Dark Energy: Theory vs. Observation

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Dark Energy Theory vs. Observation
http//helios.augustana.edu/physics/club/2005/dark
-energy.jpg
Holger Schlagenhaufer
23.01.2007
2
Overview

• general relativity gt standard cosmology
• current constraints
• theory
• observation methods

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FRW-Metric

• We take here natural units c h/(2?p) 1 and
  for the metric signature
• (-,,,).
• Assumptions for the space-time
• homogeneity on large scales
• isotropy on large scales
• Both assumptions are verified from observations
  from the Cosmic Microwave
• Background.
• Taking this assumptions leads to the
  Friedmann-Roberston-Walker metric

with
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Evolution Equations

• To obtain a evolution equation for the scale
  factor, you have to solve
• the Einstein Equation with the FRW-Metric.
• This leads to the following two independent
  equations
• 
  (1)
• 
  (2)
• H Hubble Parameter
• Hubble Parameter today H0728 km/s 1/Mpc
• Pressure and energy density p and ? contain all
  mater parts contributing to the
• energy momentum tensor.

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Evolution Equations

• Bianchi identity leads to the continuity equation
• This equation can be obtained from (1) and (2).
• Special cases
• Every fluid can be described with these formulas,
  especially for wp/?, k0 and ?0. We get
• Let us consider a static dust dominated universe
  gt p0 and we get
• In this case ? gt 0 and thus ? gt 0 and
  consequently k 1 but SN Ia and
• CMB observations give a nearly flat universe.

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Current Constraints

• Age of the universe
• Wilkilson-Micorwave-Anisotropy-Probe 3 year data
  (WMAP3) Gyr
• CMB
• We get O0 1, O? 0.7 and Om 0.3
• Supernova Ia
• We get for the crossover from deceleration to
  acceleration zC 0.67
• CMB SNe LSS combination
• We get from this combination for the equation of
  state parameter for the dark energy

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Current Constraints
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Theoretical Explanations

• There are three widespread theoretical
  explanations for an accelerated
• universe.
• Cosmological Constant ?
• - equation of state w -1
• - no dynamic evolution
• Dark Energy models with scalar fields so called
  Quintessence model
• - minimal coupled to gravitation
• - new particles 1035 lighter than electron gt
  new long range force
• - dynamic equation of state
• - equation of state parameter can vary from
• Modifications of General Relativity
• - nonlinear terms in the curvature terms
  (Plantini formalism)
• - higher dimensional corrections to gravitation
  (DGP model)

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Future Observations

• There are four favoured observational techniques
  to constraint Dark Energy
• (DE). We choose the following parameterization
  w(a) w0 (1 - a) wa, but
• only valid if dark energy is prominent at late
  times and negligible at early times.
• Baryonic Acoustic Oscillations (BAOs)
• Galaxy Clusters (GC)
• Supernova Ia (SN Ia)
• Weak Lensing (WL)

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Baryonic Acoustic Oscillations

• At the end of inflation the universe is filled
  with ionized gas.
• Baryonic matter and radiation are coupled. Dark
  matter only interacts gravitationally.
• From any initial density fluctuation a
  perturbation propagates spherical with the speed
  of sound cs c/v3.
• The pressure waves propagate until recombination
  then photons and baryonic matter decouple.
• The total propagation distance is called sound
  horizon rs1483 Mpc which serves as a standard
  ruler.
• We can see the BAOs in the wiggles of the CMB
  from z 1100 and the physic of the BAOs is well
  understood.

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Baryonic Acoustic Oscillations

• Dark energy observables are
• angular diameter distance dA(z) (geometry)
• with k 0 (flat universe) we get for the
  angular diameter distance
• For a given cosmological model we can constrain
  the equation of state parameter with the chosen
  parameterization.

