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

@misc{ivanov2026galaxy,
  title = {{Galaxy Power Spectrum at Two-Loop Order: Implications for Weak Lensing Surveys and New Physics}},
  author = {Mikhail M. Ivanov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.30713},
  eprint = {2606.30713},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.30713},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Galaxy Power Spectrum at Two-Loop Order: Implications for Weak Lensing Surveys and New Physics
AU  - Mikhail M. Ivanov
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2606.30713
UR  - https://arxiv.org/abs/2606.30713
AB  - 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 their bias coefficients. We also derive the relevant higher-derivative and stochastic contributions, and implement IR resummation using time-sliced perturbation theory. We obtain the complete dark-matter and galaxy renormalization conditions for the higher-derivative operators at the power spectrum, bispectrum, and trispectrum level. Having identified the redundant operators, we find that the two-loop galaxy power spectrum requires 21 additional bias, higher derivative and stochastic parameters per galaxy sample relative to the one-loop model. 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 hMpc^−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 σ_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 (``2×2 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 $(0.4-0.8)~hMpc^{-1}$ such as the presence of ultra-light axion dark matter sub-components with masses m_a∼ 10^−24 eV.
ER  -