The 2-loop matter power spectrum and the IR-safe integrand
  Large scale structure surveys are likely 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, where dark matter correlation functions are computed in an expansion of
the wavenumber k over the wavenumber associated to the non-linear scale knl. To
push the predictions to higher wavenumbers, it is necessary to compute the
2-loop matter power spectrum. For equal-time correlators, exactly as with
standard perturturbation theory, there are IR divergences present in each
diagram that cancel completely in the final result. We develop a method by
which all 2-loop diagrams are computed as one integral, with an integrand that
is manifestly free of any IR divergences. This allows us to compute the 2-loop
power spectra in a reliable way that is much less numerically challenging than
standard techniques. We apply our method to scaling universes where the linear
power spectrum is a single power law of k, and where IR divergences can
particularly easily interfere with accurate evaluation of loop corrections if
not handled carefully. We show that our results are independent of IR cutoff
and, after renormalization, of the UV cutoff, and comment how the method
presented here naturally generalizes to higher loops.
