Quintessence

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Quintessence Phenomenology
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How can quintessence be distinguished from a
cosmological constant ?
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Early dark energy
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predicted in models where dark energy is
naturally of the same order as matter
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Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
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Early dark energy

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

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Structure formation

• Structures in the Universe grow from tiny
• fluctuations in density distribution
• stars , galaxies, clusters
• One primordial fluctuation spectrum describes
• all correlation functions !

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Early quintessence slows down the growth of
structure
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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
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Fluctuation spectrum
Caldwell,Doran,Müller,Schäfer,
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normalization of matter fluctuations
rms density fluctuation averaged over 8h-1 Mpc
spheres
compare quintessence with cosmological constant
Doran, Schwindt,
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Early quintessence and growth of matter
fluctuations
early quintessence
for small Oh e/2 3/5
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for varying early dark energy weighted average
of O
influence of late evolution of quintessence
through conformal time t0 and averaged equation
of state
atr transition from slow early evolution of Oh
to more rapid late evolution
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at most a few percent dark energyin the early
universe !
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effect of early quintessence
presence of early dark energy decreases ? for
given t slower growth of perturbation
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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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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

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exact relation between whand change in Oh
eq
eq
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(
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Time dependence of dark energy
cosmological constant Oh t² (1z)-3
M.Doran,
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Quintessence becomes important today
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wh close to -1inferred from supernovae and WMAP
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Supernova cosmology
Riess et al. 2004
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Dark energy and SN

• OM 0.29
• 0.05-0.03
• (SN alone, for Otot1)

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SN and equation of state
Riess et al. 2004
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Supernova cosmology
Riess et al. 2004
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supernovae negative equation of state
andrecent increase in fraction of dark
energyare consistent !
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quintessence and CMB anisotropies

• influence by
• early dark energy
• present equation of state

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Anisotropy of cosmic background radiation
Caldwell,Doran,Müller,Schäfer,
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separation of peaks depends on dark energy at
last scattering
and on conformal time
involves the integral ( with weighted w )
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Peak location in quintessence models for fixed
cosmological parameters
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phenomenological parameterization of quintessence
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based on parameterization of O
natural time variable
use relation
( matter domination )
define
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three parameter family of models
fraction in matter OM present
equation of state w0 bending parameter
b
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relation of b to early dark energy
Taylor expansion
does nor make much sense for large z
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average equation of state
yields simple formula for H
simple relation with b
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equation of state changes between w0 and 0
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reconstruction of cosmon potential or kinetial
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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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for standard exponential potential
construction of kinetial from equation of state
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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

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end
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cosmological equations