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- The Effective Field Theory of Large Scale Structures

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PIRSA Number:

13030110

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

corrections.

©2012 Institut Périmètre de Physique Théorique