On the renormalization of the effective field theory of large scale structures

Abstract

Standard perturbation theory (SPT) for large-scale matter inhomogeneities is unsatisfactory for at least three reasons: there is no clear expansion parameter since the density contrast is not small on all scales; it does not fully account for deviations at large scales from a perfect pressureless fluid induced by short-scale non-linearities; for generic initial conditions, loop corrections are UV-divergent, making predictions cutoff dependent and hence unphysical. The Effective Field Theory of Large Scale Structures successfully addresses all three issues. Here we focus on the third one and show explicitly that the terms induced by integrating out short scales, neglected in SPT, have exactly the right scale dependence to cancel all UVdivergences at one loop, and this should hold at all loops. A particularly clear example is an Einstein deSitter universe with no-scale initial conditions P in ∼ k n . After renormalizing the theory, we use self-similarity to derive a very simple result for the final power spectrum for any n, excluding two-loop corrections and higher. We show how the relative importance of different corrections depend on n. For n ∼ −1.5, relevant for our universe, pressure and dissipative corrections are more important than the two-loop corrections.

The Effective Field Theory of Large Scale Structures at two loops

“…For the n = −2 scaling universe, the one-loop diagrams are given by 29 [7] P finite 13 = (2π) 5π 2 56…”

“…We here describe in detail, following [2,7,8], how we expect perturbation theory in the EFTofLSS to be organized when applied to the real universe.…”

“…For IR-safe quantities there is no issue in principle 7 . One such example is the equal-time matter power spectrum.…”

“…It is easiest to illustrate the power of the EFTofLSS in the context of a scaling universe [7,8] where…”

“…By using the renormalization techniques developed in [2], Ref. [7] has explicitly verified that indeed the EFTofLSS is able to make predictions for the scaling universes.…”