cosmology zhaoming ma july 25, 2007. the standard model - not the one you’re thinking smooth,...
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![Page 1: Cosmology Zhaoming Ma July 25, 2007. The standard model - not the one you’re thinking Smooth, expanding universe (big bang). General relativity controls](https://reader030.vdocument.in/reader030/viewer/2022032704/56649d435503460f94a1fe5b/html5/thumbnails/1.jpg)
Cosmology
Zhaoming MaJuly 25, 2007
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The standard model - not the one you’re thinking
Smooth, expanding universe (big bang).
General relativity controls the dynamics (evolution).
The universe is homogenous and isotropic, on large scales at least (convenience/we know how to deal with).
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Supports to the standard model
Nucleosynthesis CMB Hubble diagram
distance
velocity
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Beyond the standard model - perturbations
Inflation
Baryon anddark matter
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Put them together
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Cosmological probes
NucleosynthesisCMBSupernovaWeak gravitational lensingGalaxy clusterBaryon acoustic oscillation
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Precision cosmology - where we stand
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Precision cosmology - the future
What is dark energy? Or do we need to modify gravity theory instead?
More and more supernova is and will be collected.
Deeper, wider and higher precision weak lensng surveys are planed.
Dedicated BAO surveys are in consideration.…
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Weak gravitational lensing
Ellipticity describe the shape of a galaxy.Shear if the unlensed galaxies are circular.Shear power spectrum constrains cosmology
iε2ii εγ ≈
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Weak lensing as cosmological probe
Shear power spectrum Matter power spectrum
Source galaxy distributionWeighting function
To constrain cosmology, we have to know this!
Kaiser 1998
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Photo-z parametrization
€
P(zp | zs) = Cii=1
nGauss
∑ 1
2πσ z;iexp −
(zp − zs − zbias;i)2
2σ z;i2
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
zs={2.6,2.7}
zs={0.5,0.6}
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Photo-z calibration
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Linear v.s. Nonlinear P(k)
nsuppressiogrowth
)()(
CDMfor
function growth
)1,(),()(
)(
)(),(),(
2
2
→
≡
∝→
=≡
=
+
+
+
+
aaD
aG
a
akakaDaDaD
akPakPini
iniLinLin
δδ
Theory: linear Data: nonlinear
Simulation
Higher orderpert. theory?
OR
Tegmark et al 2003
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Fitting formulas• Simulation is expensive,
so fitting formulas are developed.
• HKLM relation Hamilton et al 1991
Peacock & Dodds 1996
• Halo model
• Smith et al 2003 (10%) i) translinear regime: HKLM
ii) deep nonlinear regime: halo model fit
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Foundations of fitting formulas
• HKLM relation or Halo model.
• Nonlinear power is determined by linear power at the same epoch; history of linear power spectrum doesn’t matter.
Q: are these physically sound assumptions?
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Tools to test these assumptions
Use the public PM code developed by Anatoly Klypin & Jon Holtzman
Modified to take arbitrary initial input power spectrum
Modified to handle dark energy models with arbitrary equation of state w(z)
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The difference a spike makes
• Compare P(k) from simulations w/ and w/o a spike in the initial power
• Peak is smeared by nonlinear evolution
• More nonlinear power at all kNL with no k dependency
• HKLM scaling would predict the peak being mapped to a particular kNL
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Halo model prediction
x The peak is not smeared
The peak boosts power at all nonlinear scales
≈ Slight scale dependency
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Does P(k) depend on growth history?
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History does matter
• Linear part of the power spectra are consistent (by construction)
• Nonlinear power spectra differ by about 2% simply due to the differences in the linear growth histories
• This is not the maximum effect, but already at the level that future surveys care (1% Huterer et al 2005)
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Matching growth histories
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Same growth histories <==> same P(k)
• Linear part of the power spectra are consistent with the differences in the linear growth
• Nonlinear part of the power spectra are also consistent given the differences in the linear part
• Result validates the conventional wisdom that the same linear growth histories produce the same nonlinear power spectra