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Title: DEK


1
Dark Energy a cosmic mystery
Dunkle Energie Ein kosmisches Raetsel
2
Quintessence
  • C.Wetterich

A.Hebecker,M.Doran,M.Lilley,J.Schwindt, C.Müller,G
.Schäfer,E.Thommes, R.Caldwell,M.Bartelmann,K.Karw
an
3
What is our universe made of ?
fire , air, water, soil !
quintessence !
4
Dark Energy dominates the Universe
  • Energy - density in the Universe
  • Matter Dark Energy
  • 30 70

5
What is Dark Energy ?
6
Matter Everything that clumps
Abell 2255 Cluster 300 Mpc
7
Om 0.3
gravitational lens , HST
8
Gravitationslinse,HST
9
spatially flat universe
Otot 1
  • theory (inflationary universe )
  • Otot 1.0000.x
  • observation ( WMAP )
  • Otot 1.02 (0.02)

10
picture of the big bang
11
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12
Otot1
13
Dark Energy
  • Om X 1
  • Om 30
  • Oh 70 Dark Energy

h homogenous , often O? instead of Oh
14
Space between clumps is not empty Dark Energy
!
15
Dark Energy density isthe same at every point of
space homogeneous No force in absence of
matter In what direction should it draw ?
16
Predictions for dark energy cosmologies
  • The expansion of the Universe
  • accelerates today !

17
Power spectrum Baryon - Peak
galaxy correlation function
Structure formation One primordial
fluctuation- spectrum
SDSS
18
consistent cosmological model !
19
Composition of the Universe
  • Ob 0.045 visible clumping
  • Odm 0.22 invisible clumping
  • Oh 0.73 invisible homogeneous

20
Dark Energy- a cosmic mystery
Dunkle Energie Ein kosmisches Raetsel
21
What is Dark Energy ? Cosmological Constant
or Quintessence ?
22
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 ?

23
Cosm. Const. Quintessence
static dynamical
24
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
25
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?

26
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
27
Prediction homogeneous dark energyinfluences
recent cosmology- of same order as dark matter -
Original models do not fit the present
observations . modifications
28
Quintessence
Cosmon Field f(x,y,z,t) similar
to electric field , but no direction ( scalar
field )
  • Homogeneous und isotropic Universe
    f(x,y,z,t)f(t)
  • Potential und kinetic energy of the cosmon -field
  • contribute to a dynamical energy density of the
    Universe !

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
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 !

32
Cosmon
  • Tiny mass
  • mc H
  • New long - range interaction

33
Cosmological equations
34
Quintessence becomes important today
35
Equation of state
  • pT-V pressure
    kinetic energy
  • ?TV energy density
  • Equation of state
  • Depends on specific evolution of the scalar field

36
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
37
Quintessence becomes important today
No reason why w should be constant in time !
38
How can quintessence be distinguished from a
cosmological constant ?
39
Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
40
Early Dark Energy
  • A few percent in the early Universe
  • Not possible for a cosmological constant

1s and 2s limits
Doran,Karwan,..
41
Little Early Dark Energy can make large effect !
Cluster number relative to ?CDM
More clusters at high redshift
Two models with 4 Dark Energy during structure
formation Fixed s8 ( normalization
dependence ! )
Early Quintessence slows downs the growth of
structure
Dark Energy during structure formation
42
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
  • C) Apparent violation of equivalence principle

43
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

44
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)
45
Violation of equivalence principle
  • Different couplings of cosmon to proton and
    neutron
  • Differential acceleration
  • Violation of equivalence principle

p,n
earth
cosmon
p,n
only apparent new fifth force !
46
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47
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48
Differential acceleration
  • Two bodies with equal mass experience
  • a different acceleration !
  • ? ( a1 a2 ) / ( a1 a2 )

49
Quintessence and time variation of fundamental
constants
Strong, electromagnetic, weak interactions
Generic prediction Strength unknown
C.Wetterich , Nucl.Phys.B302,645(1988)
gravitation
cosmodynamics
50
Time varying constants
  • It is not difficult to obtain quintessence
    potentials from higher dimensional or string
    theories
  • Exponential form rather generic
  • ( after Weyl scaling)
  • But most models show too strong time dependence
    of constants !

51
Are fundamental constantstime dependent ?
  • Fine structure constant a (electric charge)
  • Ratio nucleon mass to Planck mass

52
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,
53
Standard Model of electroweak interactions
Higgs - mechanism
  • The masses of all fermions and gauge bosons are
    proportional to the ( vacuum expectation ) value
    of a scalar field fH ( Higgs scalar )
  • For electron, quarks , W- and Z- bosons
  • melectron helectron fH
    etc.

54
Restoration of symmetryat high temperature in
the early Universe
high T less order more symmetry example magn
ets
High T SYM ltfHgt0
Low T SSB ltfHgtf0 ? 0
55
In the hot plasma of the early Universe No
difference in mass for electron and myon !
56
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57
Quintessence Couplings are still varying now
!Strong bounds on the variation of couplings
-interesting perspectives for observation !
58
baryons the matter of stars and humans
Ob 0.045
59
Abundancies of primordial light elements from
nucleosynthesis
A.Coc
60
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,
61
Variation of fine structure constant as function
of redshift
  • 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
62
Time variation of coupling constants
must be tiny would be of very high
significance ! Possible signal for
Quintessence
63
?a?ta ?e?
Everything is flowing
64
Apparent violation of equivalence principle
and time variation of
fundamental couplings measure
both the cosmon coupling to ordinary matter
65
Differential acceleration ?
  • For unified theories ( GUT )

??a/2a
Q time dependence of other parameters
66
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 ( MICROSCOPE , )
67
small change of couplings in space
  • Fine structure constant depends on location in
    space
  • Experiments with satellites ?
  • for r 2 RE
  • d aem / aem 3 10 -19 / k2

68
Quintessence and solution of cosmological
constant problem should be related !
69
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

70
Dilatation symmetry
  • Lagrange density
  • Dilatation symmetry for
  • Conformal symmetry for d0

71
Dilatation anomaly
  • Quantum fluctuations responsible for
  • dilatation anomaly
  • Running couplings hypothesis
  • Renormalization scale µ ( momentum scale )
  • ?(?/µ) A
  • E gt 0 crossover Quintessence

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

74
????????????????????????
  • 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 ?

75
End
76
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)
77
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

78
cosmon mass changes with time !
  • for standard kinetic term
  • mc2 V
  • for standard exponential potential , k
    const.
  • mc2 V/ k2 V/( k2 M2 )
  • 3 Oh (1 - wh ) H2 /( 2 k2 )

79
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 -

80
More models
  • Phantom energy ( Caldwell )
  • negative kinetic term ( w lt -1 )
  • consistent quantum theory ?
  • K essence ( Amendariz-Picon, Mukhanov,
    Steinhardt )
  • higher derivative kinetic terms
  • why derivative expansion not valid ?
  • Coupling cosmon / (dark ) matter ( C.W., Amendola
    )
  • why substantial coupling to dark matter and
    not to ordinary matter ?
  • Non-minimal coupling to curvature scalar f(f) R
    -
  • can be brought to standard form by Weyl
    scaling !

81
kinetial
  • Small almost constant k
  • Small almost constant Oh
  • Large k
  • Cosmon dominated universe ( like inflation )

82
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
83
Atomic clocks and OKLO
assumes that both effects are dominated by
change of fine structure constant
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