The paper is quite complex, and focuses on redshift space distortions. This can be difficult to understand, but here goes. We've mentioned a couple of times that matter in the Universe is arranged on a cosmic web, with clusters, clumps, filaments and voids. In fact, it looks something like this:
What do we see when we look out into the Universe? Well, we can measure the position to a galaxy on the sky very accurately, but distance is not. But we can easily measure the redshift, or the amount features in the spectrum are moving to longer wavelength, and use our cosmology to turn this into a distance using the famous Hubble law.
However, there is a problem. The redshift we see is a mixture of two parts, one due to the cosmic expansion (the Hubble law bit) and one due to the `peculiar velocity, or how much the galaxy is whizzing about. By comparing to the Microwave Background, we know that our Milky Way is moving with a speed of about 500 km/s.
As we measure redshifts, not distances, these peculiar velocities distort the distances we calculate via the Hubble law. So, this happens
In fact, clusters of galaxies, where velocities are typically several thousands of km/s, get stretched out into what are known as Fingers of God - although what they have to do with the Higgs boson, I don't know (and no, that's not a serious statement). Here's a real set of observations;
Mapping Growth and Gravity with Robust Redshift Space Distortions
Juliana Kwan, Geraint F. Lewis, Eric V. Linder
(Submitted on 6 May 2011 (v1), last revised 3 Feb 2012 (this version, v2))
Redshift space distortions caused by galaxy peculiar velocities provide a window onto the growth rate of large scale structure and a method for testing general relativity. We investigate through a comparison of N-body simulations to various extensions of perturbation theory beyond the linear regime, the robustness of cosmological parameter extraction, including the gravitational growth index, \gamma. We find that the Kaiser formula and some perturbation theory approaches bias the growth rate by 1-sigma or more relative to the fiducial at scales as large as k > 0.07 h/Mpc. This bias propagates to estimates of the gravitational growth index as well as \Omega_m and the equation of state parameter and presents a significant challenge to modelling redshift space distortions. We also determine an accurate fitting function for a combination of line of sight damping and higher order angular dependence that allows robust modelling of the redshift space power spectrum to substantially higher k.