Dynamic dark energystep beyond CDM

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Dynamic dark energystep beyond ?CDM

• Zhiqi Huang, Dick Bond, Lev kofman

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Introduction Dark Energy EOS

• Dark Energy Equation of state (pressure to
  density ratio)

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Introduction DE EOS

• wconst. ? static DE model (special case w -1?
  ?CDM)
• w varies with redshift z? dynamic DE model.

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Introduction Reconstructing Dark Energy EOS

• Two approaches to reconstruct w(z)
• 1. Top-down approach
• theory? w(z) ? observation
• 2. Bottom-up approach
• observation ? w(z) ? theory

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Introduction Reconstructing Dark Energy EOS

• Observations that can be used
• 1. SN Ia (SNLS, SNAP)
• 2. CMB (WMAP, PLANK)
• 3. Cluster/Galaxy Survey (SDSS, 2dFGRS)
• 4. Weak Lensing
• 5. Baryon Acoustic Oscillation
• 6. Others (ISW effect, long GRB )

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Introduction parameterize w(z)

• Constraints on w(z) depend on parametrizations
  (Upadhye et al, 2005).
• Current and near future data can not constrain
  more than two parameters. (Linder 2005)
• So
• w w0 wa(1-a)
• or
• w w0 w1 z ?

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A generic description

• W w (z) w is an arbitrary function ?
  uncountable number of parameters.
• Parametrization taking a subset of W (i.e. a
  bunch of trajectories) as a prior.
• Question why do we take
• w(z) w(z)w0w1z or
• w(a) w(a)w0wa(1-a) but not
  others?

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Current status

• ?CDM (w-1)
• far from being ruled out in the w0, w1 framework.

losing a lot of information
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The first step of first step
Do we need dynamic DE?
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Maximally extract the information of dynamic DE

• dynamic information in data
• dynamic information of w(z) (if exists)
• observation errors (always exists)
• Idea maximally separate the two.

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How to maximally extract the information of
dynamic DE

• The dynamics depends on the integral of w over
  lna
• Fast oscillating terms in w(x) does not
  contribute.
• x defined as x -ln a ln (1z).
• Fourier transformation w(x)?w(k)
• w(k) of large k does not contribute.

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Uncountable?Countable
We have information about w(x) at 0ltxltxlss, where
xlssln(1zlss) 7. Mathematically extend to -8 lt
x lt 8 w(-x)w(x) w(xxlss)w(x-xlss) P
eriodic function, can be written w(x)w0
w1coskx w2cos2kx w3cos3kx w4cos4kx
where kp/xlss.
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Infinite to finite

• dynamics of w(z)?dynamics of universe?observation
  data
• in this process, the information of wn of
  large n is lost.
• observation error in CMB and BAO (single
  redshift measurement)? an error of integral of
  w(x)? effectively a shift of w0
• observation error in SNIa (multiple redshift
  measurements)? effectively fast oscillation of
  w(x)? wn of large n.

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Infinite?finite

• It is possible to find a cutoff N, so that
  w0,w1,w2,,wN contain most of the information of
  dynamics of w(z), but information of observation
  noise is mostly contained in w0 and wN1,wN2,
• But how to find N?

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WCDM package

• WCDM package MCMC algorithm (available at
  http//www.astro.utoronto.ca/zqhuang/academic)
• Use the likelihood in literature (Wang et al,
  2006)
• 157 gold SN WMAP3BAO2dF
• Trajectory pool
• PNw w(x)w0 w1coskx w2cos2kx w3cos3kx
  w4cos4kx wNcosNkx, -1 w(x)1

Physical constraint
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Reconstructed model

• RNw w?PN , L(w)gtL(?CDM) where L is the
  likelihood. This is a continuous subset of PN.
• If P(RN PN) gt95 (i.e. if ?CDM is out of 95
  contour) , can we say an epoch of dynamic dark
  energy is coming?

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Some quantities we are interested in

• P(RN PN)
• BE(RN) Bayesian Evidence of the reconstructed
  model RN.
• BE(PN ) Bayesian Evidence of the trajectory
  pool PN.
• All these quantities depend on the cutoff N.

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SNIaWMAP3SDSS2dF
Peaks at roughly the same N
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BE(PN) ?

• Hard to calculate using MCMC algorithm
• Decrease as N increases (penalty for introducing
  more parameters), soon approach zero for large N.

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wavespace parametrization

• Take the best cutoff N that maximize P(RN PN)
  and BE(RN)
• w(x)w0 w1coskx w2cos2kx w3cos3kx
  w4cos4kx wNcosNkx
• where xln(1z)

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Better than w(a)w0wa(1-a)

• Comparing our parametrization with
  w(a)w0wa(1-a)
• No difference for present data. ?CDM has high
  Bayesian Evidence and is far from being ruled out
  .
• They are different for the next generation data.

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A fiducial dynamic DE model

• w(z)

-1, if zlt0.5 -0.8, if z0.5

next generation data SNAP, PLANK ?simulation
data
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Applying parametrizations to the simulation data
(BEBayesian Evidence)