DEK

1
Quintessence
Dunkle Energie Ein kosmisches Raetsel
2
Dark energy a cosmic mystery

• C.Wetterich

A.Hebecker,M.Doran,M.Lilley,J.Schwindt, C.Müller,G
.Schäfer,E.Thommes, R.Caldwell
3
What is our Universemade of ?
4
Quintessence !
fire , air, water, soil !
5
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

6
Composition of the universe

• Ob 0.045
• Odm 0.225
• Oh 0.73

7
Ob0.045 from nucleosynthesis, cosmic
background radiation
8
Dark Matter

• Om 0.27 total matter
• Most matter is dark !
• So far tested only through gravity
• Every local mass concentration
  gravitational potential
• Orbits and velocities of stars and galaxies
  measurement of gravitational potential
• and therefore of local matter distribution

9
Om0.3
gravitational lens , HST
10
spatially flat universe
Otot 1

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

11
picture of the big bang
12
mean values Otot 1.02 Om 0.27 Ob
0.045 Odm 0.225
13
Otot1
14
Dark Energy

• Om X 1
• Om 30
• Oh 70 Dark Energy

h homogenous , often O? instead of Oh
15
Dark Energy homogeneously distributed
16
Confirmation by Supernovae
17
Supernova cosmology
Riess et al. 2004
18
Structure formation

• Structures in the Universe grow from tiny
• fluctuations in density distribution
• stars , galaxies, clusters
• One primordial fluctuation spectrum describes
• all correlation functions !

19
Structure formation fluctuation spectrum
CMB agrees with galaxy distribution Lyman a
forest and gravitational lensing effect !
Waerbeke
20
What is Dark Energy ? Cosmological Constant
or Quintessence ?
21
Cosmological Constant- Einstein -

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

22
Cosm. Const. Quintessence
static dynamical
23
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
24
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?

25
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
26
Prediction homogeneous dark energyinfluences
recent cosmology- of same order as dark matter -
Original models do not fit the present
observations . modifications
27
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 !
  

28
Cosmon

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

29
Fundamental Interactions
Strong, electromagnetic, weak interactions
On astronomical length scales graviton cosm
on
gravitation
cosmodynamics
30
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 !

31
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
32
Quintessence becomes important today
33
Equation of state

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

34
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
35
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

36
SN and equation of state
Riess et al. 2004
37
How can quintessence be distinguished from a
cosmological constant ?
38
Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
39
Measure this curve !
40
Early dark energy

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

41
Quintessence and time variation of fundamental
constants
Strong, electromagnetic, weak interactions
Generic prediction Strength unknown
C.Wetterich , Nucl.Phys.B302,645(1988)
gravitation
cosmodynamics
42
Are fundamental constantstime dependent ?

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

43
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,
44
Field dependent gauge coupling( gauge invariance
maintained )
for GUT C.Hill Q.Shafi , CW
45
GUT running of electromagneticand strong gauge
coupling related
strong effect from variation of nucleon mass for
time dependent couplings !
X.Calmet , H.Fritzsch
46
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

47
Abundancies of primordial light elements from
nucleosynthesis
A.Coc
48
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
C.Mueller,G.Schaefer,
49
Variation of fine structure constant as function
of redshift
Webb et al
Srianand et al
50
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
51
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 !

52

• 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 !

53
Variation of fine structure constant as function
of redshift
Webb et al
54
Atomic clocks and OKLO
assumes that both effects are dominated by
change of fine structure constant
55
Time variation of coupling constants must
be tiny would be of very high significance
! Possible signal for Quintessence
56
?a?ta ?e?
everything flows
57
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

58
Violation of equivalence principle

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

p,n
earth
cosmon
p,n
59
Differential acceleration ?

• For unified theories ( GUT )

??a/2a
Q time dependence of other parameters
60
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
61
Summary

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

62
????????????????????????

• 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 ?

63
Quintessence and solution of cosmological
constant problem should be related !
64
Quintessenceandfundamental mass scale
65
Fundamental mass scale

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

66
Fundamental mass scale

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

67
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

68
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)
69
Dilatation symmetry

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

70
Dilatation anomaly

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

71
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 !

72
Weyl scaling

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

73
Realistic cosmology

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

74
End
75
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)
76
Dilatation anomaly

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

77
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

78
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

79
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

80
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 -
  

81
Early quintessence slows down the growth of
structure
82
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
83
Fluctuation spectrum
Caldwell,Doran,Müller,Schäfer,
84
Anisotropy of cosmic background radiation
Caldwell,Doran,Müller,Schäfer,