DEK

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Quintessence
Dunkle Energie Ein kosmisches Raetsel
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Quintessence a fifth force from
variation of the fundamental scale ?
Durham 04
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Quintessence

• C.Wetterich

A.Hebecker,M.Doran,M.Lilley,J.Schwindt, C.Müller,G
.Schäfer,E.Thommes, R.Caldwell
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What is our Universemade of ?
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Quintessence !
fire , air, water, soil !
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critical density

• ?c 3 H² M²
• critical energy density of the universe
• ( M reduced Planck-mass , H Hubble
  parameter )
• Ob?b/?c
• fraction in baryons
• energy density in baryons over critical energy
  density

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Composition of the universe

• Ob 0.045
• Odm 0.225
• Oh 0.73

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gravitational lens , HST
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spatially flat universe
Otot 1

• theory (inflationary universe )
• Otot 1.0000.x
• observation ( Boomerang,WMAP )
• Otot 1.02 (0.02)

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picture of the big bang
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mean values Otot 1.02 Om 0.27 Ob
0.045 Odm 0.225
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Otot1
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Dark Energy

• Om X 1
• Om 30
• Oh 70 Dark Energy

h homogenous , often O? instead of Oh
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Dark Energy homogeneously distributed
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Dark Energy prediction The
expansion of the Universe
accelerates today !
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Supernova cosmology
Riess et al. 2004
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Structure formation fluctuation spectrum
CMB agrees with galaxy distribution Lyman a
forest and gravitational lensing effect !
Waerbeke
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consistent cosmological model !
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Composition of the Universe

• Ob 0.045 visible clumping
• Odm 0.225 invisible clumping
• Oh 0.73 invisible homogeneous

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What is Dark Energy ? Cosmological Constant
or Quintessence ?
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Cosmological Constant

• Constant ? compatible with all symmetries
• No time variation in contribution to energy
  density
• Why so small ? ?/M4 10-120
• Why important just today ?

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Cosm. Const. Quintessence
static dynamical
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Cosmological mass scales

• Energy density
• ? ( 2.410 -3 eV )- 4

• Reduced Planck mass
• M2.441018GeV
• Newtons constant
• GN(8pM²)

Only ratios of mass scales are observable !
homogeneous dark energy ?h/M4 6.5 10¹²¹
matter
?m/M4 3.5 10¹²¹
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Time evolution
t² matter dominated universe t3/2
radiation dominated universe

• ?m/M4 a³
• ?r/M4 a4 t -2 radiation dominated
  universe
• Huge age small ratio
• Same explanation for small dark energy?

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Quintessence

• Dynamical dark energy ,
• generated by scalar field
• (cosmon)

C.Wetterich,Nucl.Phys.B302(1988)668,
24.9.87 P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L1
7, 20.10.87
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Cosmon

• Scalar field changes its value even in the
  present cosmological epoch
• Potential und kinetic energy of cosmon contribute
  to the energy density of the Universe
• Time - variable dark energy
• ?h(t) decreases with time !
  

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Cosmon

• Tiny mass
• mc H
• New long - range interaction

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Fundamental Interactions
Strong, electromagnetic, weak interactions
On astronomical length scales graviton cosm
on
gravitation
cosmodynamics
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Evolution of cosmon field

• Field equations
• Potential V(f) determines details of the
  model
• e.g. V(f) M4 exp( - f/M )
• for increasing f the potential decreases
  towards zero !

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Cosmic Attractors
Solutions independent of initial conditions
typically Vt -2 f ln ( t ) Oh
const. details depend on V(f) or kinetic term
early cosmology
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Quintessence becomes important today
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Equation of state

• pT-V pressure
  kinetic energy
• ?TV energy density
• Equation of state
• Depends on specific evolution of the scalar field

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Negative pressure

• w lt 0 Oh increases (with decreasing
  z )
• w lt -1/3 expansion of the Universe is
• accelerating
• w -1 cosmological constant

late universe with small radiation component
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small early and large presentdark energy

• fraction in dark energy has substantially
  increased since end of structure formation
• expansion of universe accelerates in present
  epoch

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How can quintessence be distinguished from a
cosmological constant ?
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Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
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Early dark energy

• A few percent in the early Universe
• Not possible for a cosmological constant

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Quintessence and solution of cosmological
constant problem should be related !
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Fundamental mass scale

• Unification fixes parameters with dimensions
• Special relativity c
• Quantum theory h
• Unification with gravity
• fundamental mass scale
• ( Planck mass , string tension , )

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Fundamental mass scale

• Fixed parameter or dynamical scale ?
• Dynamical scale Field
• Dynamical scale compared to what ?
• momentum versus mass
• ( or other parameter with dimension )

