1. Cosmology Zhaoming Ma July 25, 2007

2. 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).

3. Supports to the standard model Nucleosynthesis CMBHubble diagram distance velocity

4. Beyond the standard model - perturbations Inflation Baryon and dark matter

5. Put them together

6. Cosmological probes  Nucleosynthesis  CMB  Supernova  Weak gravitational lensing  Galaxy cluster  Baryon acoustic oscillation

7. Precision cosmology - where we stand

8. 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.  …

9. Weak gravitational lensing  Ellipticity describe the shape of a galaxy.  Shear if the unlensed galaxies are circular.  Shear power spectrum constrains cosmology

10. Weak lensing as cosmological probe Shear power spectrumMatter power spectrum Source galaxy distributionWeighting function To constrain cosmology, we have to know this! Kaiser 1998

11. Photo-z parametrization z s ={2.6,2.7} z s ={0.5,0.6}

12. Photo-z calibration

13. Linear v.s. Nonlinear P(k) Theory: linear Data: nonlinear Simulation Higher order pert. theory? OR Tegmark et al 2003

14. 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

15. 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?

16. 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)

17. 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 k NL with no k dependency HKLM scaling would predict the peak being mapped to a particular k NL

18. Halo model prediction xThe peak is not smeared The peak boosts power at all nonlinear scales ≈Slight scale dependency

19. Does P(k) depend on growth history?

20. 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)

21. Matching growth histories

22. 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