The Redshift-Space Galaxy Power Spectrum at Two-Loop Order
Abstract
Contemporary large-scale structure analyses center around the galaxy power spectrum, modeled with one-loop perturbation theory. This description naturally breaks down at large wavenumbers, prohibiting the extraction of cosmological information from small-scale clustering. In this work, we present a complete model for the redshift-space galaxy power spectrum up to two-loop order, derived in the framework of the Effective Field Theory of Large Scale Structure. This accounts for a wide variety of effects, including fifth-order galaxy bias, redshift-space distortions, small-scale non-linearities, spatial non-locality, bulk flows, coordinate distortions, and stochasticity, involving 49 free coefficients. Our model additionally encodes all deterministic and counterterm contributions to the one-loop bispectrum and trispectrum (as well as the tree-level quadspectrum and pentaspectrum), which depend on many of the same parameters. We implement the model numerically, using the VEGAS algorithm to precompute the loop integrals; this allows the full likelihood to be evaluated in milliseconds. The approach is validated using power spectra measured from high-resolution simulations, considering both dark matter and realistic galaxy samples. The extension to two-loop order greatly increases the range of scales over which the power spectrum can be modeled, with kmax rising from 0.20h Mpc−1 to 0.34h Mpc−1 for a luminous red galaxy sample at z=0.5, or 0.27h Mpc−1 to 0.42h Mpc−1 for an emission line galaxy sample at z=1.1. Much of the additional information is absorbed by the numerous fifth-order biases and counterterms; for this reason, constraints on σ8 are not significantly enhanced by the inclusion of two-loop terms. Future work will assess the implications of the two-loop model for cosmological parameter inference.
Related
- Constraints on Primordial Oscillatory Features from the Power Spectrum and Bispectrum of Redshift-Space Galaxy Clustering in DESI DR1
- Galaxy Power Spectrum at Two-Loop Order: Implications for Weak Lensing Surveys and New Physics
- Forecast for the detectability of patchy hydrogen reionization in WEAVE-QSO measurements of the Lyman-α forest power spectrum at redshift z ≥ 4
- Forecast for the detectability of patchy hydrogen reionization in WEAVE-QSO measurements of the Lyman-α forest power spectrum at redshift z ≥ 4
- Full-Shape Analysis of the Redshift-Space Galaxy Trispectrum in the EFTofLSS
BibTeX
@misc{philcox2026redshiftspace,
title = {{The Redshift-Space Galaxy Power Spectrum at Two-Loop Order}},
author = {Oliver H. E. Philcox},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13867},
eprint = {2610.13867},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13867},
}
RIS
TY - UNPB
TI - The Redshift-Space Galaxy Power Spectrum at Two-Loop Order
AU - Oliver H. E. Philcox
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.13867
UR - https://arxiv.org/abs/2610.13867
AB - Contemporary large-scale structure analyses center around the galaxy power spectrum, modeled with one-loop perturbation theory. This description naturally breaks down at large wavenumbers, prohibiting the extraction of cosmological information from small-scale clustering. In this work, we present a complete model for the redshift-space galaxy power spectrum up to two-loop order, derived in the framework of the Effective Field Theory of Large Scale Structure. This accounts for a wide variety of effects, including fifth-order galaxy bias, redshift-space distortions, small-scale non-linearities, spatial non-locality, bulk flows, coordinate distortions, and stochasticity, involving 49 free coefficients. Our model additionally encodes all deterministic and counterterm contributions to the one-loop bispectrum and trispectrum (as well as the tree-level quadspectrum and pentaspectrum), which depend on many of the same parameters. We implement the model numerically, using the VEGAS algorithm to precompute the loop integrals; this allows the full likelihood to be evaluated in milliseconds. The approach is validated using power spectra measured from high-resolution simulations, considering both dark matter and realistic galaxy samples. The extension to two-loop order greatly increases the range of scales over which the power spectrum can be modeled, with k_max rising from 0.20h Mpc^−1 to 0.34h Mpc^−1 for a luminous red galaxy sample at z=0.5, or 0.27h Mpc^−1 to 0.42h Mpc^−1 for an emission line galaxy sample at z=1.1. Much of the additional information is absorbed by the numerous fifth-order biases and counterterms; for this reason, constraints on σ_8 are not significantly enhanced by the inclusion of two-loop terms. Future work will assess the implications of the two-loop model for cosmological parameter inference.
ER -