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The Effective Field Theory of Large Scale Structures

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An analytical understanding of large-scale matter
inhomogeneities is an important cornerstone of our cosmological model and helps
us interpreting current and future data. The standard approach, namely Eulerian
perturbation theory, is unsatisfactory for at least three reasons: there is no
clear expansion parameter since the density contrast is not small everywhere;
it does not consistently 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.


I will present the systematic construction of an
Effective Field Theory of Large Scale Structures and show that it successfully
addresses all of the above issues. The idea is to smooth the density and
velocity fields on a scale larger than the non-linear scale. The resulting
smoothed fields are then small everywhere and provide a well-defined small
parameter for perturbation theory. Smoothing amounts to integrating out the
short scales, whose non-linear dynamics is hard to describe analytically. Their
effects on the large scales are then determined by the symmetries of the
problems. They introduce additional terms in the fluid equations such as an
effective pressure, dissipation and stochastic noise. These terms have exactly
the right scale dependence to cancel all divergences at one loop, and this
should hold at all loops.
I will present a clean example of the renormalization
of the theory in an Einstein de Sitter universe with self-similar initial
conditions and discuss the relative importance of loop and effective