Determine the true CMB power spectra after model-dependent corrections

Determine the physically correct cosmic microwave background power spectra by recalculating foreground, weak-lensing, Sunyaev–Zeldovich, and Sachs–Wolfe corrections from the raw microwave data using the actual structure-formation history of the cosmological model under consideration.

Background

The paper argues that the published Planck CMB spectra are reconstructed rather than directly observed. Their extraction requires corrections whose values depend on the growth of cosmic structure, and the authors contend that the corrections were computed under the SMoC. Since alternative cosmological models predict different structure formation, the paper identifies the model-independent or physically correct spectra as unresolved.

References

The true CMB power spectra thus remain unknown.

— The relevance of the cosmic microwave background for cosmology  (2609.10672 - Kroupa et al., 9 Sep 2026) in Section 3.1, “The CMB is not observable, it must be calculated from the raw data assuming a cosmological model”

At the moment we do not know how large the error is when, for example, forcing the AeST model into the current Planck-CMB data. The calculations have not yet been done how the four corrections, when applied for example using the opt-$\nu$HDM model to reduce the raw Planck data to obtain the physically correct self-consistent initial conditions for the opt-$\nu$HDM model, affect the power spectra.

— The relevance of the cosmic microwave background for cosmology  (2609.10672 - Kroupa et al., 9 Sep 2026) in Conclusion to Section 3, “Lesson II”