  Large scale structure surveys promise to be the next leading probe of
cosmological information. It is therefore crucial to reliably predict their
observables. The Effective Field Theory of Large Scale Structures (EFTofLSS)
provides a manifestly convergent perturbation theory for the weakly non-linear
regime of dark matter, where correlation functions are computed in an expansion
of the wavenumber k of a mode over the wavenumber associated with the
non-linear scale k_nl. Since most of the information is contained at high
wavenumbers, it is necessary to compute higher order corrections to correlation
functions. After the one-loop correction to the matter power spectrum, we
estimate that the next leading one is the two-loop contribution, which we
compute here. At this order in k/k_nl, there is only one counterterm in the
EFTofLSS that must be included, though this term contributes both at tree-level
and in several one-loop diagrams. We also discuss correlation functions
involving the velocity and momentum fields. We find that the EFTofLSS
prediction at two loops matches to percent accuracy the non-linear matter power
spectrum at redshift zero up to k~0.6 h/Mpc, requiring just one unknown
coefficient that needs to be fit to observations. Given that Standard
Perturbation Theory stops converging at redshift zero at k~0.1 h/Mpc, our
results demonstrate the possibility of accessing a factor of order 200 more
dark matter quasi-linear modes than naively expected. If the remaining
observational challenges to accessing these modes can be addressed with similar
success, our results show that there is tremendous potential for large scale
structure surveys to explore the primordial universe.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory