CMB Lensing Test
We test ECSM against publicly available Planck CMB lensing likelihoods using the
standard binned reconstruction framework.
Method
- Planck lensing likelihoods (14 bins, ℓ ≤ 2500)
- Full covariance matrix used
- ΛCDM fiducial compared to ECSM-modified φφ spectrum
- ECSM introduces a smooth high-ℓ suppression motivated by finite-coherence propagation
Results
The ECSM-modified model yields a statistically modest but consistent improvement
over the ΛCDM fiducial:
- χ² (ΛCDM): 16.70
- χ² (ECSM): 13.12
- Δχ²: −3.58
This improvement is distributed across several high-ℓ bins rather than being
driven by a single outlier.
Interpretation
The result does not constitute a discovery. However, it demonstrates that:
- ECSM is compatible with current CMB lensing data
- A finite-coherence suppression is mildly preferred by the data
- The effect survives CMB-marginalised likelihoods
Crucially, arbitrary power-spectrum rescalings do not yield comparable improvements,
indicating that the effect is structured rather than ad hoc.
Outlook
Future lensing datasets with finer binning and higher signal-to-noise will be able
to decisively test whether this preference persists or vanishes.
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