DEK

1
Quintessence- a dynamical Dark Energy
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
Otot1
9
Dark Energy

• Om X 1
• Om 30
• Oh 70 Dark Energy

h homogenous , often O? instead of Oh
10
Space between clumps is not empty Dark Energy
!
11
Dark Energy density isthe same at every point of
space homogeneous No force In what
direction should it draw ?
12
Two important predictions

• Structure formation One primordial
• fluctuation- spectrum

• The expansion of the Universe
• accelerates today !

13
Baryon - Peak
SDSS
galaxy correlation function
14
consistent cosmological model !
15
Composition of the Universe

• Ob 0.045 visible clumping
• Odm 0.22 invisible clumping
• Oh 0.73 invisible homogeneous

16
Dark Energy- a cosmic mystery
Dunkle Energie Ein kosmisches Raetsel
17
What is Dark Energy ? Cosmological Constant
or Quintessence ?
18
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 ?

19
Cosm. Const. Quintessence
static dynamical
20
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
21
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?

22
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
23
Prediction homogeneous dark energyinfluences
recent cosmology- of same order as dark matter -
Original models do not fit the present
observations . modifications
24
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 !

25
Fundamental Interactions
Strong, electromagnetic, weak interactions
On astronomical length scales graviton cosm
on
gravitation
cosmodynamics
26
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 !

27
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 !
  

28
Cosmon

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

29
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

30
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 )

31
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 -
  

32
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 !

33
kinetial

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

34
cosmological equations
35
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
36
Quintessence becomes important today
37
Equation of state

• pT-V pressure
  kinetic energy
• ?TV energy density
• Equation of state
• Depends on specific evolution of the scalar field

38
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
39
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

40
Quintessence becomes important today
No reason why w should be constant in time !
41
How can quintessence be distinguished from a
cosmological constant ?
42
Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
43
Measure Oh(z) !
44
Early dark energy

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

45
Early quintessence slows down the growth of
structure
46
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
47
A few percent Early Dark Energy

• If linear power spectrum fixed today ( s8 )
• More Structure at high z !

Bartelmann,Doran,
48
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

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
(No Transcript)
57
Quintessence Couplings are still varying now
!Strong bounds on the variation of couplings
-interesting perspectives for observation !
58
Abundancies of primordial light elements from
nucleosynthesis
A.Coc
59
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,
60
Time variation of coupling constants
must be tiny would be of very high
significance ! Possible signal for
Quintessence
61
?a?ta ?e?
Everything is flowing
62
Summary

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

63
Quintessence and solution of cosmological
constant problem should be related !
64
????????????????????????

• 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 ?

65
End
66
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)
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
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 !
69
Differential acceleration ?

• For unified theories ( GUT )

??a/2a
Q time dependence of other parameters
70
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 by MICROSCOPE
71
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