Integrated Sachs-Wolfe Effect

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Integrated Sachs-Wolfe EffectDark Energy

• Tommaso Giannantonio
• ICG, University of Portsmouth

In collaboration with Asantha Cooray, Pier-Stefan
o Corasaniti Alessandro Melchiorri
Paris, 7 dec 2005
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Introduction to Dark Energy
Perlmutter et al. 99
Spergel et al. 03

• General Relatvity
• High-z supernovae
• Cosmic microwave background anisotropies (WMAP)
• All together they give

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The Dark Energy

• Strongly supported (even by universe's age)
• Difficult to understand with standard physics
• Different models, different equation of state
• Different sound speed
• This is related with clustering via Jeans
  length

• Quintessence
• Chaplygin gas

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CMB perturbations
WMAP data

• Perturbations exists in a proportion of 10-5
• Primary and secondary perturbations
• Perturbative metric variables

neutral H
e-
Free propagation
Compton scattering
but gravitational interactions!
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Sachs-Wolfe effects
T
r

• Unintegrated SW
• Integrated SW
• No effect in matter epoch (
  )
• Early ISW in radiation epoch
• Late ISW in DE epoch

Sachs Wolfe, 67
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Early late ISW
Total spectrum
Early ISW
Late ISW
The peak position corresponds to the horizons
size at the epoch of origin
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What we can measure

• The multipole momenta
• They are strongly dependent on DE features
• But the ISW is only 10 of the total!
• Cosmic variance problem

LCDM
LCDM, no ISW
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The cross-correlation
WMAP SDSS

• Late ISW is coupled with matter distribution
• Primary anisotropies are not
• Cross-correlation CMB-matter can extract the late
  ISW Crittenden, Turok 95
• The bias must be estimated
• depends mostly on the survey
• on , ,

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Dependence on w (cs21)

• If the effect decreases due to loss of
  DE
• As well if the dark energy becomes
  important in more recent times, giving a smaller
  effect

Matter visibility function gaussian, ltzgt 0.5
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Dependence on w (cs20)

• As before if
• Conversely, if the clustering effect
  causes ulterior growth

Matter visibility function gaussian, ltzgt 0.5
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Dependence on ltzgt

• A higher z means older times, and so less DE and
  smaller horizon (bigger l)
• A lower z means more DE, but a bigger horizon
  (smaller l)
• The correlation is best observed at intermediate z

Matter visibility function gaussian
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Experimental correlations
Survey band ltzgt Correlation authors
2MASS IR 0.1 Afshordi et al. 04
APM vis 0.15 Fosalba, Gaztañaga 04
SDSS vis 0.3 0.5 Fosalba, Gaztañaga 03
SDSS vis 0.3 0.5 Scranton et al. 03
NVSS radio 0.9 Boughn, Crittenden 04
HEAO X 0.9 Boughn, Crittenden 04

Fosalba, Gaztañaga 04
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Theory and practice
The five experimental correlations at peak in
function of ltzgt Fosalba, Gaztañaga 04
w-0.8
w-0.4
w-4
The cross-correlation amplitude at the peak
in function of ltzgt, w and cs2
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Likelihood analysis
Corasaniti, TG, Melchiorri 04

• The likelihood function is defined and plotted

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Results Corasaniti, TG, Melchiorri 04

• For cs2 1 we have a degeneracy that is
  orthogonal to the Snae Ia one.
• Constraints on w
• -1.51 lt w lt -0.72, if cs2 0
• -1.81 lt w lt -0.53, if cs2 1
• _at_ 95 c. l.
• No valid constraints on cs2

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Discussion

• Results are similar to previous, but obtained in
  an independent way Bean Doré 04 Weller
  Lewis 03
• Not dependent on many parameters
• Only 5 points possible improvements in future
  (LSST, KAOS, ALPACA PLANCK)

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Tensor modes of perturbations

• Can be originated by inflation
• We can study their evolution separately in linear
  regime
• The Einstein equation is
• Freely propagating until horizon entering
  , after damped
• At recombination ( ), only large
  scale modes survive
• G waves they cant produce structures

Tensor perturbed FRW metric
Perfect fluid appr. Relativistic particle
damping term
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Limit on tensor amplitude

• Commonly measured with
• CMB TT, matter or polarization (search for B
  modes)
• New method
• CMB anisotropies amplitude is
• ISW-gal cross-correlation amplitude is
• (because clustered structures arise from
  scalar fuctuations)
• We can constrain r assuming a model (flat ?CDM).

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Results
Seljak et al. 04

• Bias estimation introduce an extra 20 error
  (only linear dependence)
• DE dependent
• Small O? gives small ISW, so less r allowed
• (in fact to increase r one must increase O?)
• r lt 0.5 _at_ 95 c. l.
• From WMAP alone r lt 0.9

Cooray, Corasaniti, TG, Melchiorri 05
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How can it be improved?

• At large scale
• If we know all parameters with only cosmic
  variance error, we have
• This can be slightly improved considering
  cross-correlation to extract ISW to