Extend the emulator to test DESI–CMB power-spectrum-shape consistency

Determine which primordial power-spectrum shape is preferred by DESI galaxy-clustering observations when distances and growth are fitted simultaneously without imposing the cosmic-microwave-background shape prior, by extending the Gaussian-process emulator to a training region broad enough to support a substantially loosened prior.

Background

In the multi-template DESI DR1 LRG2 analysis, the cold-dark-matter density, baryon density, and scalar spectral index are varied, but only within tight Planck-prior ranges. The recovered posteriors reproduce those priors, indicating that the DESI data add essentially no independent information about the shape at the scales and survey volume used.

A direct comparison between the shape preferred by DESI and that inferred from the CMB would require relaxing the Planck prior and retraining the emulator over a correspondingly wider parameter domain. The paper identifies this as a concrete unresolved task.

References

Asking whether DESI and Planck prefer the same shape would require a looser prior, and in our framework also an emulator trained over a correspondingly wider box; we leave that to future work.

— Model-independent parameters from DESI DR1 LRG2 with an explicitly varying power-spectrum shape  (2610.21235 - Song et al., 15 Oct 2026) in Section 2, subsection “Measured values with a Multi-template case”

The question that follows is the one the present analysis cannot yet answer, namely which shape of the power spectrum the DESI observations themselves prefer, measured simultaneously with the distances and the growth rate and without borrowing the answer from the cosmic microwave background.

— Model-independent parameters from DESI DR1 LRG2 with an explicitly varying power-spectrum shape  (2610.21235 - Song et al., 15 Oct 2026) in Section 4, Conclusions