Two-loop EFT galaxy power spectrum achieves per-mille agreement with simulations to k=0.85 h/Mpc and yields three times narrower unbiased σ8 errors than linear theory.
On the non-linear scale of cosmological perturbation theory
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abstract
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
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Galaxy Power Spectrum at Two-Loop Order: Implications for Weak Lensing Surveys and New Physics
Two-loop EFT galaxy power spectrum achieves per-mille agreement with simulations to k=0.85 h/Mpc and yields three times narrower unbiased σ8 errors than linear theory.