Title: DEK
1 Dark Energy a cosmic mystery
Dunkle Energie Ein kosmisches Raetsel
2Quintessence
A.Hebecker,M.Doran,M.Lilley,J.Schwindt, C.Müller,G
.Schäfer,E.Thommes, R.Caldwell,M.Bartelmann, K.Kar
wan,G.Robbers
3What is our universe made of ?
fire , air, water, soil !
quintessence !
4Dark Energy dominates the Universe
- Energy - density in the Universe
-
- Matter Dark Energy
- 25 75
5What is Dark Energy ?
6Matter Everything that clumps
Abell 2255 Cluster 300 Mpc
7Dark 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
8Om 0.25
gravitational lens , HST
9Gravitationslinse,HST
10spatially flat universe
Otot 1
- theory (inflationary universe )
- Otot 1.0000.x
- observation ( WMAP )
- Otot 1.02 (0.02)
11picture of the big bang
12(No Transcript)
13(No Transcript)
14Otot1
15WMAP 2006
Polarization
16Dark Energy
- Om X 1
- Om 25
- Oh 75 Dark Energy
h homogenous , often O? instead of Oh
17Space between clumps is not empty Dark Energy
!
18Dark Energy density isthe same at every point of
space homogeneous No force in absence of
matter In what direction should it draw ?
19Predictions for dark energy cosmologies
- The expansion of the Universe
- accelerates today !
20Power spectrum Baryon - Peak
galaxy correlation function
M.Tegmark
Structure formation One primordial
fluctuation- spectrum
SDSS
21baryon acoustic peak
22 consistent cosmological model !
23Composition of the Universe
- Ob 0.045 visible clumping
- Odm 0.2 invisible clumping
- Oh 0.75 invisible homogeneous
-
24Dark Energy- a cosmic mystery
Dunkle Energie Ein kosmisches Raetsel
25What is Dark Energy ? Cosmological Constant
or Quintessence ?
26Cosmological 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
28Cosmological 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
29Time 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?
30Quintessence
- 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
31Prediction homogeneous dark energyinfluences
recent cosmology- of same order as dark matter -
Original models do not fit the present
observations . modifications
32Quintessence
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 !
33Fundamental Interactions
Strong, electromagnetic, weak interactions
On astronomical length scales graviton cosm
on
gravitation
cosmodynamics
34Evolution 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 !
35Cosmon
- 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 !
36Cosmon
- Tiny mass
- mc H (depends on time ! )
- New long - range interaction
37observation will decide !
38Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
39Quintessence becomes important today
40Equation of state
- pT-V pressure
kinetic energy - ?TV energy density
- Equation of state
- Depends on specific evolution of the scalar field
41Negative 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
42small early and large presentdark energy
- fraction in dark energy has substantially
increased since end of structure formation - expansion of universe accelerates in present
epoch
43Quintessence becomes important today
No reason why w should be constant in time !
44coincidence problem
- What is responsible for increase of Oh for z lt 10
?
45a) 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
46Dynamics 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)
47attractor solutions
- Small almost constant k
- Small almost constant Oh
- This can explain tiny value of Dark
Energy ! - Large k
- Cosmon dominated universe ( like inflation )
48Transition 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
49b) 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
50How can quintessence be distinguished from a
cosmological constant ?
51Early Dark Energy
- A few percent in the early Universe
- Not possible for a cosmological constant
1s and 2s limits 05
Doran,Karwan,..
52effects of early dark energy
- modifies cosmological evolution (CMB)
- slows down the growth of structure
53Early quintessence slows down the growth of
structure
54bounds on Early Dark Energy after
WMAP06 G.Robbers,M.Doran,
55interpolation of Oh
56Little 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,
57How 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
58Quintessence and time variation of fundamental
constants
Strong, electromagnetic, weak interactions
Generic prediction Strength unknown
C.Wetterich , Nucl.Phys.B302,645(1988)
gravitation
cosmodynamics
59Time 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 !
60Are fundamental constantstime dependent ?
- Fine structure constant a (electric charge)
- Ratio electron mass to proton mass
- Ratio nucleon mass to Planck mass
61Quintessence 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,
62baryons the matter of stars and humans
Ob 0.045
63Abundancies of primordial light elements from
nucleosynthesis
A.Coc
64Allowed 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,
65variation 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
67Cosmodynamics
- 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
68Fifth 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)
69Violation 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 !
70Differential acceleration
- Two bodies with equal mass experience
- a different acceleration !
- ? ( a1 a2 ) / ( a1 a2 )
bound ? lt 3 10-14
71Cosmon 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 )
72Apparent violation of equivalence principle
and time variation of
fundamental couplings measure
both the cosmon coupling to ordinary matter
73Differential acceleration ?
- For unified theories ( GUT )
??a/2a
Q time dependence of other parameters
74Link 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 , )
75Summary
- 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 ?
77Quintessence and solution of cosmological
constant problem should be related !
78End
79Cosmon 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
80Dilatation symmetry
- Lagrange density
- Dilatation symmetry for
- Conformal symmetry for d0
81Dilatation anomaly
- Quantum fluctuations responsible for
- dilatation anomaly
- Running couplings hypothesis
- Renormalization scale µ ( momentum scale )
- ?(?/µ) A
- E gt 0 crossover Quintessence
82Asymptotically vanishing effective cosmological
constant
- Effective cosmological constant V/M4
- ? (?/µ) A
- V (?/µ) A ?4
- M ?
- V/M4 (?/µ) A
83Weyl scaling
- Weyl scaling gµ?? (M/?)2 gµ? ,
- f/M ln (? 4/V(?))
- Exponential potential V M4 exp(-f/M)
- No additional constant !
84A 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)
85Quintessence 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 -
86More 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 !
87crossover quintessence
k(f) increase strongly for f corresponding to
present epoch
Example (LKT)
exponential quintessence
88Growth 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
89cosmon 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 )
90Cosmological equations
91Cosmic Attractors
Solutions independent of initial conditions
typically Vt -2 f ln ( t ) Oh
const. details depend on V(f) or kinetic term
early cosmology