Rapid cosmological inference with the two-loop matter power spectrum

We compute the two-loop effective field theory (EFT) power spectrum of dark matter density fluctuations in $\Lambda$CDM using the recently proposed COBRA method (Bakx. et al, 2025). With COBRA, we are able to evaluate the two-loop matter power spectrum in $\sim 1$ millisecond at $\sim 0.1\%$ precision on one CPU for arbitrary redshifts and on scales where perturbation theory applies. As an application, we use the nonlinear matter power spectrum from the Dark Sky simulation to assess the performance of the two-loop EFT power spectrum compared to the one-loop EFT power spectrum at $z=0$. We find that, for volumes typical for Stage IV galaxy surveys, $V = 25 \,(\text{Gpc}/h)^3$, the two-loop EFT can provide unbiased cosmological constraints on $\Omega_m,H_0$ and $A_s$ using scales up to $k_\text{max}=0.26\, h/\text{Mpc}$, thereby outperforming the constraints from the one-loop EFT ($k_\text{max}=0.11\, h/\text{Mpc}$). The Figure of Merit on these three parameters increases by a factor $\sim 2.6$ and the one-dimensional marginalized constraints improve by $\sim35\%$ for $\Omega_m$, $\sim20\%$ for $H_0$ and $\sim 15\%$ for $A_s$.