Wednesday, June 26, 2013

CMB as an ideal black body

why is the cosmic microwave background such a perfect black body with a Planck-spectrum and why don't we see the recombination lines of the atomic levels?

maths bonus question: what's the reason why Christoffel symbols $\Gamma^{a}_{bc}$ are required to be symmetric in the lower indices?

Wednesday, June 19, 2013

CMB recombination

the CMB photosphere has a thickness of $\Delta z\simeq 100$ in redshift. how much time (in years) does it take for the atoms to recombine?

maths bonus: can you show that the Gauss-distribution is shape-invariant under convolution? what about the Cauchy-distribution?

Wednesday, June 12, 2013

bonus question: can you show that the determinant of a skew-symmetric matrix $A$, $A^t=-A$, is equal to zero if the dimension is odd?
if you observe a supernova at redshift $z=2$, does the lightcurve get time-dilated due to the Hubble expansion? if yes, by how much? at what redshift would you need to place a supernova if you want to stretch the lightcurve to last a year?
math bonus: just using a compass and a ruler, it is easily possible to construct $\sin(\alpha)$ and $\cos(\alpha)$ of an angle $\alpha$ (how?). can you construct $\sinh(\alpha)$ and $\cosh(\alpha)$ as well for arbitrary angles $\alpha$?