The Nature of Dark Energy, IFT UAM/CSIC, May 30-June 3, 2011
The magnetic side of dark energy Antonio L. MAROTO, Jose BELTRÁN JIMÉNEZ Universidad Complutense de Madrid Université de Genève JCAP 0903:016 (2009) JCAP 0910:029 (2009) Phys. Lett. B 686 (2010) 175 Phys. Rev. D83 (2011) 023514 Gerrit Dou (1613-1675)
What is the nature of dark energy? Cosmological constant: simple and accurate description for cosmic acceleration, but … … its tiny value has to be introduced by hand in the theory. Is there a more fundamental explanation? Large-distance modifications of gravity suggested What about electromagnetism on large scales?. Its behaviour on astrophysical and cosmological scales still far from clear: unknown origin of G magnetic fields observed in galaxies and clusters May 31, 2011
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EM quantization in Minkowski space-time
Gauge invariance Maxwell’s equations
Coulomb/Lorenz gauge
BUT …. • Photon propagator ? • “Unphysical” degrees of freedom
Covariant quantization
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EM quantization in Minkowski space-time Coulomb/Lorenz gauge
Covariant quantization
Lorenz condition
Modified action: only residual symmetry Residual gauge symmetry
Maxwell’s equations
Free field + boundary conditions= Lorenz condition
Residual gauge (free fields)
2 physical states Positive energies May 31, 2011
Quantize UAM/IFT
2 physical states. Positive energies
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EM quantization in an expanding universe
Non-conformally coupled to gravity
Higuchi, Parker, Wang, (1990) Beltran, Maroto, (2010)
can be amplified from quantum vacuum fluctuations by the expanding background (e.g. during inflation)
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Lorenz condition?
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A toy model Mode equations Flat Robertson-Walker metric
super-Hubble Lorenz condition FAILS.
IN
OUT
sub-Hubble OK
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Problems with covariant quantization An initial physical state is not necessarily physical at a later time
A possible solution: introduce ghosts
Appropriate boundary conditions: (Adler, Lieberman and Ng, 1977 )
… but see Zhitnitsky 2010 and Ohta 2010, in Rindler space (ghost contribution)
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Extended EM without the Lorenz condition Fundamental EM action. Gauge non-invariant, but reduces to ordinary EM for transverse photons
propagating field
POSSIBLE PROBLEMS: • Modification
of classical Maxwell’s equations
• Unobserved new photon polarization • Negative norm (energy) states • Conflict with QED phenomenology
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Extended EM without the Lorenz condition
General solution
Photon
New scalar state
Pure residual gauge
The pure gauge mode can be eliminated so that all the physical states have positive norm and positive energy May 31, 2011
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Extended EM without the Lorenz condition Free theory contains three physical states:
Residual gauge symmetry allows to choose them with positive norm (energy):
and canonical commutators:
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Extended EM without the Lorenz condition Ordinary QED recovered in Minkowski space-time Ordinary QED effective action: gauge fixing procedure
Ghosts decoupled
Extended EM effective action: no gauge fixing required
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Extended EM without the Lorenz condition
Evolution of the new state in an expanding universe
New state decoupled from charged currents
DARK ENERGY COSMIC MAGNETIC FIELDS
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Extended EM without the Lorenz condition
• New scalar state can only be excited by gravity • No negative norm (energy) states • Classical Maxwell’s equations modified on sub-Hubble scales, but new term can generate cosmic magnetic fields • QED recovered in Minkowski space-time (ghosts play no role)
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Cosmological electromagnetic fields
Cosmological constant Isotropy OK
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An absolute cosmic electric potential What is the predicted dark energy density?
What is the field amplitude generated during inflation?
Inflation
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Radiation
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Matter
EM Dark Energy
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Initial conditions from inflation Initial conditions from vacuum fluctuations during inflation
Predicted dark energy density Friedmann equation (MI scale of inflation)
The cosmological constant value can be explained by physics at the electroweak scale May 31, 2011
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Stability and local gravity tests PPN parameters All parameters agree with GR for arbitrary A0
Classical and quantum stability v = c for scalar, vector and tensor perturbations. No ghosts.
CMB and LSS
Beltrán, Koivisto, Maroto, Mota, (2009).
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Cosmic magnetic fields: observations - Magnetic fields with strengths
B~10 G and ~ 10 kpc observed in spiral galaxies. - Magnetic fields observed in elliptical galaxies: random distribution, smaller scales G fields in the intracluster medium with ~ 10 kpc G fields observed in high-redshift galaxies
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Cosmic magnetic fields: observations Extragalactic fields
B > 3 x 10-16 G on ~ 3000 h-1 Mpc
A. Neronov & I. Vovk. Science 328, 73 (2010)
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Generation of cosmic magnetic fields Modified Maxwell’s equations
Effective current conserved
Effective electric charge density:
Longitudinal electric waves : May 31, 2011
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Generation of cosmic magnetic fields
Primordial power spectrum from inflation
Effective charge power spectrum
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Generation of cosmic magnetic fields Infinite conductivity
Neutral cosmic plasma
Ohm’s law:
Modified Maxwell’s equations:
An electrically charged universe generates magnetic field and vorticity Vorticity growth
A. Dolgov, J. Silk. (1993), C. Caprini, S. Biller, P.G. Ferreira (2005)
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Generation of cosmic magnetic fields
Upper limits on vorticity from CMB imply lower limits on magnetic fields
B lower limits on galactic scales
B lower limits on horizon scales m=0 m=-3
B(G)
B (G)
m=-5 m=0
m=-5
m=-3
n May 31, 2011
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Conclusions Extended EM theory with three physical states: new state generates an effective cosmological constant The small value of the cosmological constant naturally explained in the context of inflationary cosmology Nature of dark energy can be established without resorting to new physics Cosmic background of longitudinal electric waves: cosmic magnetic field and vorticity on sub-Hubble scales Magnetic fields with B> 10-12 G can be generated from sub-galactic scales up to the present Hubble radius Georges de la Tour (1593-1652)
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