# New constraints on time-dependent variations of fundamental constants using Planck data

## TL;DR

This paper investigates how variations in fundamental constants like the fine-structure constant and electron mass affect the CMB, providing improved constraints and demonstrating the potential to probe their time dependence using Planck data.

## Contribution

It introduces a detailed analysis of time-dependent variations of fundamental constants using CMB data, validating simpler recombination models, and extends constraints on their possible variations.

## Key findings

- Planck data constrains constant variations to within a few parts per thousand.
- Time-dependent variation parameter p is consistent with zero within uncertainties.
- Simpler recombination codes are validated for accurate modeling of fundamental constant variations.

## Abstract

Observations of the CMB today allow us to answer detailed questions about the properties of our Universe, targeting both standard and non-standard physics. In this paper, we study the effects of varying fundamental constants (i.e., the fine-structure constant, $\alpha_{\rm EM}$, and electron rest mass, $m_{\rm e}$) around last scattering using the recombination codes CosmoRec and Recfast++. We approach the problem in a pedagogical manner, illustrating the importance of various effects on the free electron fraction, Thomson visibility function and CMB power spectra, highlighting various degeneracies. We demonstrate that the simpler Recfast++ treatment (based on a three-level atom approach) can be used to accurately represent the full computation of CosmoRec. We also include explicit time-dependent variations using a phenomenological power-law description. We reproduce previous Planck 2013 results in our analysis. Assuming constant variations relative to the standard values, we find the improved constraints $\alpha_{\rm EM}/\alpha_{\rm EM,0}=0.9993\pm 0.0025$ (CMB only) and $m_{\rm e}/m_{\rm e,0}= 1.0039 \pm 0.0074$ (including BAO) using Planck 2015 data. For a redshift-dependent variation, $\alpha_{\rm EM}(z)=\alpha_{\rm EM}(z_0)\,[(1+z)/1100]^p$ with $\alpha_{\rm EM}(z_0)\equiv\alpha_{\rm EM,0}$ at $z_0=1100$, we obtain $p=0.0008\pm 0.0025$. Allowing simultaneous variations of $\alpha_{\rm EM}(z_0)$ and $p$ yields $\alpha_{\rm EM}(z_0)/\alpha_{\rm EM,0} = 0.9998\pm 0.0036$ and $p = 0.0006\pm 0.0036$. We also discuss combined limits on $\alpha_{\rm EM}$ and $m_{\rm e}$. Our analysis shows that existing data is not only sensitive to the value of the fundamental constants around recombination but also its first time derivative. This suggests that a wider class of varying fundamental constant models can be probed using the CMB.