Wednesday, November 28, 2012

Hubble expansion and superluminality

why do we observe light from galaxies if their recession velocity exceeds the speed of light? at what redshift in a $\Lambda$CDM cosmology would a galaxy move as fast as light? why isn't that a problem with special relativity?

bonus question: can you show the property $\Gamma(x+1) = x\Gamma(x)$ of the $\Gamma$-function which is defined by $\Gamma(x)\equiv \int_0^\infty\mathrm{d}t\:t^{x-1}\mathrm{e}^{-t}$?


  1. Expanding Space: the Root of all Evil?

    Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe

  2. bonus question: it's a matter of integration by parts, with the integrand vanishing at the integration boundaries: \begin{equation} \Gamma(x+1) = \int_0^\infty\mathrm{d}t\:t^x\mathrm{e}^{-t} = \left.-t^x\mathrm{e}^{-t}\right|_0^\infty + x\int_0^\infty\mathrm{d}t\:t^{x-1}\mathrm{e}^{-t} = x\Gamma(x).\end{equation}