Wednesday, November 27, 2013

classical photons

the flux density of a blackbody would have form
S(\omega) \propto \omega^3\exp\left(-\frac{\hbar\omega}{k_BT}\right)
if the photons were classical distinguishable particles. can you derive Wien's displacement law and the Stefan-Boltzmann law and point out the differences to the Planck-spectrum?

Wednesday, November 20, 2013

radiation density

can you express the density parameter $\Omega_\gamma$ of a Planck-distributed relativistic species as a function of temperature only?

Wednesday, November 13, 2013

slow acoustic waves

the scale of baryon acoustic oscillation is set by the distance a sound wave can travel from the end of inflation until recombination. it is very important in this context that the sound wave is driven by photon pressure which makes the wave so fast. could you estimate the size of the BAO-scale if the acoustic wave traveled as a normal sound wave, i.e. driven by adiabatic compression of an ideal gas?

Wednesday, November 6, 2013

natural scale of the Universe

can you express the Universe's current

  • age $1/H_0$
  • size $c/H_0$
  • density $\rho_\mathrm{crit}=3H_0^2/(8\pi G)$ 
  • temperature 

in Planck-units?