Current and Future Constraints on the Primordial Power Spectrum

arXiv:2609.35964 · astro-ph.CO, hep-ph, hep-th · Submitted 2026-09-28 · Read on arXiv

astro-ph.CO, hep-ph, hep-th

Submitted: 2026-09-28

Updated: 2026-09-28

Comments: 28 pages, 11 figures, 7 tables. The code used here to generate the current and projected constraints is available at https://github.com/CMB-HD/hdInitPk , and the CMB-HD likelihood and Fisher codes at https://github.com/CMB-HD/hdfisher and https://github.com/CMB-HD/hdlike are updated to support CLASS

Code: https://github.com/CMB-HD/hdMockData

License: http://creativecommons.org/licenses/by/4.0/

The gist: The primordial scalar power spectrum provides a powerful window onto early-universe physics, including a broad class of inflationary scenarios.

Terminology

Abstract

The primordial scalar power spectrum provides a powerful window onto early-universe physics, including a broad class of inflationary scenarios. These models often predict a characteristic scalar spectral index (n s), nonzero running (α s), or more general deviations from a pure power-law form. We find that freeing the number of light relic species (N eff) and the sum of the neutrino masses (sum m ν) broadens the n s error contours enough that key early-Universe models are no longer excluded. In particular, while both Starobinsky inflation and the Bi-thermal Big Bang model are ruled out at about the 95% confidence level in the six-parameter Λ CDM model, we find that in the nine-parameter Λ CDM + α s + N eff + sum m ν model, CMB data from Planck, ACT, and SPT (CMB-PAS) combined with DESI DR2 give n s = 0.9758 plus or minus 0.0064 and α s = 0.0080 plus or minus 0.0064, consistent with both models. Future CMB facilities will sharply improve constraints on n s, α s, and, more generally, the binned primordial power spectrum P(k). For example, CMB-PAS constrains e-2τ P(k = 0.2, Mpc-1) to 0.5%, while SO-like and CMB-HD-like surveys would tighten this to 0.1%; CMB-HD would also extend this measurement to smaller, previously unprobed scales, constraining e-2τ P(k = 30, Mpc-1) to within a factor of ten. We release our forecast code and update the public CMB-HD likelihood and Fisher codes to support CLASS in addition to CAMB.

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