Temperature of the Vacuum

TL;DR

This work investigates how a virial temperature ${\cal T}$, derived from a Statistical Theory of Gravity, imprints structure on the quantum vacuum of spacetime and couples to curvature through $\langle R\rangle_\beta \approx 16\pi G{\cal T}/c^4\bar{\upsilon}$. It analyzes a real massless scalar field in a Local Lorentz Frame to derive the vacuum pair-correlation function $g(x,x')$ and a temperature-dependent vacuum energy density, yielding $\rho \approx \frac{\Lambda^4}{16\pi^2}-2\kappa{\cal T}$ under simplifying approximations. Three approximations connect LLF results to curved spacetime, enabling a temperature-sensitive description of the spacetime vacuum's structure and predicting oscillatory temporal features at low ${\cal T}$. Overall, the study frames the quantum vacuum as a curvature‑coupled, thermally driven medium with potential implications for dark energy and cosmological evolution.

Abstract

In a recent trilogy we proposed a Statistical Theory of General Relativity spacetime. Here we apply our new theory to determine the (energy) ``density'' and (virial) ``temperature'' dependence of the structure of the spacetime quantum vacuum working on the simple case of a real massless scalar field in a local Lorentz frame.

Figures (2)

• Figure 1: The LLF pair correlation function $g(\xi)$ of Eq. (\ref{['eq:pcf']}): when the separation of the events $x$ and $x'$ is time-like for ${\boldsymbol r}={\boldsymbol r}'$, $\Delta\xi=|t-t'|$ and when it is space-like for $t=t'$, $\Delta\xi=|{\boldsymbol r}-{\boldsymbol r}'|$.
• Figure 2: The GR pair correlation function $g(\xi)$ of Eq. (\ref{['eq:pcfgr']}) at two temperatures ${\cal T}=0,1$: when the separation of the events $x$ and $x'$ is time-like for ${\boldsymbol r}={\boldsymbol r}'$, $\Delta\xi=|t-t'|$ and when it is space-like for $t=t'$, $\Delta\xi=|{\boldsymbol r}-{\boldsymbol r}'|$.