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

IR-safe and UV-safe integrands in the EFTofLSS with exact time dependence