On the Renormalization of the Effective Field Theory of Large Scale Structures

TL;DR

This paper demonstrates how the Effective Field Theory of Large Scale Structures can cancel UV divergences in perturbation theory, providing a more consistent prediction of the matter power spectrum across different scales.

Contribution

It explicitly shows the cancellation of UV divergences at one loop via renormalization, extending the understanding of EFT in large-scale structure analysis.

Findings

UV divergences are canceled at one loop by EFT counterterms.

Renormalized power spectrum derived using self-similarity for any spectral index n.

For n=-1.5, pressure and dissipative effects surpass two-loop corrections.

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 UV-divergences 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=A 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.