Perturbation Theory and Effective Field Theory of Large Scale Structure
The collisionless dark matter distribution is modeled using the collisionless Boltzmann equation, whose hierarchy is commonly truncated after its second moment, yielding the so called pressureless perfect fluid model. The resulting fluid equations are then solved perturbatively .
The validity of these perturbative techniques is typically confined to scales k < 0.1 h/Mpc at redshift z=0. The recently developed Effective Field Theory (EFT) treatments of LSS clustering tries to go beyond this by introducing an effective stress tensor that sources the fluid Euler equation and accounts for non-linearities and higher moments of the Vlaslov equations. This comes at the expense of having to introduce new time dependent parameters in front of the new effective operators that parametrize the effect of non-perturbative small scale physics on larger scales.
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