DEK

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Dark Energy a cosmic mystery
Dunkle Energie Ein kosmisches Raetsel
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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
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What is our universe made of ?
fire , air, water, soil !
quintessence !
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Dark Energy dominates the Universe

• Energy - density in the Universe
• Matter Dark Energy
• 25 75

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What is Dark Energy ?
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Matter Everything that clumps
Abell 2255 Cluster 300 Mpc
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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

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Om 0.25
gravitational lens , HST
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Gravitationslinse,HST
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spatially flat universe
Otot 1

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

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picture of the big bang
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(No Transcript)
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Otot1
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WMAP 2006
Polarization
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Dark Energy

• Om X 1
• Om 25
• Oh 75 Dark Energy

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

• The expansion of the Universe
• accelerates today !

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Power spectrum Baryon - Peak
galaxy correlation function
M.Tegmark
Structure formation One primordial
fluctuation- spectrum
SDSS
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baryon acoustic peak
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consistent cosmological model !
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Composition of the Universe

• Ob 0.045 visible clumping
• Odm 0.2 invisible clumping
• Oh 0.75 invisible homogeneous

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

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

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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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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 (depends on time ! )
• New long - range interaction

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observation will decide !
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Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
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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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Quintessence becomes important today
No reason why w should be constant in time !
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coincidence problem

• What is responsible for increase of Oh for z lt 10
  ?

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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

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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
• models characterized by kinetial k(f)

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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 )

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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

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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

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How can quintessence be distinguished from a
cosmological constant ?
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Early Dark Energy

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

1s and 2s limits 05
Doran,Karwan,..
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effects of early dark energy

• modifies cosmological evolution (CMB)
• slows down the growth of structure

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Early quintessence slows down the growth of
structure
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bounds on Early Dark Energy after
WMAP06 G.Robbers,M.Doran,
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interpolation of Oh
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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,
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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 C) Apparent violation of equivalence
principle D) Possible coupling between Dark
Energy and Dark Mater
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Quintessence and time variation of fundamental
constants
Strong, electromagnetic, weak interactions
Generic prediction Strength unknown
C.Wetterich , Nucl.Phys.B302,645(1988)
gravitation
cosmodynamics
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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 !

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Are fundamental constantstime dependent ?

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

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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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baryons the matter of stars and humans
Ob 0.045
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Abundancies of primordial light elements from
nucleosynthesis
A.Coc
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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,
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variation of Li- abundance
Coc,Nunes,Olive, Uzan,Vangioni 10/06
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Time variation of coupling constants
must be tiny would be of very high
significance ! Possible signal for
Quintessence
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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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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 !
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Differential acceleration

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

bound ? lt 3 10-14
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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 )

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Apparent violation of equivalence principle
and time variation of
fundamental couplings measure
both the cosmon coupling to ordinary matter
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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 ( 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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Quintessence and solution of cosmological
constant problem should be related !
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End
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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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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
• E gt 0 crossover Quintessence

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Asymptotically vanishing effective cosmological
constant

• Effective cosmological constant V/M4
• ? (?/µ) A
• V (?/µ) A ?4
• M ?
• V/M4 (?/µ) A

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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 !

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)
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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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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 !

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

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Cosmological equations
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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