Wednesday, October 17, 2012

gravitational interaction of photons

why do gravitational interactions of (CMB) photons with the cosmic large-scale structure such as gravitational lensing or the integrated Sachs-Wolfe effect conserve the Planckian shape of the photon energy distribution?

bonus question: what's $\sum_{i=0}^n{n\choose i}$ with the binomial coefficient ${n\choose i}=n!/i!/(n-i)!$?


  1. let me add an impromptu bonus question: could you construct other spectra that would be conserved by the iSW-effect?

  2. bonus question: you can apply the general binomial formula in a funny way:
    \sum_{i=0}^n{n \choose i} = \sum_{i=0}^n{n \choose i} 1 \times 1 = \sum_{i=0}^n{n \choose i} 1^i 1^{n-i} = (1+1)^n = 2^n

    1. and of course you're welcome to use this result for next week's bonus question!

  3. i'm actually not quite sure as to why that is. my best guess would be the equivalence principle, because you can always get rid any gravitational effect by transforming into a free-falling frame. then, i'd say, one can use the fact that Planck-spectra are relativistically invariant.