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Cosmon and fundamental mass scale

• Assume all mass parameters are proportional to
  scalar field ? (GUTs, superstrings,)
• Mp ? , mproton ? , ?QCD ? , MW ? ,
• ? may evolve with time cosmon
• mn/M ( almost ) constant - observation !
• Only ratios of mass scales are observable

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Example Field ? denotes scale of
transition from higher dimensional physics to
effective four dimensional description in theory
without fundamental mass parameter (except for
running of dimensionless couplings)
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Dilatation symmetry

• Lagrange density
• Dilatation symmetry for
• Conformal symmetry for d0

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Dilatation anomaly

• Quantum fluctuations responsible for
• dilatation anomaly
• Running couplings hypothesis
• Renormalization scale µ ( momentum scale )
• ?(?/µ) -A

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Dilatation anomaly

• V?4-A , Mp(? ) ?
• V/Mp4 ?-A
• decreases for increasing ? !!
• Egt0 crossover quintessence

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Cosmology

• Cosmology ? increases with time !
• ( due to coupling of ? to curvature scalar )
• for large ? the ratio V/M4 decreases to zero
• Effective cosmological constant vanishes
  asymptotically for large t !

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Weyl scaling

• Weyl scaling gµ?? (M/?)2 gµ? ,
• f/M ln (? 4/V(?))
• Exponential potential V M4 exp(-f/M)
• No additional constant !

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Crossover Quintessence

• 
  ( like QCD gauge coupling)
• critical ? where d grows large
• critical f where k grows large
  k²(f )d(?)/4
• k²(f ) 1/(2E(fc f)/M)
• if j c 276/M ( tuning ! )
• Relative increase of dark energy in
  present
• cosmological epoch

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Realistic cosmology

• Hypothesis on running couplings
• yields realistic cosmology
• for suitable values of A , E , fc

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Dilatation anomaly

• Computation of running couplings ( beta functions
  ) needs unified theory !
• Dominant contribution from modes with momenta ?
  !
• No prejudice on natural value of anomalous
  dimension should be inferred from tiny
  contributions at QCD- momentum scale !
• Almost flat direction in potential for f
• Pseudo-Goldstone boson of dilatation symmetry

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Are fundamental constantstime dependent ?

• Fine structure constant a (electric charge)
• Ratio nucleon mass to Planck mass

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Fifth Force

• Mediated by scalar field
• Coupling strength weaker than gravity
• ( nonrenormalizable interactions M-2 )
• Composition dependence
• violation of equivalence principle
• Quintessence connected to time variation of
• fundamental couplings

R.Peccei,J.Sola,C.Wetterich,Phys.Lett.B195,183(198
7)
C.Wetterich , Nucl.Phys.B302,645(1988)
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Quintessence and Time dependence of
fundamental constants

• Fine structure constant depends on value of
• cosmon field a(f)
• (similar in standard model couplings depend
  on value of Higgs scalar field)
• Time evolution of f
• Time evolution of a

Jordan,
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Field dependent gauge coupling( gauge invariance
maintained )
for GUT C.Hill Q.Shafi , CW
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GUT running of electromagneticand strong gauge
coupling related
strong effect from variation of nucleon mass for
time dependent couplings !
X.Calmet , H.Fritzsch
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Where to look for time variation of fundamental
couplings ?

• Nucleosynthesis
• Molecular absorption lines in the light of
  distant Quasars
• Oklo natural reactor
• Atomic clocks
• CMB

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Abundancies of primordial light elements from
nucleosynthesis
A.Coc
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Relative change of He4 abundance vs. relative
change of couplings
C.Mueller, G.Schaefer,
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if present 2-sigma deviation of He
abundance from CMB/nucleosynthesis prediction
would be confirmed
?a/a ( z1010 ) -1.0 10-3 GUT 1 ?a/a (
z1010 ) -2.7 10-4 GUT 2
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Variation of fine structure constant as function
of redshift
Webb et al
Srianand et al
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Variation of fine structure constant

• Three independent data sets from Keck/HIRES
• ?a/a - 0.54 (12) 10-5
• Murphy,Webb,Flammbaum, june
  2003
• VLT
• ?a/a - 0.06 (6) 10-5
• Srianand,Chand,Petitje
  an,Aracil, feb.2004

z 2
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Crossover quintessence andtime variation of
fundamental constants

• Upper bounds for relative variation of the
• fine structure constant
• Oklo natural reactor ?a/a lt 10 -7
  z0.13
• Meteorites ( Re-decay ) ?a/a lt 3 10 -7
  z0.45
• Crossover Quintessence compatible with QSO
• and upper bounds !

