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Cosmology. Zhaoming Ma July 25, 2007. The standard model - not the one you’re thinking. Smooth, expanding universe (big bang). General relativity controls the dynamics (evolution).

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Zhaoming Ma

July 25, 2007

the standard model not the one you re thinking
The standard model - not the one you’re thinking
  • Smooth, expanding universe (big bang).
  • General relativitycontrols 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
Supports to the standard model




Hubble diagram


beyond the standard model perturbations
Beyond the standard model -perturbations


Baryon and

dark matter

cosmological probes
Cosmological probes
  • Nucleosynthesis
  • CMB
  • Supernova
  • Weak gravitational lensing
  • Galaxy cluster
  • Baryon acoustic oscillation
precision cosmology the future
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
Weak gravitational lensing
  • Ellipticity describe the shape of a galaxy.
  • Shear if the unlensed galaxies are circular.
  • Shear power spectrum constrains cosmology
weak lensing as cosmological probe
Weak lensing as cosmological probe

Shear power spectrum

Matter power spectrum

Weighting function

Source galaxy distribution

To constrain cosmology, we have to know this!

Kaiser 1998

photo z parametrization
Photo-z parametrization



linear v s nonlinear p k
Linearv.s.Nonlinear P(k)





Higher order

pert. theory?

Tegmark et al 2003

fitting formulas
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
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
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
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
Halo model prediction
  • The peak is not smeared
  • The peak boosts power at all nonlinear scales
  • Slight scale dependency
history does matter
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)
same growth histories same p k
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