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Running of the spectral index: Reconciling the CMB with the Lyman-α forest

Malcolm Fairbairn*, Lucien Heurtier†, and María Olalla Olea-Romacho‡

  • *Contact author: malcolm.fairbairn@kcl.ac.uk
  • †Contact author: lucien.heurtier@kcl.ac.uk
  • ‡Contact author: maria_olalla.olea_romacho@kcl.ac.uk
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Phys. Rev. D 114, 043507 – Published 6 August, 2026

DOI: https://doi.org/10.1103/pwfl-mt4g

Abstract

We investigate the scale dependence of the primordial power spectrum by combining Planck, ACT DR6, SPT-3G, and eBOSS Lyman-α forest data, extending sensitivity to smaller comoving scales than those probed by the cosmic microwave background (CMB) alone. Within a parametrization based on a Taylor expansion around the pivot scale, we constrain the running of the spectral index αs and its running βs. By using eBOSS likelihoods exhibiting a suppression of small-scale power either in amplitude or spectral index, we show that the latter can be accommodated by correlated variations of (αs,βs), leading to a preference for nonzero running. We show that inflationary potentials with localized features—such as Gaussian dips, bumps, or axion-monodromy modulations—can reproduce the inferred scale dependence while remaining compatible with current CMB constraints. We release the public pipe code to enable systematic tests of inflationary potentials against current CMB datasets.

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Phys. Rev. D 114, 043507– Published 6 August, 2026
  • Received 30 November 2025
  • Accepted 15 June 2026
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