Aquila

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Quintessence
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
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What is our Universemade of ?
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Quintessence !
fire , air, water, soil !
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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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Composition of the universe

• Ob 0.045
• Odm 0.225
• Oh 0.73

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gravitational lens , 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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Wilkinson Microwave Anisotropy Probe
A partnership between NASA/GSFC and Princeton
Science Team
NASA/GSFC Chuck Bennett (PI) Michael Greason Bob
Hill Gary Hinshaw Al Kogut Michele Limon Nils
Odegard Janet Weiland Ed Wollack
Brown Greg Tucker
UCLA Ned Wright
Princeton Chris Barnes Norm Jarosik Eiichiro
Komatsu Michael Nolta
Chicago Stephan Meyer
UBC Mark Halpern
Lyman Page Hiranya Peiris David Spergel Licia
Verde
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mean values Otot 1.02 Om 0.27 Ob
0.045 Odm 0.225
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Otot1
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Dark Energy

• Om X 1
• Om 30
• Oh 70 Dark Energy

h homogenous , often O? instead of Oh
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Dark Energy homogeneously distributed
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Dark Energy prediction The
expansion of the Universe
accelerates today !
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Supernova cosmology
Riess et al. 2004
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Structure formation fluctuation spectrum
CMB agrees with galaxy distribution Lyman a
forest and gravitational lensing effect !
Waerbeke
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consistent cosmological model !
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Composition of the Universe

• Ob 0.045 visible clumping
• Odm 0.225 invisible clumping
• Oh 0.73 invisible homogeneous

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What is Dark Energy ? Cosmological Constant
or Quintessence ?
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Dynamics of Dark Energy
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Cosmological Constant

• 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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? ? 0
( ? ?)
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asymptotic solution for cosmological constant
(k0)
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problems with small ?

• no symmetry explanation for ?/M4 10 -120
• quantum fluctuations contribute

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Anthropic principle
Banks Weinberg Linde
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Cosmological Constant

• 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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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
• 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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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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Cosmological equations
matter


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Cosmological equations
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asymptotic solution for large time
M ? M
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exponential potentialconstant fraction in dark
energy
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General mechanism for cosmic attractor
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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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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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many models
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kinetial
choose field variable such that potential has
standard units advantage f acts as dark energy
clock in cosmology
M1
A.Hebecker,
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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

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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) not tiny or huge !
• - else explanation needed -
  

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crossover quintessence
k(f) increase strongly for f corresponding to
present epoch
example
exponential quintessence
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Quintessence becomes important today
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scale factor as time-variable
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determine kinetial k(f)by observation !
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end
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cosmological equations