IR-safe and UV-safe integrands in the EFTofLSS with exact time
  dependence
  Because large-scale structure surveys may very well be the next leading
sources of cosmological information, it is important to have a precise
understanding of the cosmological observables; for this reason, the Effective
Field Theory of Large-Scale Structure (EFTofLSS) was developed. So far, most
results in the EFTofLSS have used the so-called Einstein-de Sitter
approximation, an approximation of the time dependence which is known to be
accurate to better than one percent. However, in order to reach even higher
accuracy, the full time dependence must be used. The computation with exact
time dependence is sensitive to both infrared (IR) and ultraviolet (UV) effects
in the loop integrands, and while these effects must cancel because of
diffeomorphism invariance, they make numerical computation much less efficient.
We provide a formulation of the one-loop, equal-time exact-time-dependence
power spectrum of density perturbations which is manifestly free of these
spurious IR and UV divergences at the level of the integrand. We extend our
results to the total matter mode with clustering quintessence, show that IR and
UV divergences cancel, and provide the associated IR- and UV-safe integrand.
This also establishes that the consistency conditions are satisfied in this
system. We then use our one-loop result to do an improved precision comparison
of the two-loop dark-matter power spectrum with the Dark Sky N-body simulation.