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• Time evolution of fundamental couplings traces
  time evolution of quintessence
• today wh close to -1
• Small kinetic energy
• Slow change of f
• Slow change of a
• Very small ?a/a for low z !

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Variation of fine structure constant as function
of redshift
Webb et al
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Atomic clocks and OKLO
assumes that both effects are dominated by
change of fine structure constant
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Time variation of coupling constants is
tiny would be of very high significance !
Possible signal for Quintessence
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?a?ta ?e?
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Cosmodynamics

• Cosmon mediates new long-range interaction
• Range size of the Universe horizon
• Strength weaker than gravity
• photon electrodynamics
• graviton gravity
• cosmon cosmodynamics
• Small correction to Newtons law

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Violation of equivalence principle

• Different couplings of cosmon to proton and
  neutron
• Differential acceleration
• Violation of equivalence principle

p,n
earth
cosmon
p,n
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Differential acceleration ?

• For unified theories ( GUT )

??a/2a
Q time dependence of other parameters
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Link between time variation of a and
violation of equivalence principle
typically ? 10-14 if
time variation of a near Oklo upper bound
to be tested by MICROSCOPE
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Summary

• Oh 0.7
• Q/? dynamical und static dark energy
• will be distinguishable
• Q time varying fundamental coupling
  constants
• violation of equivalence principle

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????????????????????????

• Why becomes Quintessence dominant in the present
  cosmological epoch ?
• Are dark energy and dark matter related ?
• Can Quintessence be explained in a fundamental
  unified theory ?

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End
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A few references C.Wetterich ,
Nucl.Phys.B302,668(1988) , received
24.9.1987 P.J.E.Peebles,B.Ratra ,
Astrophys.J.Lett.325,L17(1988) , received
20.10.1987 B.Ratra,P.J.E.Peebles ,
Phys.Rev.D37,3406(1988) , received
16.2.1988 J.Frieman,C.T.Hill,A.Stebbins,I.Waga ,
Phys.Rev.Lett.75,2077(1995) P.Ferreira, M.Joyce
, Phys.Rev.Lett.79,4740(1997) C.Wetterich ,
Astron.Astrophys.301,321(1995) P.Viana, A.Liddle
, Phys.Rev.D57,674(1998) E.Copeland,A.Liddle,D.Wa
nds , Phys.Rev.D57,4686(1998) R.Caldwell,R.Dave,P
.Steinhardt , Phys.Rev.Lett.80,1582(1998) P.Stein
hardt,L.Wang,I.Zlatev , Phys.Rev.Lett.82,896(1999)
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Dynamics of quintessence

• Cosmon j scalar singlet field
• Lagrange density L V ½ k(f) j j
• (units reduced Planck mass M1)
• Potential Vexp-j
• Natural initial value in Planck era j0
• today j276

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Quintessence models

• Kinetic function k(f) parameterizes the
• details of the model - kinetial
• k(f) kconst. Exponential
  Q.
• k(f ) exp ((f f1)/a) Inverse power
  law Q.
• k²(f ) 1/(2E(fc f)) Crossover Q.
• possible naturalness criterion
• k(f0)/ k(ftoday) not tiny or huge !
• - else explanation needed -
  

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Simple parameterization of quintessence
parameter b
natural time variable
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Early quintessence slows down the growth of
structure
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Growth of density fluctuations

• Matter dominated universe with constant Oh
• Dark energy slows down structure formation
• Oh lt 10 during structure
  formation
• Substantial increase of Oh(t) since structure has
  formed!
• negative wh
• Question why now is back ( in mild form )

P.Ferreira,M.Joyce
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Fluctuation spectrum
Caldwell,Doran,Müller,Schäfer,
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Anisotropy of cosmic background radiation
Caldwell,Doran,Müller,Schäfer,
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How to distinguish Q from ? ?

• A) Measurement Oh(z) H(z)
• i) Oh(z) at the time of
• structure formation , CMB - emission
• or nucleosynthesis
• ii) equation of state wh(today) gt -1
• B) Time variation of fundamental constants

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Diracs hypothesis

• The very small dimensionless numbers in
  physics are due to huge age of the universe .

(A) may be true for ratio of dark energy over M4

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Cosmon and time variation of couplings

• small coupling of cosmon to matter due to fixed
  points behavior

close to fixed point small time evolution of
couplings coupling to matter weaker than
gravitational strength
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dependence of fixed point on dcould induce
observable effect
adjusting b6 to reproduce results by Webb et al
smaller for Srianand et al !
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