Validate a compressed CMB likelihood for interacting dark energy

Determine whether the proposed compressed CMB-likelihood strategy for the interacting dark-energy model—replacing the physical cold-dark-matter density omega_c with the effective early-time density omega_c^{\mathrm{eff}}=\omega_c+\xi\omega_x/(3w_x+\xi) and consistently recalibrating its central values and parameter correlations—reproduces the information content of the full CMB likelihood.

Background

The paper argues that, after matching the acoustic scale, matter-radiation equality, and the background expansion history, the primary CMB contains little direct sensitivity to the perturbative signatures of the chosen interacting dark-energy model. This motivates compressing the CMB information into a small set of parameters rather than applying standard \LambdaCDM distance priors without modification.

The authors propose replacing the usual physical cold-dark-matter density in a three-dimensional compressed likelihood with an effective early-time density that accounts for the interaction. However, the appropriate central values and parameter correlations would need to be recalculated, and it remains unresolved whether this modified compression faithfully captures the full CMB likelihood.

References

Of course, these modified compression schemes would need to be recalibrated against the full CMB likelihood. While we expect the above to be a reasonable compression strategy for the information content of the primary CMB, checking whether this is indeed the case is well beyond the scope of this work, and is left to follow-up work.

— Cosmological anatomy of interacting dark energy  (2609.18288 - Sabogal et al., 16 Sep 2026) in Section 6, Discussion