Assessing the consistency of the CPL dark-energy model with cosmological data: Simulation-calibrated neural posterior disagreement

Recent DESI observations hint at a preference for dynamical dark energy with an equation of state that crosses the phantom divide within the Chevallier-Polarski-Linder (CPL) parameterization. In this work, we assess the consistency of the CPL parameterization with current cosmological observations. We develop a model check based on the disagreement between posteriors inferred by neural posterior estimation and flow-matching posterior estimation. Both estimators are trained on the same CPL simulations, and their posterior disagreement is calibrated using independent simulations to obtain a global $p$-value. Controlled simulations assess the reliability of the calibrated $p$-values and show how detection sensitivity depends on the form of departure from the assumed model. Applying the test to the compressed CMB+DESI+DESY5 data vector yields $p_{\mathrm{g}\mathrm{l}\mathrm{o}\mathrm{b}\mathrm{a}\mathrm{l}}=0.524$, indicating that the current observations are consistent with the CPL model. The method has a median evaluation time of only $0.53\mathrm{s}$, enabling efficient assessments of cosmological model adequacy. This framework enables efficient tests of dark-energy models, providing a firmer basis for investigating the physical origin of cosmic acceleration.