Is $\Lambda$CDM on the run? Reconciling the CMB with the Lyman-$\alpha$ Forest

TL;DR

This paper combines multiple cosmological datasets to constrain the primordial power spectrum's scale dependence, revealing potential deviations from standard inflationary models and introducing a new code for testing inflationary potentials.

Contribution

It provides the first joint constraints on the running and its running using combined CMB and Lyman-alpha data, and introduces the PIPE code for testing inflationary models.

Findings

Evidence for nonzero running and its running at >2σ significance.

Inflationary models with dips, bumps, or oscillations fit the data better.

Constraints extend to smaller scales than previous analyses.

Abstract

We present new constraints on the scale dependence of the primordial power spectrum by combining Planck, ACT DR6, SPT-3G and eBOSS Lyman-$\alpha$ forest data, extending sensitivity to smaller comoving scales. While ACT results previously indicated a mild preference for positive running of the spectral index, our joint analysis constrains both the running $\alpha_s$ and its running $\beta_s$. Including eBOSS markedly tightens these constraints, yielding a $>2\sigma$ indication of nonzero $\alpha_s$ and/or $\beta_s$, challenging predictions from vanilla slow-roll inflation potentials. Comparing reconstructed spectral parameters with theoretical models, we find that inflationary potentials with localised dips, bumps, or oscillations better reproduce the observed scale dependence. We release the public PIPE code to test arbitrary inflationary potentials against these datasets.