Controlled ensemble null tests of dynamical dark energy hints: single-probe recovery of \(\Lambda \)CDM with BAO, compressed-CMB, and SNe mocks

Abstract

Recent combined cosmological analyses have reported mild apparent departures from the cosmological-constant equation of state. Such departures are difficult to interpret because BAO, compressed CMB distance priors, and Type Ia supernovae constrain different projections of the expansion history and carry different calibration degeneracies. We perform controlled ensemble null tests using observable-level Gaussian BAO-like, CMB-like, and supernova-like mock datasets generated from a common fiducial flat \(\Lambda \)CDM cosmology. The aim is to determine whether each constituent single-probe likelihood block can produce an apparent DDE-like marginalized-posterior displacement, or spuriously exclude the fiducial model, through its own degeneracy structure and calibration freedom. The analysis adopts probe-adapted parameterizations for the BAO scale, the CMB physical matter density, and the supernova normalization degeneracy. With explicit convergence diagnostics, percentile-based posterior coverage tests, and realization-level pull statistics, none of the three single-probe analyses spuriously excludes the fiducial input at the 95% level. All completed BAO and SNe chains enter their final ensembles after adaptive extension of the originally rejected runs; for compressed CMB, a mock-data-space audit finds no detectable selection dependence within the sensitivity of the 208-mock ensemble. The compressed CMB-only likelihood nevertheless exhibits stable displaced marginalized medians together with broad late-time posterior intervals, illustrating that posterior location and model exclusion are distinct diagnostics. These results show that a displaced marginalized posterior in a single realization is not, by itself, evidence for dynamical dark energy. Such shifts must be interpreted through mock-ensemble recovery, convergence diagnostics, and the probe-dependent geometry of the likelihood.