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Title: DEK Author: C. Wetterich Last modified by: wetterich Created Date: 7/5/2003 8:41:24 AM Document presentation format: Bildschirmpr sentation – PowerPoint PPT presentation

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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.Kar
wan,G.Robbers
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
  • 25 75

5
What is Dark Energy ?
6
Matter Everything that clumps
Abell 2255 Cluster 300 Mpc
7
Dark Matter
  • Om 0.25 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

8
Om 0.25
gravitational lens , HST
9
Gravitationslinse,HST
10
spatially flat universe
Otot 1
  • theory (inflationary universe )
  • Otot 1.0000.x
  • observation ( WMAP )
  • Otot 1.02 (0.02)

11
picture of the big bang
12
(No Transcript)
13
(No Transcript)
14
Otot1
15
WMAP 2006
Polarization
16
Dark Energy
  • Om X 1
  • Om 25
  • Oh 75 Dark Energy

h homogenous , often O? instead of Oh
17
Space between clumps is not empty Dark Energy
!
18
Dark Energy density isthe same at every point of
space homogeneous No force in absence of
matter In what direction should it draw ?
19
Predictions for dark energy cosmologies
  • The expansion of the Universe
  • accelerates today !

20
Power spectrum Baryon - Peak
galaxy correlation function
M.Tegmark
Structure formation One primordial
fluctuation- spectrum
SDSS
21
baryon acoustic peak
22
consistent cosmological model !
23
Composition of the Universe
  • Ob 0.045 visible clumping
  • Odm 0.2 invisible clumping
  • Oh 0.75 invisible homogeneous

24
Dark Energy- a cosmic mystery
Dunkle Energie Ein kosmisches Raetsel
25
What is Dark Energy ? Cosmological Constant
or Quintessence ?
26
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 ?

27
Cosm. Const. Quintessence
static dynamical
28
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
29
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?

30
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
31
Prediction homogeneous dark energyinfluences
recent cosmology- of same order as dark matter -
Original models do not fit the present
observations . modifications
32
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 !

33
Fundamental Interactions
Strong, electromagnetic, weak interactions
On astronomical length scales graviton cosm
on
gravitation
cosmodynamics
34
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 !

35
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 !

36
Cosmon
  • Tiny mass
  • mc H (depends on time ! )
  • New long - range interaction

37
observation will decide !
38
Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
39
Quintessence becomes important today
40
Equation of state
  • pT-V pressure
    kinetic energy
  • ?TV energy density
  • Equation of state
  • Depends on specific evolution of the scalar field

41
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
42
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

43
Quintessence becomes important today
No reason why w should be constant in time !
44
coincidence problem
  • What is responsible for increase of Oh for z lt 10
    ?

45
a) Properties of cosmon potential or kinetic term
  • Early quintessence
  • Oh changes only modestly
  • w changes in time
  • transition
  • special feature in cosmon potential or kinetic
    term becomes important now
  • tuning at level
  • Late quintessence
  • w close to -1
  • Oh negligible in early cosmology
  • needs tiny parameter, similar to cosmological
    constant

46
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
  • models characterized by kinetial k(f)

47
attractor solutions
  • Small almost constant k
  • Small almost constant Oh
  • This can explain tiny value of Dark
    Energy !
  • Large k
  • Cosmon dominated universe ( like inflation )

48
Transition to cosmon dominated universe
  • Large value k gtgt 1 universe is dominated by
    scalar field
  • k increases rapidly evolution of scalar fied
    essentially stops
  • Realistic and natural quintessence
  • k changes from small to large values after
    structure formation

49
b) Quintessence reacts to some special event in
cosmology
  • Onset of
  • matter dominance
  • K- essence
  • Amendariz-Picon, Mukhanov,
  • Steinhardt
  • needs higher derivative
  • kinetic term
  • Appearance of
  • non-linear structure
  • Back-reaction effect
  • needs coupling between
  • Dark Matter and
  • Dark Energy

