Quantum Vacuum energy as the origin of Gravity

TL;DR

The paper proposes that quantum vacuum energy $\rho_{\rm vac}$ is the origin of gravity within a semi-classical framework, formulating a gravitational Casimir effect that reproduces Friedmann dynamics with an environmental $G_N$ given by $G_N = \tfrac{c^2}{2}\, \dfrac{R_{\infty}}{M_{\infty}}$. It motivates a finite, non-perturbative vacuum energy density proportional to the lightest mass scale via $\rho_{\rm vac} = \dfrac{3}{4}\dfrac{c^5}{\hbar^3}\dfrac{m_z^4}{\mathfrak g}$, and shows how a marginally irrelevant coupling $\mathfrak g$ induces an RG flow that makes $G_N$ run with energy scale $\mu$, effectively tying the gravitational coupling to cosmological temperature via $\mu/\mu_0 = 1+z$. The resulting cosmology features a non-singular Gaussian de Sitter-like evolution with a minimal scale factor $a_{\min}=e^{-1/\hat b}$ and a symmetry $a(t) = a(-t + 2 t_{\min})$, plus small log corrections in a $\Lambda$CDM framework that can address the Hubble tension. The framework yields testable signatures, including a modest running of $G_N$ today and potential bench-top tests of temperature-dependent gravity, while remaining broadly consistent with current observational constraints. Key quantities include $\rho_{\rm vac}$, $m_z$, $\mathfrak g$, $\hat b$, $a_{\min}$, $M_{\infty}$, and $R_{\infty}$, all combined to reproduce a cosmology where gravity emerges from quantum vacuum properties.

Abstract

We explore the idea that quantum vacuum energy $ρ_{\rm vac} $ is at the origin of Gravity. We formulate a gravitational version of the electromagnetic Casimir effect, and provide an argument for how gravity can arise from $ρ_{\rm vac} $ by showing how Einstein's field equations emerge in the form of Friedmann's equations. This leads to the idea that Newton's constant $G_N$ is environmental, namely it depends on the total mass-energy of the Universe $M_\infty $ and its size $R_\infty $, with $G_N = c^2 R_\infty /2 M_\infty$. 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 $λ= 2 πR_\infty$. We assume a recently proposed formula for $ρ_{\rm vac} \sim m_z^4/\mathfrak{g}$, where $m_z$ is the mass of the lightest particle, and $\mathfrak{g}$ is a marginally irrelevant coupling. This leads to an effective, induced RG flow for Newton's constant $G_N$ as a function of an energy scale, which indicates that $G_N$ decreases at higher energies until it reaches a Landau pole at a minimal value of the cosmological scale factor $a(t) > a_{\rm min}$, 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 $a(t) = a(-t + 2 t_{\rm min})$, where $a(t_{\rm min}) = a_{\rm min}$. We propose that this energy scale dependent $G_N$ can explain the Hubble tension and we thereby constrain the coupling constant $\mathfrak{g}$ and its renormalization group parameters. For the $Λ{\rm CDM}$ model we estimate $a_{\rm min} \approx e^{-1/\hat{b} }$ where $\hat{b} \approx 0.02$ based on the Hubble tension data.