The Loop Tension

The S₈ tension — a discrepancy between the amplitude of matter clustering measured by weak gravitational lensing surveys and the value predicted by the cosmic microwave background — has been interpreted as evidence for new physics. Modified gravity, dark energy, neutrino masses, and decaying dark matter have all been proposed to resolve the ~2-3σ disagreement.

The first two-loop effective field theory analysis of DES-Y3 cosmic shear data finds S₈ = 0.783, and when combined with CMB, baryon acoustic oscillation, and supernova data under dynamical dark energy, the tension with Planck vanishes entirely. The discrepancy was not a signal of new physics but an artifact of insufficiently rigorous perturbative modeling.

The mechanism: standard weak lensing analyses use one-loop perturbation theory or halo-model-based emulators to relate the observed shear power spectrum to the underlying cosmological parameters. These approaches are accurate at large scales but biased at smaller scales where nonlinear structure formation matters. The bias is systematic — it consistently shifts the inferred S₈ low. Two-loop perturbation theory extends the regime of accurate modeling to smaller scales, removing the systematic shift.

The bias was invisible within the one-loop framework because the framework itself could not diagnose its own insufficiency — the residuals looked like noise, not like a missing perturbative order. Only by computing the next order and observing the shift could the bias be identified.

The structural observation: a tension between datasets was a tension between analysis methods applied to the same underlying cosmology. The perturbation theory was not wrong — it was truncated, and the truncation produced a systematic bias that mimicked a physical signal. The "tension" was the sound of a missing loop.