Cosmology

Zhaoming MaJuly 25, 2007

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).

Supports to the standard model

Nucleosynthesis CMB Hubble diagram

distance

velocity

Beyond the standard model - perturbations

Inflation

Baryon anddark matter

Put them together

Cosmological probes

NucleosynthesisCMBSupernovaWeak gravitational lensingGalaxy clusterBaryon acoustic oscillation

Precision cosmology - where we stand

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.…

Weak gravitational lensing

Ellipticity describe the shape of a galaxy.Shear if the unlensed galaxies are circular.Shear power spectrum constrains cosmology

iε2ii εγ ≈

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

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}

Photo-z calibration

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

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

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?

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)

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

Halo model prediction

x The peak is not smeared

The peak boosts power at all nonlinear scales

≈ Slight scale dependency

Does P(k) depend on growth history?

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)

Matching growth histories

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