Computing Nonlinear Power Spectra Across Dynamical Dark Energy Model Space with Neural ODEs

TL;DR

This paper introduces a neural ODE approach to accurately compute the nonlinear power spectrum for a wide range of dynamical dark energy models, enabling efficient analysis of cosmic evolution.

Contribution

The paper presents a neural ODE method that generalizes to any $w(z)$ dark energy model, providing accurate nonlinear power spectrum predictions without extensive simulations.

Findings

Achieves within 4% accuracy up to k=5 h/Mpc

Generalizes across the entire $w(z)$ model space

Extends naturally to other summary statistics

Abstract

I show how to compute the nonlinear power spectrum across the entire $w(z)$ dynamical dark energy model space. Using synthetic $\Lambda$CDM data, I train a neural ordinary differential equation (ODE) to infer the evolution of the nonlinear matter power spectrum as a function of the background expansion and mean matter density across $\sim$$9 {\rm \ Gyr}$ of cosmic evolution. After training, the model generalises to {\it any} dynamical dark energy model parameterised by $w(z)$. With little optimisation, the neural ODE is accurate to within $4\%$ up to k = $5 \ h {\rm Mpc}^{-1}$. Unlike simulation rescaling methods, neural ODEs naturally extend to summary statistics beyond the power spectrum that are sensitive to the growth history.