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Quintessence from time evolution of fundamental mass scale

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New long - range interaction. cosmon mass changes with time ! for ... ii) equation of state wh(today) -1. B) Time variation of fundamental 'constants' ... – PowerPoint PPT presentation

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Title: Quintessence from time evolution of fundamental mass scale


1
Quintessence from time evolution of fundamental
mass scale
2
  • Om X 1
  • Om 30
  • Oh 70
  • Dark Energy

?
3
Quintessence
  • C.Wetterich

A.Hebecker,M.Doran,M.Lilley,J.Schwindt, C.Müller,G
.Schäfer,E.Thommes, R.Caldwell,M.Bartelmann
4
Dark Energy dominates the Universe
  • Energy - density in the Universe
  • Matter Dark Energy
  • 30 70

5
Matter Everything that clumps
Abell 2255 Cluster 300 Mpc
6
Om 0.3
gravitational lens , HST
7
Otot1
8
Dark Energy
  • Om X 1
  • Om 30
  • Oh 70 Dark Energy

h homogenous , often O? instead of Oh
9
Space between clumps is not empty Dark Energy
!
10
Dark Energy density isthe same at every point of
space homogeneous
11
Two important predictions
  • Structure formation One primordial
  • fluctuation- spectrum
  • The expansion of the Universe
  • accelerates today !

12
consistent cosmological model !
13
What is Dark Energy ? Cosmological Constant
or Quintessence ?
14
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 ?

15
Cosm. Const. Quintessence
static dynamical
16
Quintessence and solution of cosmological
constant problem should be related !
17
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
18
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 ?

19
Time dependent Dark Energy Quintessence
  • What changes in time ?
  • Only dimensionless ratios of mass scales
  • are observable !
  • V potential energy of scalar field or
    cosmological constant
  • V/M4 is observable
  • Imagine the Planck mass M increases

20
Quintessence from time evolution of fundamental
mass scale
21
Fundamental mass scale
  • Fixed parameter or dynamical scale ?
  • Dynamical scale Field
  • Dynamical scale compared to what ?
  • momentum versus mass
  • ( or other parameter with dimension )

22
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

23
Example Field ? denotes scale of
transition from higher dimensional physics to
effective four dimensional description in theory
without fundamental mass parameter (except for
running of dimensionless couplings)
24
Dilatation symmetry
  • Lagrange density
  • Dilatation symmetry for
  • Conformal symmetry for d0

25
Dilatation anomaly
  • Quantum fluctuations responsible for
  • dilatation anomaly
  • Running couplings hypothesis
  • Renormalization scale µ ( momentum scale )
  • ?(?/µ) A
  • E gt 0 crossover Quintessence

26
Dilatation anomaly and quantum fluctuations
  • Computation of running couplings ( beta functions
    ) needs unified theory !
  • Dominant contribution from modes with momenta ?
    !
  • No prejudice on natural value of anomalous
    dimension should be inferred from tiny
    contributions at QCD- momentum scale !

27
Cosmology
  • Cosmology ? increases with time !
  • ( due to coupling of ? to curvature scalar )
  • for large ? the ratio V/M4 decreases to zero
  • Effective cosmological constant vanishes
    asymptotically for large t !

28
Asymptotically vanishing effective cosmological
constant
  • Effective cosmological constant V/M4
  • ? (?/µ) A
  • V (?/µ) A ?4
  • M ?
  • V/M4 (?/µ) A

29
Weyl scaling
  • Weyl scaling gµ?? (M/?)2 gµ? ,
  • f/M ln (? 4/V(?))
  • Exponential potential V M4 exp(-f/M)
  • No additional constant !

30
Without dilatation anomaly V const.
Massless Goldstone boson dilaton Dilatation
anomaly V (f ) Scalar with tiny time dependent
mass cosmon
31
Crossover Quintessence

  • ( like QCD gauge coupling)
  • critical ? where d grows large
  • critical f where k grows large
    k²(f )d(?)/4
  • k²(f ) 1/(2E(fc f)/M)
  • if j c 276/M ( tuning ! )
  • This will be responsible for relative increase
    of dark energy in present cosmological epoch

32
Realistic cosmology
  • Hypothesis on running couplings
  • yields realistic cosmology
  • for suitable values of A , E , fc

33
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
34
Prediction homogeneous dark energyinfluences
recent cosmology- of same order as dark matter -
Original models do not fit the present
observations . Modifications ( i.e. E gt 0 )
35
Quintessence
Cosmon Field f(x,y,z,t)
  • 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 !

36
Fundamental Interactions
Strong, electromagnetic, weak interactions
On astronomical length scales graviton cosm
on
gravitation
cosmodynamics
37
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

38
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 -

39
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 !

40
Cosmon
  • Tiny mass
  • mc H
  • New long - range interaction

41
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 )

42
Realistic model Crossover Quintessence

  • ( like QCD gauge coupling)
  • critical ? where d grows large
  • critical f where k grows large
    k²(f )d(?)/4
  • k²(f ) 1/(2E(fc f)/M)
  • if j c 276/M ( tuning ! )
  • Relative increase of dark energy in
    present
  • cosmological epoch

43
Quintessence becomes important today
44
Equation of state
  • pT-V pressure
    kinetic energy
  • ?TV energy density
  • Equation of state
  • Depends on specific evolution of the scalar field

45
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
46
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

47
Quintessence becomes important today
No reason why w should be constant in time !
48
How can quintessence be distinguished from a
cosmological constant ?
49
Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
50
Measure Oh(z) !
51
Early dark energy
  • A few percent in the early Universe
  • Not possible for a cosmological constant

52
Early quintessence slows down the growth of
structure
53
A few percent Early Dark Energy
  • If linear power spectrum fixed today ( s8 )
  • More Structure at high z !

Bartelmann,Doran,
54
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

55
Quintessence and time variation of fundamental
constants
Strong, electromagnetic, weak interactions
Generic prediction Strength unknown
C.Wetterich , Nucl.Phys.B302,645(1988)
gravitation
cosmodynamics
56
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 !

57
Are fundamental constantstime dependent ?
  • Fine structure constant a (electric charge)
  • Ratio nucleon mass to Planck mass

58
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,
59
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.

60
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
61
In the hot plasma of the early Universe No
difference in mass for electron and myon !
62
(No Transcript)
63
Quintessence Couplings are still varying now
!Strong bounds on the variation of couplings
-interesting perspectives for observation !
64
Abundancies of primordial light elements from
nucleosynthesis
A.Coc
65
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,
66
Time variation of coupling constants
must be tiny would be of very high
significance ! Possible signal for
Quintessence
67
?a?ta ?e?
Everything is flowing
68
Summary
  • Oh 0.7
  • Q/? dynamical und static dark energy
  • will be distinguishable
  • Q time varying fundamental coupling
    constants
  • violation of equivalence principle

69
????????????????????????
  • 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 ?

70
End
71
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)
72
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

73
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 !
74
Differential acceleration ?
  • For unified theories ( GUT )

??a/2a
Q time dependence of other parameters
75
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
76
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
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