Quantum Vacuum energy as the origin of Gravity

We explore the idea that quantum vacuum energy ρvac is at the origin of Gravity as a theoretical exercise. We formulate a gravitational version of the electromagnetic Casimir effect, and provide an argument for how gravity can arise from ρvac by showing how Einstein's field equations emerge in the form of Friedmann's equations. This leads to the idea that Newton's constant GN is environmental, namely it depends on the total mass-energy of the Universe M_∞ and its size R_∞, with GN = c² R_∞ /2 M_∞. This leads to a new interpretation of the Gibbons-Hawking entropy of de Sitter space, and also the Bekenstein-Hawking entropy for black holes, wherein the quantum information bits are quantized massless particles at the horizon with wavelength λ= 2 πR_∞. We assume a recently proposed formula for ρvac ~ mz⁴/g, where mz is the mass of the lightest particle, and g is a marginally irrelevant coupling. This leads to an effective, induced RG flow for Newton's constant GN as a function of an energy scale, which indicates that GN decreases at higher energies until it reaches a Landau pole at a minimal value of the cosmological scale factor a(t) > aₘᵢₙ, thus avoiding the usual geometric singularity at $a=0$. The solution to the scale factor satisfies an interesting symmetry between the far past and far future due to a(t) = a(-t + 2 tₘᵢₙ), where a(tₘᵢₙ) = aₘᵢₙ. We propose that this energy scale dependent GN can explain the Hubble tension and we thereby constrain the coupling constant g and its renormalization group parameters. For the Λ CDM model we estimate aₘᵢₙ ≈ e-1/b̂ where b̂ ≈ 0.02 based on the Hubble tension data.