CMB Lensing Imposes 10^{-3}c Limits on Warm Decay Products in DESI-Motivated DDM Models

The analysis deploys CLASSIER-DDM, an integral-equation extension of CLASS, to evolve perturbations for a three-parameter DDM model (f, Gamma, epsilon) motivated by the 5% lower late-time matter density reported by DESI. Planck temperature, polarization, and lensing spectra plus DESI DR2 BAO measurements are jointly sampled; the lensing convergence power spectrum directly limits the velocity kick imparted at decay because free-streaming erases small-scale power that would otherwise source lensing. No statistically significant preference for DDM over LCDM emerges once lensing is included.

These bounds close the window on explanations of the DESI-Planck tension that rely on decays to one massive and one massless daughter particle, because the massless channel produces even larger kicks. The surviving region still permits f approximately 0.3-0.5 with kicks below 0.01c at z less than 10, sufficient to suppress the matter power spectrum at k greater than 1 h/Mpc and potentially alleviate the too-big-to-fail problem in Milky Way satellites.

Future Stage-4 CMB experiments will tighten the same lensing observable by another factor of three, translating into sub-percent constraints on epsilon for any decay after recombination. Cross-correlation with galaxy weak lensing from LSST and Euclid will further break the degeneracy between decay timing and warm-particle velocity dispersion.