DEK

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Dark Energy a cosmic mystery
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Quintessence

• C.Wetterich

A.Hebecker, M.Doran, M.Lilley, J.Schwindt, C.Mülle
r, G.Schäfer, E.Thommes, R.Caldwell,
M.Bartelmann, K.Kharwan, G.Robbers, T.Dent,
S.Steffen, L.Amendola, M.Baldi , N.Brouzakis ,
N.Tetradis, D.Mota, V.Pettorino, T.Krüger,
M.Neubert
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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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Composition of the universe

• Ob 0.045
• Odm 0.225
• Oh 0.73

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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

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Baryons/Atoms

• Dust
• Ob0.045
• Only 5 percent of our Universe consist of known
  
• matter !

SDSS
60,000 of gt300,000 Galaxies
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Abell 2255 Cluster 300 Mpc
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Ob0.045 from nucleosynthesis, cosmic
background radiation
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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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Gravitationslinse,HST
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Matter Everything that clumps
Om 0.25
Abell 2255 Cluster 300 Mpc
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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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Mean values WMAP 2003 Otot 1.02 Om 0.27 Ob
0.045 Odm 0.225
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Otot1
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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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Structure formation One primordial fluctuation
spectrum
CMB agrees with Galaxy distribution Lyman
a and Gravitational Lensing !
Waerbeke
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Power spectrum Baryon - Peak
galaxy correlation function
M.Tegmark
Structure formation One primordial
fluctuation- spectrum
SDSS
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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
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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
• M2.4410 27 eV
• 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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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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Evolution of cosmon field

• Field equations
• Potential V(f) determines details of the
  model
• V(f) M4 exp( - af/M )
• for increasing f the potential decreases
  towards zero !

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Cosmon

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

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Fundamental Interactions
Strong, electromagnetic, weak interactions
On astronomical length scales graviton cosm
on
gravitation
cosmodynamics
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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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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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exponential potentialconstant fraction in dark
energy
Oh 3/a2

• can explain order
• of magnitude
• of dark energy !

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effects of early dark energy

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

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observational bounds on Oh
G.Robbers , M.Doran ,
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realistic quintessence

• fraction in dark energy has to
• increase in recent time !

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Quintessence becomes important today
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coincidence problem

• What is responsible for increase of Oh for z lt 6 ?

Why now ?
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growing neutrinoquintessence
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growing neutrino mass triggers transition to
almost static dark energy
growing neutrino mass
L.Amendola, M.Baldi,
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effective cosmological triggerfor stop of cosmon
evolution neutrinos get non-relativistic

• this has happened recently !
• sets scales for dark energy !

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connection between dark energy and neutrino
properties
1.27
present dark energy density given by neutrino mass
present equation of state given by neutrino mass !
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cosmological selection

• present value of dark energy density set by
  cosmological event
• neutrinos become non relativistic
• not given by ground state properties !

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cosmon coupling to neutrinos
basic ingredient
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Cosmon coupling to neutrinos

• can be large !
• interesting effects for cosmology if neutrino
  mass is growing
• growing neutrinos can stop the evolution of the
  cosmon
• transition from early scaling solution to
  cosmological constant dominated cosmology

Fardon,Nelson,Weiner
L.Amendola,M.Baldi,
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dark energy fraction determined by neutrino mass
constant neutrino - cosmon coupling ß
variable neutrino - cosmon coupling
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cosmon evolution
stopped
scaling
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stopped scalar fieldmimicks acosmological
constant( almost )

• rough approximation for dark energy
• before redshift 5-6 scaling ( dynamical )
• after redshift 5-6 almost static
• ( cosmological constant )

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crossover to dark energy dominated universe
starts at time when neutrino force becomes
important for the evolution of the cosmon field
cosmological selection !
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growing neutrinos change cosmon evolution
modification of conservation equation for
neutrinos
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Hubble parameter
as compared to ?CDM
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Hubble parameter ( z lt zc )
only small difference from ?CDM !
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bounds on average neutrino mass
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Can time evolution of neutrino mass be observed ?

• Experimental determination of neutrino mass may
  turn out higher than upper bound in model for
  cosmological constant
• ( KATRIN, neutrino-less double beta decay )

GERDA
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neutrino fluctuations

• neutrino structures become nonlinear at z1 for
  supercluster scales
• stable neutrino-cosmon lumps exist

D.Mota , G.Robbers , V.Pettorino ,
N.Brouzakis , N.Tetradis ,
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Conclusions

• Cosmic event triggers qualitative change in
  evolution of cosmon
• Cosmon stops changing after neutrinos become
  non-relativistic
• Explains why now
• Cosmological selection
• Model can be distinguished from cosmological
  constant

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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 Matter
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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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primordial abundances for three GUT models
present observations 1s
He
D
Li
T.Dent, S.Stern,
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three GUT models

• unification scale Planck scale
• 1) All particle physics scales ?QCD
• 2) Fermi scale and fermion masses unification
  scale
• 3) Fermi scale varies more rapidly than ?QCD
• ?a/a 4 10-4 allowed for GUT 1 and 3 , larger
  for GUT 2
• ?ln(Mn/MP) 40 ?a/a 0.015 allowed

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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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Summary

• Oh 0.75
• Q/? dynamical und static dark energy will be
  distinguishable
• growing neutrino mass can explain why now
  problem
• Q time varying fundamental coupling
  constants
• violation of equivalence principle

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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)
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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 0.75
• Q/? dynamical und static dark energy will be
  distinguishable
• growing neutrino mass can explain why now
  problem
• Q time varying fundamental coupling
  constants
• violation of equivalence principle

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????????????????????????

• 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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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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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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oscillating neutrino mass
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neutrino fluctuations

• time when neutrinos become non relativistic
• sets free streaming scale
• neutrino structures become nonlinear at z1 for
  supercluster scales
• stable neutrino-cosmon lumps exist

D.Mota , G.Robbers , V.Pettorino ,
N.Brouzakis , N.Tetradis ,