Random Fields in Cosmology
The idea of the course
is to get familiar with the properties of the random
(mostly gaussian) fields in cosmological context. Random fields is fundamental
concept in many areas of cosmology - for example development
of the Large Scale Structure is understood in terms of evolution
of the random density field.
Rich statistical and structural properties of initial density field,
viewed as a random one, are directly responsible for many aspects of the
If you have any questions
e-mail me at
Here is the current list of problems suggested.
The due date is mid April.
Calculate and discuss \gamma, R_0, and R_* parameters for
- 3-dimensional Gaussian random density field with the spectrum P(k)=k^n,
- the corresponding to this density field of gravitational potential.
- For the density field compare results when the high-k smoothing is done
with different (commonly used) filters W(kRf), Rf is an (arbitrary) smoothing scale
- Sharp k-cutoff --- Ws(k Rf)=step_function[1-k Rf]
- "Top-hat" filter -- Wt(k Rf)=9 [Sin(k Rf)/(k Rf)-Cos(k Rf)]^2/(k Rf)^4
- Gaussian filter --- Wg(k Rf)=exp[-(k Rf)^2]
- In case some integrals do not formally converge, discuss how
they behave after artifical cutoff is imposed, and then taken away
- In discussion make connection between calculated parameters and overall
shape of a field.