Controlled Tension Forecasting: Quantifying Cross-Probe Biases in $ω_0ω_a$CDM

Abstract

Recent analyses combining DESI DR2 BAO, Planck CMB, and Pantheon+ SNe have reported mild deviations from the \LambdaCDM model. A central challenge is to determine whether these deviations reflect genuine dark-energy evolution or instead arise from cross-probe inconsistencies, prior choices, or mismatches in likelihood construction. Previous work demonstrated that imposing a biased supernova-motivated prior on Ω_{m0} can artificially displace the BAO-inferred (w_0,w_a) values from the \LambdaCDM expectation. A complementary pedagogic study further showed that differing degeneracy geometries among BAO, CMB, and SNe can generate apparent dark-energy evolution even when the underlying cosmology is exactly \LambdaCDM. Here we present a controlled tension-injection framework designed as a simplified mock-based diagnostic tool for studying how selected probe-level inconsistencies propagate into inferred dark-energy parameters. Self-consistent BAO, CMB, and SNe mock datasets are augmented with parameterized shifts in (Ω_{m0}, H_0), supernova absolute calibration, and the BAO sound-horizon scale r_d. The resulting datasets are analyzed through a unified MCMC pipeline, enabling a direct assessment of how these controlled tensions propagate into biases in (w_0,w_a) and the pivot equation-of-state parameter w_p. The results should be interpreted within the restricted setup adopted here: the late-time sector is described in the CPL parametrization and the CMB is represented through compressed distance priors. In this sense, the framework is intended primarily as an illustrative and diagnostic device for identifying probe combinations and degeneracy directions that are more vulnerable to tension-induced dynamical-dark-energy-like shifts, rather than as a parametrization-independent or fully realistic prediction tool.