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

TL;DR

This study develops a controlled tension-injection framework to quantify how cross-probe inconsistencies among BAO, CMB, and SNe affect inferred dark-energy properties within a CPL parametrization. By generating self-consistent mocks and applying data-level, prior-level, and hybrid tensions, the authors map how biases propagate into $(\omega_0,\omega_a)$ and the pivot $w_p$ using a unified MCMC pipeline and complementary Fisher forecasts. The results show that modest tensions can produce DDE-like posteriors even when the underlying cosmology is ΛCDM, with distinct, probe-dependent degeneracy geometries driving these effects; the multi-probe combination is essential to recover fiducial parameters. The paper also constructs empirical one- and two-dimensional tension–bias transfer functions, highlighting when linear approximations fail and underscoring the need for higher-order or emulator-based approaches for future precision surveys. Overall, the framework provides a principled way to diagnose cross-probe inconsistencies, assess the robustness of multi-probe inferences, and guide the design of DESI, Pantheon$+$, and Planck-era analyses to avoid spurious dynamical dark energy signals.

Abstract

Recent analyses combining DESI DR2 BAO, Planck CMB, and Pantheon+ SNe have reported mild but intriguing deviations from the LambdaCDM model. A central challenge is to determine whether these deviations reflect genuine dynamical dark energy behavior 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 Omega_{m0} can artificially displace the BAO-inferred w_0,w_a values from the LambdaCDM expectation. A complementary pedagogic study further showed that the differing degeneracy geometries of BAO, CMB, and SNe can generate apparent dark energy evolution even when the underlying cosmology is exactly LambdaCDM. In this manuscript, we develop a controlled tension injection framework that provides a systematic means of quantifying how probe-level tensions influence inferred dark energy parameters. Self-consistent BAO, CMB, and SNe mock datasets are augmented with parameterized shifts in (Omega_{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. This forecasting framework provides practical guidance for identifying probe combinations that are most susceptible to spurious signatures of dynamical dark energy, and helps ensure robust multi-probe inference in forthcoming precision surveys.

Figures (9)

• Figure 1: Run1 (tension-free baseline). Joint posterior for BAO + CMB + SNe without any injected tension. The recovered parameters are fully consistent with the input $\Lambda$CDM cosmology, demonstrating the internal consistency of the mock datasets and validating the unified likelihood pipeline.
• Figure 2: Run2 (SNe $H_0$ +3$\sigma$ tension). Joint BAO+CMB+SNe posterior when the SNe zero-point is shifted by $\Delta M=-0.09$, mimicking a higher SNe-inferred Hubble constant. BAO and CMB remain fiducial. The contours move along the composite BAO+CMB degeneracy direction toward $(\omega_0>-1,\ \omega_a>0)$, demonstrating how a pure SNe calibration bias can generate an entirely spurious dynamical-DE signal.
• Figure 3: Run3 (BAO $\Omega_{m0}$ tension). Triangle plot from the joint BAO+CMB+SNe analysis. The BAO sector is biased toward a lower matter density, while the CMB and SNe mocks remain fiducial. The resulting posterior is displaced toward $\Omega_{m0}\simeq 0.287$, $H_0\simeq 70.6$, and $(\omega_0,\omega_a)\simeq(-1.20,\,0.74)$, producing a strongly dynamical, phantom-like effective EoS, even though the underlying cosmology is exactly $\Lambda$CDM.
• Figure 4: Run4 (CMB-side $H_0$ / acoustic-scale tension). Joint posterior for BAO+CMB+SNe when only the CMB mock is biased toward lower $H_0$. The resulting displacement toward $\Omega_{m0}\simeq 0.338$, $H_0\simeq 69.9$, and $(\omega_0,\omega_a)\simeq(-1.18,\,1.08)$ traces a steep, phantom-like degeneracy direction. This apparent DDE signature is produced entirely by the CMB side tension, despite the underlying cosmology being exactly $\Lambda$CDM.
• Figure 5: Run5 (opposite-directed BAO--CMB tensions). Joint posterior for BAO+CMB+SNe when the BAO mock is biased toward high $\Omega_{m0}$ and the CMB mock toward low $H_0$. The recovered parameters, $\Omega_{m0}\simeq 0.337$, $H_0\simeq 69.6$, and $(\omega_0,\omega_a)\simeq(-1.15,\,1.06)$, reflect a compromise between mutually inconsistent ridge directions. The apparent DDE signature is weaker than in run4 due to the partial cancellation of BAO and CMB shifts.