Renormalization group neural operators for precision cosmology

Accurate predictions of the nonlinear matter power spectrum P(k,z) over k in [10^-3, 10] h Mpc^-1 and z in [0,3] are a computational bottleneck for Rubin Observatory cosmological analyses, where Monte Carlo Markov Chain parameter estimation requires O(10^6) likelihood evaluations. We present a physics-informed neural operator framework, hereafter CosmoRGNet, that addresses this by embedding the structure of the functional renormalization group (FRG) directly into the architecture. The framework rests on three theoretical pillars: (i) the FRG equations governing the scale-dependent effective action of cosmological density fields, which motivate a hierarchical multi-scale architecture whose depth corresponds to RG scale; (ii) Fourier neural operators that learn resolution-consistent mappings between function spaces; and (iii) the effective field theory of large-scale structure (EFTofLSS), whose consistency conditions (mass conservation, the Euler-equation residual, and the BBGKY-hierarchy bispectrum relation) are enforced as soft penalty terms in the loss functional with GradNorm-adapted weights.