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Baryonic Acoustic Oscillations

• Hubble Parameter H(z)
• from the Friedmann equation and
  we get with the
• assumption of a time-independent vacuum density
• or for a variable w(a) we get

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Baryonic Acoustic Oscillations
Françoise Combes, SKA-PNC, 27 Octobre 2006
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Baryonic Acoustic Oscillations

• BAOs use the standard ruler method.
• Distances deduced from redshift surveys in h-1
  Mpc thus the main length from large scale
  structure is D Om? h-1 Mpc.
• This technique has the least systematic
  uncertainties but possible in the theory of
  non-linear evolution and galaxy biasing.
• It is possible to detect galaxy distributions and
  thereby BAOs in the optical, NIR and with the 21
  cm emission or to measure the distribution of
  neutral hydrogen at z gt 5.
• This model is not sensitive to the chosen
  parameterization for a ?CDM model because of the
  measurements made at z gt 1 where dark energy is
  relatively unimportant.

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Baryonic Acoustic Oscillations
REPORT OF THE - DARK ENERGY TASK FORCE

• First detection of BAOs outside the CMB are from
  the Sloan Digital Sky Survey (SDSS). A peak was
  found around 100 h-1 Mpc separation with
• h H0/(100 km/s 1/Mpc).

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Galaxy Clusters

• Galaxy clusters are the biggest known structures
  which undergoes
• gravitational collapse. They are also markers for
  the highest energy
• density fluctuations in the early universe.
• Features of galaxy clusters
• mass 1014 1015 Msun
• mass luminosity relation M/L 100 .. 500
  Msun/Lsun
• X-ray from thermal emission from hot gas 107
  108 K
• gas density 102 103 m-3
• Sunyaev-Zeldovich effect CMB photons scatter on
  an electron of the hot gas in the galaxy cluster.
  Through the inverse Compton effect the CMB
  photons get energy from the electrons. This leads
  to an increase in the frequency of these photons
  and to less temperature of the CMB in the centre
  of the galaxy cluster.
• Largest viralized dark matter objects. The
  overall dynamics is dominated by dark matter but
  astrophysical processes taking place in galaxies
  have sizeable effect on the observables.

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Galaxy Clusters

• Dark energy observables are
• structure growth history g(z)
• growth of structure is described by
• with
• for ? 0 we get the Jeans wavelength
• where ?m is the homogenous isotropic time
  independent background

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Galaxy Clusters

• number counts
• with
• where dn/dM is the mass function which is
  determined from N-body simulations and is given
  by

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Galaxy Clusters

• observables can be measured through
• Sunyaev-Zeldovich Flux decrement seen as a
  shadow on the CMB background
• X-ray temperature and surface brightness through
  emission of hot gas
• good tracer for gravitational potential and thus
  for the mass of the cluster. This is the most
  efficient method today.
• The accuracy depends on
• S/N of the data
• spatial resolution of the temperature
• spatial extent of the X-ray gas
• optical by detection of their member galaxies
  with high velocity dispersions mark the galaxy
  cluster
• problems foreground and background galaxies
• weak lensing effect on the background galaxies
• none of first three of these methods can detect
  the mass of the galaxy clusters directly gt
  greatest systematic errors of these methods

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Galaxy Clusters

• systematic errors
• cluster mass uncertainties (no defined edge,
  active galaxy nuclei heating the intergalactic
  gas by missing cooling flow)
• cluster sample completeness and contamination
  (understood in X-ray)
• theoretical uncertainties (nonrelaxed and merging
  clusters must be more studied)
• redshift accuracy
• Evolution of the mass function is governed by the
  growth of structure and therefore sensitive to
  the density parameters and the equation of state
  of dark energy.

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Galaxy Clusters
http//cosmology.uiuc.edu/jmohr/Homepage/Research
/Harvard-Bok'02/Harvard'02.pdf
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Supernova Ia

• Binary system with different star mass.
• High mass star develops faster than the low mass
  star.
• If the high mass star is between 0.5 Msun lt
  Mstar lt 2.5 Msun it will become a white dwarf.
• The low mass star develops to a red giant and
  through the Roche lobe the white dwarf accretes
  mass from the red giant.
• A runaway fusion is triggered when the white
  dwarf has reached the Chandrasekar mass limit at
  1.4 Msun.
• The released energy in the runaway fusion let the
  white dwarf explode.
• This event is supposed the same for all of these
  types of Supernova.

