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

I show how to compute the nonlinear power spectrum across the entire $w(z)$ dynamical dark energy model space. Using synthetic $\mathrm{\Lambda }$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\mathrm{G}\mathrm{y}\mathrm{r}$ 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 $4\mathrm{\%}$ up to k = $5h{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$. Unlike simulation rescaling methods, neural ODEs naturally extend to summary statistics beyond the power spectrum that are sensitive to the growth history.