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Quintessence from time evolution of fundamental mass scale

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k(f=0)/ k(ftoday) : not tiny or huge ! - else: explanation needed - More models ... Warning : not scale - free ! Dilatation anomaly replaced by explicit ... – 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
Quintessence and solution of cosmological
constant problem should be related !
3
  • Om X 1
  • Om 25
  • Oh 75
  • Dark Energy

?
4
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

5
Fundamental mass scale
  • Unification fixes parameters with dimensions
  • Special relativity c
  • Quantum theory h
  • Unification with gravity
  • fundamental mass scale
  • ( Planck mass , string tension , )

6
Fundamental mass scale
  • Fixed parameter or dynamical scale ?
  • Dynamical scale Field
  • Dynamical scale compared to what ?
  • momentum versus mass
  • ( or other parameter with dimension )

7
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

8
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)
9
Dilatation symmetry
  • Lagrange density
  • Dilatation symmetry for
  • Conformal symmetry for d0

10
Dilatation anomaly
  • Quantum fluctuations responsible for
  • dilatation anomaly
  • Running couplings hypothesis
  • Renormalization scale µ ( momentum scale )
  • ?(?/µ) A
  • E gt 0 crossover Quintessence

11
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 !

12
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 !

13
Asymptotically vanishing effective cosmological
constant
  • Effective cosmological constant V/M4
  • ? (?/µ) A
  • V (?/µ) A ?4
  • M ?
  • V/M4 (?/µ) A

14
Weyl scaling
  • Weyl scaling gµ?? (M/?)2 gµ? ,
  • f/M ln (? 4/V(?))
  • Exponential potential V M4 exp(-f/M)
  • No additional constant !

15
Without dilatation anomaly V const.
Massless Goldstone boson dilaton Dilatation
anomaly V (f ) Scalar with tiny time dependent
mass cosmon
16
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

17
Realistic cosmology
  • Hypothesis on running couplings
  • yields realistic cosmology
  • for suitable values of A , E , fc

18
Quintessence cosmology- models -
19
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

20
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 -

21
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 !

22
kinetial
  • Small almost constant k
  • Small almost constant Oh
  • Large k
  • Cosmon dominated universe ( like inflation )

23
Cosmon
  • Tiny mass
  • mc H
  • New long - range interaction

24
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 )

25
Quintessence becomes important today
26
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

27
crossover quintessence
k(f) increase strongly for f corresponding to
present epoch
Example (LKT)
exponential quintessence
28
Why has quintessence become important now ?
29
coincidence problem
  • What is responsible for increase of Oh for z lt 10
    ?

30
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

31
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 )

32
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

33
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

34
Back-reaction effect
  • Needs large inhomogeneities after structure has
    been formed
  • Local cosmon field participates in structure

35
End
36
Quintessence from higher dimensions
work with J. Schwindt hep-th/0501049
37
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 !

38
Quintessence from higher dimensions
  • An instructive example
  • Einstein Maxwell theory in six dimensions

Warning not scale - free ! Dilatation anomaly
replaced by explicit mass scales.
39
Field equations
40
Energy momentum tensor
41
Metric
  • Ansatz with particular metric ( not most general
    ! )
  • which is consistent with
  • d4 homogeneous and isotropic Universe
  • and internal U(1) x Z2 isometry

B ? 1 football shaped internal geometry
42
Exact solution
m monopole number ( integer)
cosmology with scalar
and potential V
43
Free integration constants
M , B , F(t0) , (dF/dt)(t0) continuous m
discrete
44
Conical singularities
  • deficit angle
  • singularities can be included with
  • energy momentum tensor on brane
  • bulk point of view describe everything in terms
    of bulk geometry ( no modes on brane without tail
    in bulk )

45
Asymptotic solution for large t
46
Naturalness
  • No tuning of parameters or integration constants
  • Radiation and matter can be implemented
  • Asymptotic solution depends on details of model,
    e.g. solutions with constant Oh ? 1

47
problem time variation of fundamental constants
48
Dimensional reduction
49
Time dependent gauge coupling
50
????????????????????????
  • 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 ?

51
Cosmon dark matter ?
  • Can cosmon fluctuations account for dark matter ?
  • Cosmon can vary in space

52
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