can you show that the Wien displacement law for frequencies for a Planck-spectrum in $n$ dimensions is identical to the displacement law for wave lengths in $n+2$ dimensions?

# cosmology question of the week

CQW is an educational resource for theoretical astrophysics and cosmology. we post a new question every week for students to get and for teachers to stay in shape.

## Wednesday, April 16, 2014

## Wednesday, April 9, 2014

### braking by scattering

can you estimate the time-scale on which a cluster of galaxies slows down due to the kinetic Sunyaev-Zel'dovich effect? (PS: there's something remarkable about the solution if one assumes small velocities and if CQW didn't make a mistake)

## Wednesday, April 2, 2014

### Planck, Bose and Boltzmann

the Planck-spectrum is determined by the Bose-distribution for indistinguishable integer-spin particles and not by the Boltzmann-distribution for classical distinguishable particles. can you show that the difference between the Stefan-Boltzmann-laws derived with both distributions vanishes in the limit of many dimensions? can you show this mathematically and give an intuitive argument?

## Wednesday, March 26, 2014

### fundamentals of cosmology

can you give an intuitive explanation why one needs general relativity for describing the dynamics of the Universe?

## Wednesday, March 19, 2014

### fat Hubble sphere

the Hubble sphere is a spherical surface around an observer in a FLRW-universe at which the recession velocity becomes larger than the speed of light. at what scale factor are the recession velocities stationary?

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