge conserving atrractor
)log()( ,EcEEe
14.5e
monopoles mobile close to
phase transition
CMB gets polarized at large angles !
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pressure at one-loop
3
26675.0
..
condmon
today
CMBtoday
P
P
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energy density at one-loop
E65.11, Ec
today 3)2(,
105.4
CMBSUgs
eVE4102.1
small correction to dark-energy content of the Universe
(Planck-scale axion)
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electric-magnetic coincidence
at : Ec, electric coupling , magnetic coupling
(dynamically stabilized)
e
0g
1. 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
W
DUSU
USU
)1()2(
)1()2(
coincide!
(neither dynamical magnetic charges (screening) nor condensed electric charges (photon mass) measureable)
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CMB fluctuations at large angles as radiative corrections
subject to compositeness constraints
(plane-wave quantum fluctuations softer than , harder fluctuations integrated out into )
[Herbst, RH, Rohrer 2004]
||bga
radiative corrections to pressure at most 0.2%
W
W
,WW
,WW
,WW
dominant diagram
P
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E
dominant correction
T
T
4
3for EcE ,
(computed with
upper bound for modulus when ! )
14.5e EcE ,
Ec,
dipole contribution
in temperature map of CMB:
31
1 10)006.0239.1(||
WMAPyearCMB
l
T
T
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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:
370v
)0()0( 00 zTzT ll
kin+dyn
kin
v vkin+dyn < kin
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Summary and Outlook
Universe today possibly dynamically stabilized at boundary
between deconfining and preconfining phase of
SU(2) Yang-Mills theory of scale
eVE4102.1
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)
CMBSU )2(
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future work:
Summary and Outlook
• 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)
)(lT
Tl
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Typical situation in thermal perturbation theory
taken from Kajantie et al. 2002
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taken from van Baal & Kraan 1998
SU(2)
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Does fluctuate?
quantum mechanically:
)2
( 13 332
2
EEE
l
E Tl
Vl
No !
thermodynamically:
compositeness scale
112 222
2
lT
VEl
No !
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.
pressure (one-loop):
however:
Higgs-induced masses and ground-state pressure both
- dependentT
PdT
dPT
relations between thermod.quantities violated:
Thermodynamical self-consistency:
- derivatives involve also implicit dependencesT
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Relaxation to the minima