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

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

Jan, 2013

24 pages

Published in:

JCAP 08 (2013) 037

Published: Aug 20, 2013

e-Print:

1301.7182 [astro-ph.CO]

DOI:

10.1088/1475-7516/2013/08/037

View in:

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Abstract: (IOP)

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 Pin ~ kn. 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 depends on n. For n ~ −1.5, relevant for our universe, pressure and dissipative corrections are more important than the two-loop corrections.

Note:

24 pages, 2 figures, 1 mathematica notebook

power spectrum
cosmic flows
cosmic web
effective field theory
boundary condition
power spectrum
structure
perturbation theory
scale dependence
renormalization

References(16)

Figures(4)

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