Quantum Vacuum energy as the origin of Gravity

Abstract

We explore the idea that quantum vacuum energy ${\rho }_{\mathrm{vac}}$ 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 ${\rho }_{\mathrm{vac}}$ 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 $G_N=c^2{R}_{\infty }/2M_{\infty }$. 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 $\lambda =2\pi R_{\infty }$. We assume a recently proposed formula for ${\rho }_{\mathrm{vac}}\sim m_z^4/\mathfrak{g}$, 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 $a(t)>a_{\min }$, 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 $a(t)=a(-t+2t_{\min })$, where $a(t_{\min })=a_{\min }$. 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 $\Lambda \mathrm{CDM}$ model we estimate $a_{\min }\approx e^{-1/\hat{b}}$ where $\hat{b}\approx 0.02$ based on the Hubble tension data.

Comments: This version: in our reinterpretation of the entropy, \hbar in E_\lambda should have been h, otherwise \lambda is the reduced wavelength. Some comments added connecting with the Matsubara temperature for dS