50
How can quintessence be distinguished from a
cosmological constant ?
51
Early Dark Energy
  • A few percent in the early Universe
  • Not possible for a cosmological constant

1s and 2s limits 05
Doran,Karwan,..
52
effects of early dark energy
  • modifies cosmological evolution (CMB)
  • slows down the growth of structure

53
Early quintessence slows down the growth of
structure
54
bounds on Early Dark Energy after
WMAP06 G.Robbers,M.Doran,
55
interpolation of Oh
56
Little Early Dark Energy can make large effect
!Non linear enhancement
Cluster number relative to ?CDM
Two models with 4 Dark Energy during structure
formation Fixed s8 ( normalization
dependence ! )
More clusters at high redshift !
Bartelmann,Doran,
57
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 D) Possible coupling between Dark
Energy and Dark Mater
58
Quintessence and time variation of fundamental
constants
Strong, electromagnetic, weak interactions
Generic prediction Strength unknown
C.Wetterich , Nucl.Phys.B302,645(1988)
gravitation
cosmodynamics
59
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 !

60
Are fundamental constantstime dependent ?
  • Fine structure constant a (electric charge)
  • Ratio electron mass to proton mass
  • Ratio nucleon mass to Planck mass

61
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,
62
baryons the matter of stars and humans
Ob 0.045
63
Abundancies of primordial light elements from
nucleosynthesis
A.Coc
64
Allowed values for variation of fine structure
constant
?a/a ( z1010 ) -1.0 10-3 GUT 1 ?a/a (
z1010 ) -2.7 10-4 GUT 2
C.Mueller,G.Schaefer,
65
variation of Li- abundance
Coc,Nunes,Olive, Uzan,Vangioni 10/06
66
Time variation of coupling constants
must be tiny would be of very high
significance ! Possible signal for
Quintessence
67
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

68
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)
69
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 !
70
Differential acceleration
  • Two bodies with equal mass experience
  • a different acceleration !
  • ? ( a1 a2 ) / ( a1 a2 )

bound ? lt 3 10-14
71
Cosmon coupling to atoms
  • Tiny !!!
  • Substantially weaker than gravity.
  • Non-universal couplings bounded by tests
  • of equivalence principle.
  • Universal coupling bounded by tests of
    Brans-Dicke parameter ? in solar system.
  • Only very small influence on cosmology.
  • ( All this assumes validity of linear
    approximation )

72
Apparent violation of equivalence principle
and time variation of
fundamental couplings measure
both the cosmon coupling to ordinary matter
73
Differential acceleration ?
  • For unified theories ( GUT )

??a/2a
Q time dependence of other parameters
74
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 , )
75
Summary
  • Oh 0.7
  • Q/? dynamical und static dark energy
  • will be distinguishable
  • Q time varying fundamental coupling
    constants
  • violation of equivalence principle

76
????????????????????????
  • 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 ?

77
Quintessence and solution of cosmological
constant problem should be related !
78
End
79
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

80
Dilatation symmetry
  • Lagrange density
  • Dilatation symmetry for
  • Conformal symmetry for d0

81
Dilatation anomaly
  • Quantum fluctuations responsible for
  • dilatation anomaly
  • Running couplings hypothesis
  • Renormalization scale µ ( momentum scale )
  • ?(?/µ) A
  • E gt 0 crossover Quintessence

82
Asymptotically vanishing effective cosmological
constant
  • Effective cosmological constant V/M4
  • ? (?/µ) A
  • V (?/µ) A ?4
  • M ?
  • V/M4 (?/µ) A

83
Weyl scaling
  • Weyl scaling gµ?? (M/?)2 gµ? ,
  • f/M ln (? 4/V(?))
  • Exponential potential V M4 exp(-f/M)
  • No additional constant !

84
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)
85
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 -

86
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 !

87
crossover quintessence
k(f) increase strongly for f corresponding to
present epoch
Example (LKT)
exponential quintessence
88
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
89
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 )

90
Cosmological equations
91
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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