Do Fundamental Constants Vary on Cosmological Time Scale?

Since Dirac predicted in 1937 possible variation of gravitational constant and other coupling constants over cosmological time scales from his large number hypothesis, efforts have continued to determine such variation without success. Such efforts focus on the variation of one constant while assuming all others are pegged to their currently measured values. I have shown that the variations of the speed of light 𝑐, the gravitational constant 𝐺, the Planck constant ℎ, and the Boltzmann constant 𝑘 are interrelated - 𝐺~𝑐³~ℎ³~𝑘^3/2 - through a dimensionless function. Thus, constraining any one of the constants leads to inadvertently constraining all the others. It may not be possible to determine the variation of a constant without concurrently permitting the variation of others. I will discuss several cosmological, astrometric, and terrestrial measurements that I have explained recently with the concomitant variation of these constants using their current time variation as 𝐺'⁄𝐺 = 3 𝑐'⁄𝑐 = 3 ℎ'⁄ℎ = 3⁄2 𝑘'⁄𝑘 = 3.90(±0.04) × 10−10 yr −1 . They include gravitational lensing, gravitational waves, supernovae, quasars, gamma-ray bursts, lunar laser ranging, pulsars, and primordial nucleosynthesis used for constraining constants’ variation. The approach yields the age of the Universe 50% more than the presently accepted value; it may be better suited for explaining bewildering high redshift observations of galactic structures by the James Webb Space Telescope.