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

Abstract

Standard perturbation theory (SPT) for large-scale matter inhomogeneities is\nunsatisfactory for at least three reasons: there is no clear expansion\nparameter since the density contrast is not small on all scales; it does not\nfully account for deviations at large scales from a perfect pressureless fluid\ninduced by short-scale non-linearities; for generic initial conditions, loop\ncorrections are UV-divergent, making predictions cutoff dependent and hence\nunphysical. The Effective Field Theory of Large Scale Structures successfully\naddresses all three issues. Here we focus on the third one and show explicitly\nthat the terms induced by integrating out short scales, neglected in SPT, have\nexactly the right scale dependence to cancel all UV-divergences at one loop,\nand this should hold at all loops. A particularly clear example is an Einstein\ndeSitter universe with no-scale initial conditions P_in=A k^n. After\nrenormalizing the theory, we use self-similarity to derive a very simple result\nfor the final power spectrum for any n, excluding two-loop corrections and\nhigher. We show how the relative importance of different corrections depend on\nn. For n=-1.5, relevant for our universe, pressure and dissipative corrections\nare more important than the two-loop corrections.\n