Benchmarking Exact, GP-Emulated, and Simulation-Based Inference for Late-Time Cosmology

Forthcoming cosmological surveys require inference pipelines that are both statistically reliable and computationally scalable. In this work, we perform a systematic comparison of three complementary inference strategies for late-time CDM cosmology: exact Markov Chain Monte Carlo (MCMC), Gaussian Process (GP)-assisted MCMC, and neural Simulation-Based Inference (SBI). Using a common analysis framework based on Cosmic Chronometers, DESI DR2 baryon acoustic oscillation measurements, and the Pantheon+ Type Ia supernova compilation, we consider two dataset combinations of increasing complexity, namely CC+DESI and CC+DESI+PP, under identical cosmological assumptions and priors. For CC+DESI, both GP emulation and SBI reproduce the exact posterior constraints on (H 0, m,0) to better than 0.3 sigma. For the more constraining CC+DESI+PP combination, modest method-dependent shifts emerge, reaching at most about1.5 sigma in a single parameter. Despite these differences, all methods recover a nearly identical expansion history, with percent-level agreement across the full redshift range. From a computational perspective, GP emulation accelerates model evaluations but remains limited by MCMC sampling, whereas SBI achieves order-of-magnitude reductions in total runtime through amortized posterior learning. We further investigate the convergence of SBI as a function of simulation budget and identify the number of simulations required to obtain stable posterior constraints. Overall, our results demonstrate that accelerated inference techniques can deliver reliable cosmological constraints for realistic late-time datasets at a fraction of the computational cost of conventional likelihood-based analyses.