Cosmological measurement of the gravitational constant G using the CMB, BAO, and BBN

¹ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
² Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
³ Department of Physics & Astronomy, University of Sussex, Brighton BN1 9QH, UK

^⋆ Corresponding author: brahim.lamine@irap.omp.eu

Received: 22 July 2024
Accepted: 26 March 2025

Abstract

Recent cosmological observations have provided numerous new observations with an increasing level of precision, ushering in an era of precision cosmology. The exquisite quality of these observations opens up new possibilities in terms of measuring fundamental constants with good precision on scales that are complementary to laboratory references. In particular, the cosmic microwave background (CMB) temperature and polarisation spectra contain a wealth of information that goes well beyond the basic cosmological parameters. In this paper, we update the precision on a cosmological determination of the gravitational constant, G, by using the latest Planck data release (PR4) in combination with the latest baryon acoustic oscillation (BAO) from the Dark Energy Spectroscopic Instrument (DESI) data release 1 and the BBN prior on the primordial helium fraction. We demonstrate a precision of 1.8%, corresponding to a ∼40% improvement with regard to previous results in the literature. This is comparable to the level achieved by Cavendish in 1873 using a torsion balance. However, it is a complementary measurement because it has been obtained under wildly different physical environments compared to laboratory results or even studies of the very nearby Universe. Our analysis takes into account the modification of the primordial helium fraction predicted by Big Bang nucleosynthesis (BBN), induced by a variation in G. We also point out the importance of the polarisation data in attaining the ultimate level of precision. In particular, we discuss the constraints that can be obtained by considering either the low-ℓ or the high-ℓ part of the spectra. Within the ΛCDM model, we find G = (6.75 ± 0.12)×10⁻¹¹ m³ kg⁻¹ s⁻². This measurement is compatible with laboratory results within one standard deviation. Finally, we show that this cosmological measurement of G is robust against several assumptions made on the cosmological model, particularly when considering a non-standard dark energy fluid or non-flat models.