Wednesday, June 27, 2012

baryonic acoustic oscillations

in what way do BAOs work as a geometrical distance measurement? What happens to BAOs in nonlinear structure formation? What assumptions concerning biasing does one do?

bonus question: is there an intuitive argument why the BAOs get destroyed in nonlinear structure formation?

extra bonus: what's $\log_i(\sqrt[i]{i})$ with $i = \sqrt{-1}$


  1. Concerning the bonus question: first, we can write $\log_\mathrm{i} \sqrt[\mathrm{i}]{\mathrm{i}}=\log_\mathrm{i} \mathrm{i}^{1/\mathrm{i}}=\log_\mathrm{i} \mathrm{i}^{-\mathrm{i}}$. Thus, we search a number $x$ for which $\mathrm{i}^x=\mathrm{i}^{-\mathrm{i}}$. Obviously, this is $x=-\mathrm{i}$ and thus $\log_\mathrm{i} \sqrt[\mathrm{i}]{\mathrm{i}}=-\mathrm{i}$.

  2. well, measuring the pair density of galaxies as a function of separation (i.e. the correlation function) exibits a scale at roughly 100 Mpc/h (comoving) at which the pair density is enhanced. this enhancement in the correlation functions is caused by an enhanced density of dark matter on the same scale, by the same physical process that form the CMB flucutations. observing this scale and measuring its angular size enables us to estimate the physical distance of the galaxy sample in a geometrical way, and we can combine this information with the galaxy redshifts for constraining the cosmological model. of course one assumes that the galaxies follow the dark matter distribution and are correlated in a positive way.

    nonlinear structure formation destroys baryon acoustic oscillations. a very simple argument would be that nonlinear structure formation processes lead to relaxation, and because the BAOs are a feature in the initial conditions, they get wiped out. a more elaborate argument would be that nonlinear corrections to the CDM spectrum would involve loop integrations, i.e. integrations over the CDM-spectrum. these integrals are determined by the area under the CDM spectrum and are insensitive to small features such as BAOs.