Lorenzo Mercolli, Enrico Pajer
We present the renormalized two point functions of density, divergence and vorticity of the velocity in the Effective Field Theory of Large Scale Structures. We show that the mass-weighted velocity, as opposed to the volume-weighted velocity, is the natural variable to use. We then prove that, because of momentum and mass conservation, the corrections from short scales to the large-scale power spectra of divergence and vorticity must start at order $k^{4}$. For the vorticity this constitutes the leading term. Using exact (approximated) self-similarity of an Einstein-de Sitter ($\Lambda$CDM) background, this fixes the time dependence so that the vorticity power spectrum is uniquely determined, up to a normalization, by the symmetries of the problem. For density and divergence, all three cross- and auto-correlation functions have the same structure, but with numerically different coefficients, which we compute. Adding the information from the divergence breaks the degeneracy between the speed of sound and the viscosity, but not between shear and bulk viscosities. These results also provide a non-trivial consistency check of the EFT approach since only two counter-terms are sufficient to cancel all three loop divergences. Finally we point out a few shortcoming of using the momentum instead of the velocity.
View original:
http://arxiv.org/abs/1307.3220
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