Current and Future Constraints on the Primordial Power Spectrum
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 (ns), nonzero running (αs), or more general deviations from a pure power-law form. We find that freeing the number of light relic species (Neff) and the sum of the neutrino masses (∑ mν) broadens the ns 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 ΛCDM model, we find that in the nine-parameter ΛCDM + αs + Neff + ∑ mν model, CMB data from Planck, ACT, and SPT (CMB-PAS) combined with DESI DR2 give ns = 0.9758 ± 0.0064 and αs = 0.0080 ± 0.0064, consistent with both models. Future CMB facilities will sharply improve constraints on ns, αs, and, more generally, the binned primordial power spectrum 𝒫(k). For example, CMB-PAS constrains e−2τ𝒫(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−2τ𝒫(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.
Related
- Constraints on Primordial Oscillatory Features from the Power Spectrum and Bispectrum of Redshift-Space Galaxy Clustering in DESI DR1
- Exploring the Primordial Power Spectrum with Dark-Age 21 cm fluctuations
- Localized Enhancements of the Primordial Power Spectrum and the Abundance of Early Bright Galaxies
- Wedge-avoidance Fisher Forecasts for Primordial Features from Dark-Ages 21-cm Power Spectrum and Bispectrum
- Primordial Power Spectrum from the Lensed CMB Temperature Spectrum using Iterative Delensing and Fourier Denoising
BibTeX
@misc{cheslog2026current,
title = {{Current and Future Constraints on the Primordial Power Spectrum}},
author = {Zachary Cheslog and Emily Finson and Amanda MacInnis and Neelima Sehgal and Niayesh Afshordi and Simran K. Nerval and Renée Hložek},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35964},
eprint = {2609.35964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35964},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Current and Future Constraints on the Primordial Power Spectrum
AU - Zachary Cheslog
AU - Emily Finson
AU - Amanda MacInnis
AU - Neelima Sehgal
AU - Niayesh Afshordi
AU - Simran K. Nerval
AU - Renée Hložek
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35964
UR - https://arxiv.org/abs/2609.35964
AB - 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 (∑ 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 ΛCDM model, we find that in the nine-parameter ΛCDM + α_s + N_eff + ∑ m_ν model, CMB data from Planck, ACT, and SPT (CMB-PAS) combined with DESI DR2 give n_s = 0.9758 ± 0.0064 and α_s = 0.0080 ± 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^−2τ𝒫(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^−2τ𝒫(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.
ER -