The Hubble-Lemaitre Tension and Redshift Dependent Gravitational Constant

In this study, we analyze the Hubble-Lemaitre(H-L) tension △H_T = H₀(local) - H₀(CMB). We model △H_T and find that the tension arises from H-L constants derived from two different cosmologies, the standard model and the R=ct model. We find that an R=ct background cosmology correctly predicts the cosmic age, τ₀ = 1/( H₀) . Surprisingly, △H_T=0 requires that the Newton constant G₀ be generalized by a redshift evolving gravitational constant G(z). We propose an extension of the base ΛCDM model with G(z).

H²(z) = [8πG(z)]/3 ρ₀ E(z)

We find a relationship between the local and the CMB-determined values of the Hubble-Lemaitre constants,



H₀(local) = H₀(CMB)/0.95

Observed values are in good agreement with this relation. From Planck measurements H₀(CMB), an estimate of the expected H-L constant is H₀(local) ≈ 71 [km/(s-Mpc)].

Finally, the physical origin of the H-L tension is fundamentally rooted in assumptions of how the gravitational constant evolves through cosmic time. We discuss SN1a observations that suggest support for G(z).