Galaxy Power Spectrum at Two-Loop Order: Implications for Weak Lensing Surveys and New Physics

We compute the galaxy power spectrum at two-loop order in cosmological perturbation theory (effective field theory, EFT). We derive galaxy bias operators through the fifth order and obtain two-loop renormalization conditions for the their bias coefficients. We compute the two-loop integrals using a renormalization scheme consistent with the CLASS-PT code, allowing for an easy interface of our new computations with standard tools used in the one-loop galaxy power spectrum and bispectrum analyses. We also derive the relevant higher-derivative and stochastic contributions, and implement IR resummation using time-sliced perturbation theory. Having identified the redundant operators, we find that the two-loop galaxy power spectrum requires 21 additional EFT parameters per galaxy sample. We compare our computation with the galaxy-galaxy and galaxy-matter power spectra from the PT Challenge N-body simulation at z=0.61 and find a per mille-level agreement up to k=0.85 h Mpc-1. We show that even with conservative priors on all EFT parameters, the two-loop model produces an unbiased measurement of the mass fluctuation amplitude sigma 8 with three times narrower error-bars than the linear theory model. The improvement over the one-loop model is 40%. This suggests significant gains in the two-loop EFT analyses of galaxy clustering and galaxy--lensing two-point functions (2 times2 pt) from CMB lensing maps and imaging surveys like Euclid, LSST, and Roman. In addition, our two-loop computation offers a probe of new physics scenarios that modify the shape of the matter power spectrum at wavenumbers (0.4-0.8) h Mpc-1 such as the presence of ultra-light axion dark matter sub-components with masses m a about 10-24 eV.