How to embed any likelihood into simulation-based inference Application to Planck and stage IV galaxy surveys and dynamical dark energy

Simulation-based inference (SBI) allows fast Bayesian inference for simulators encoding implicit likelihoods. However, some explicit likelihoods cannot be easily reformulated as simulators, hindering their integration into combined analyses within SBI frameworks. One key example in cosmology is given by the Planck cosmic microwave background (CMB) likelihoods. We present a simple method to construct an effective simulator for any explicit likelihood using samples from a previously converged Markov Chain Monte Carlo (MCMC) run. This effective simulator can subsequently be combined with any forward simulator. To illustrate this method, we combine the full Planck CMB likelihoods with a 3 × 2pt simulator (cosmic shear, galaxy clustering and their cross-correlation) for a stage IV survey like Euclid, and test evolving dark energy parametrized by the w₀w_a equation of state. Assuming the w₀w_a cold dark matter cosmology hinted by the Dark Energy Spectroscopic Instrument baryon acoustic oscillations (BAO) data release 2 + Planck 2018 + PantheonPlus supernovae Ia (SNIa) datasets, we find that future 3 × 2pt data alone could detect evolving dark energy at 5σ, while its combination with current CMB, BAO, and SNIa datasets could raise the detection to almost 7σ. Moreover, thanks to simulation reuse enabled by SBI, we show that our joint analysis is in excellent agreement with MCMC while requiring zero Boltzmann solver calls. This result opens up the possibility of performing massive global scans combining explicit and implicit likelihoods in a highly efficient way.