Large Scale Structure

 

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The bispectrum is the three-point correlation function in Fourier space, a useful quantity for studying large scale structure, as it helps constrain the bias of the galaxy and DM density distributions, and gives information on departures from Gaussianity in the density field initial conditions. However, at non-linear scales, where most of the signal in large galaxy surveys is found, second order Perturbation Theory (PT) fails to give accurate predictions of the bispectrum. To correct for this, one could go to higher order corrections of PT, which however involve non-trivial computations. Another solution to this is to use phenomenological models, which can provide predictions for these statistics at non-linear scales.

For my Master's thesis I improved on a phenomenological formula of the bispectrum (Gil-Marin, Wagner, Fragkoudi et al. 2012), first proposed by Scoccimarro & Couchman (2001). The formula is based on the analytic derivation of the bispectrum using second order PT. I improved upon the original formula by fitting it to a set of much larger simulations than those used originally, which additionally included Baryon Acoustic Oscillations. To do this, I fit the formula using the downhill simplex method, while becoming well-versed in Eulerian PT, which is necessary for the analytical derivation of the tree-level bispectrum.

Based on Gil-Marín, Wagner, Fragkoudi et al., (2012), JCAP 2