Lensing Amplitude Bias (Alens = 1.18)

The Planck 2018 (PR3) analysis found that the cosmic microwave background is lensed more strongly than the best-fit ΛCDM model predicts. The phenomenological parameter A_lens, which rescales the lensing power applied to the CMB spectra and should equal exactly 1 if the model is consistent, came out at A_lens = 1.180 +/- 0.065, more than 2.5 sigma above unity (Planck 2018 VI). The signature is excess smoothing of the acoustic peaks: the observed peaks are blurred as if roughly 18 percent more gravitational lensing had occurred along the line of sight than the catalogued matter distribution in the best-fit model can supply. The same excess drives the internal preference for a closed universe and biases parameters derived from different angular-scale ranges away from each other.

ΛCDM has no physical mechanism for A_lens different from 1. The parameter is not part of the model; it is a consistency check, and its failure means either the universe lenses the CMB more than the model's matter does, or something in the data or likelihood mimics that effect. Proposed physical explanations (positive curvature, modified gravity, extra clustering) each break agreement with BAO, supernovae, or direct lensing reconstruction, which measures the lensing power directly from the four-point function and finds it consistent with the model. That internal split, smoothing says excess while reconstruction says nominal, is itself the puzzle: the two estimators should agree if the smoothing is genuinely gravitational lensing.

The standing has shifted substantially since 2018. The PR4/NPIPE reanalysis with the CamSpec likelihood gives A_lens = 1.095 +/- 0.056 (1.7 sigma), the HiLLiPoP likelihood gives 1.039 +/- 0.052 (0.75 sigma), ACT DR6 gives 1.007 +/- 0.057, and the Planck PR4 lensing reconstruction amplitude is 1.004 +/- 0.024. Much of the original anomaly therefore appears attributable to likelihood and systematics improvements, though a residual one-to-two-sigma excess persists in some pipelines. Whether a small genuine excess survives is a question for CMB-S4 and the Simons Observatory; the episode remains the cleanest example of how an unmodeled lensing-like contribution can contaminate every parameter in the standard fit.

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