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Supernova Ia
Lecture notes of Einführung in die Astronomie
und Astrophysik I II from Prof. Dr. Bender
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Supernova Ia
Lecture notes of Einführung in die Astronomie
und Astrophysik I II from Prof. Dr. Bender
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Supernova Ia

• dark energy observable is the luminosity distance
  dL defined by
• with k 0 (flat universe) we get for the
  luminosity distance
• For a given cosmological model we can constrain
  the equation of state parameter with the chosen
  parameterization.

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Supernova Ia

• main systematic errors
• unknown cause of the SN Ia variety (different
  peak luminosities, dispersion of 0.12 0.15 in
  magnitude) leads to a wrong redshift
• possible evolution of the SN Ia
• progenitor mass
• metallicity (C-O)
• radiation transport (explosion physics)
• change of explosion, peak luminosity is related
  to the produced Nickel during the explosion, this
  leads a typical decay
• gt exponential decay because released energy
  dN/dt
• gt dMabs/dt 1.086?(ln2)/t½
• extinction in the host galaxy
• intergalactic extinction
• K-corrections (emission is observed at a
  different wavelength from the one that at which
  it was emitted - due to the cosmological redshift)

leads to wrong redshift and therefore to a wrong
luminosity distance
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Supernova Ia

• Peak luminosity is equal for all Supernova Ia M
  -19.09 for the absolute magnitude. We get the
  luminosity distance dL from
• geometric probe of the expansion of the universe
• most direct evidence for accelerated expansion
• most accurate measurements of the Hubble
  parameter
• to standardize the SN Ia 500 near SNe up to z
  0.025 were measured
• To see a dynamical equation of state parameter SN
  Ia from z gt 1 must be measured accurately.
• Today equation of state parameter w can be
  determined better than 10 but it is needed to be
  under 2.

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Supernova Ia
http//www.astro.ucla.edu/wright/sne_cosmology.ht
ml
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Weak Lensing

• Light propagates unperturbated through
  space-time.
• Light is deflected near a mass density.
• We can derivate the deflection angle for b gtgt rS
• from the equation of motion for a photon in the
  Schwarzschild-metric.
• We get
• After the perturbation through the mass density
  the light propagates again unperturbated through
  space-time.

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Weak Lensing
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Weak Lensing

• dark energy observables
• angular diameter distance dA (geometry of the
  universe)
• growth rate of structure g(z)
• byproducts of WL
• galaxy galaxy lensing (matter of dark halo)
• shear selected galaxy cluster counts
• baryonic acoustic oscillations with photometric
  redshift measurements
• Today w is determined with a 50 accuracy assumed
  to be constant.
• In the future it should be possible to get w0
  with 5-10 accuracy and wa with 1-5 accuracy.
• WL has the potential to get the best method to
  constraint dark energy.

shown above
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Weak Lensing

• There are three major types of bias
• PSF correction
• most challenging technical issue
• isotropic smearing
• (multiplicative bias gt dominant source of
  error)
• PSF anisotropy corrections
• (additive bias)
• no reliable information possible without exact
  known redshift
• intrinsic distortion signal
• tidal interactions between close physical pairs
• dark halo compression
• angular momentum transfer
• overlapping galaxies (leads to wrong galaxy
  shapes)
• gt close physical pairs must be down weighted to
  get a correct weak lensing signal and therefore z
  must be known very accurate

bias the amplitude of the lensing signal
during interaction will modify the galaxy shapes
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Literature

• Dynamics of Dark Energy, Edmund J. Copeland, M.
  Sami, Shinji Tsujikawa
• Report of the dark energy task force, Andreas
  Albrecht et. al.
• arXivastro-ph/0610906 v1
• http//cosmology.uiuc.edu/jmohr/Homepage/Research
  /Paris02/Lecture1.pdf
• Lecture notes of Einführung in die Astronomie
  und Astrophysik I II
• from Prof. Dr. Bender