  The Effective Field Theory of Large-Scale Structure (EFTofLSS) attempts to
amend some of the shortcomings of the traditional perturbative methods used in
cosmology. It models the evolution of long-wavelength perturbations above a
cutoff scale without the need for a detailed description of the
short-wavelength ones. Short-scale physics is encoded in the coefficients of a
series of operators composed of the long-wavelength fields, and ordered in a
systematic expansion. As applied in the literature, the EFTofLSS corrects a
summary statistic (such as the power spectrum) calculated from standard
perturbation theory by matching it to $N$-body simulations or observations.
This `bottom-up' construction is remarkably successful in extending the range
of validity of perturbation theory. In this work, we compare this framework to
a `top-down' approach, which estimates the EFT coefficients from the stress
tensor of an $N$-body simulation, and propagates the corrections to the summary
statistic. We consider simple initial conditions, viz. two sinusoidal,
plane-parallel density perturbations with substantially different frequencies
and amplitudes. We find that the leading EFT correction to the power spectrum
in the top-down model is in excellent agreement with that inferred from the
bottom-up approach which, by construction, provides an exact match to the
numerical data. This result is robust to changes in the wavelength separation
between the two linear perturbations. However, in our setup, the leading EFT
coefficient does not always grow linearly with the cosmic expansion factor as
assumed in the literature based on perturbative considerations. Instead, it
decreases after orbit crossing takes place.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology