Varying fundamental constants principal component analysis: additional hints about the Hubble tension

TL;DR

This paper develops a model-independent PCA approach to constrain time-dependent variations of fundamental constants during recombination using Planck data, providing new insights into the Hubble tension.

Contribution

It introduces a PCA method for analyzing time-dependent fundamental constants during recombination, extending previous static analyses and applying it to Planck data.

Findings

Three VFC modes constrained at present

No significant deviations from standard model found

Future improvements could tighten constraints by a factor of three

Abstract

Varying fundamental constants (VFC) [e.g., the fine-structure constant, $\alpha_{\rm EM}$] can arise in numerous extended cosmologies. Through their effect on the decoupling of baryons and photons during last scattering and reionisation, these models can be directly constrained using measurements of the cosmic microwave background (CMB) temperature and polarization anisotropies. Previous investigations focused mainly on time-independent changes to the values of fundamental constants. Here we generalize to time-dependent variations. Instead of directly studying various VFC parameterizations, we perform a model-independent principal component analysis (PCA), directly using an eigenmode decomposition of the varying constant during recombination. After developing the formalism, we use Planck 2018 data to obtain new VFC limits, showing that three independent VFC modes can be constrained at present. No indications for significant departures from the standard model are found with Planck data. Cosmic variance limited modes are also compared and simple forecasts for The Simons Observatory are carried out, showing that in the future improvements of the current constraints by a factor of $\simeq 3$ can be anticipated. Our modes focus solely on VFC at redshifts $z\geq 300$. This implies that they do not capture some of the degrees of freedom relating to the reionisation era. This aspect provides important new insights into the possible origin of the Hubble tension, hinting that indeed a combined modification of recombination and reionisation physics could be at work. An extended PCA, covering both recombination and reionisation simultaneously, could shed more light on this question, as we emphasize here.