Deriving Entangled Relativity
Olivier Minazzoli, Maxime Wavasseur, Thomas Chehab
TL;DR
The paper investigates whether a non-linear $f(R,\mathcal{L}_m)$ gravity can reproduce General Relativity (GR) without a cosmological constant in the presence of matter. By demanding that all GR solutions with $\mathcal{L}_m = T$ on-shell also solve the $f$-theory, it derives that the scalar degree of freedom $f_R$ must be constant, leading to the entangled-relativity form $f(R,\mathcal{L}_m)=C\,\mathcal{L}_m^2/R$ and a constant coupling $\kappa$, thereby embedding all GR solutions with $\mathcal{L}_m=T$ on-shell. The analysis shows that the vacuum limit exists only as a boundary, with GR vacuum solutions recovered as matter vanishes, and discusses a broader class of intrinsic-decoupling theories in which Entangled Relativity is unique in reproducing GR in the specified limit. The work highlights that Entangled Relativity uses fewer fundamental constants and may yield testable deviations at high-density regimes, while also opening avenues to explore wormhole solutions within a consistent observational framework.
Abstract
Entangled Relativity is a non-linear reformulation of Einstein's theory that cannot be defined in the absence of matter fields. It recovers General Relativity without a cosmological constant in the weak matter density limit or whenever $\Lm = T$ on-shell, and it is also more parsimonious in terms of fundamental constants and units. In this paper, we show that Entangled Relativity can be derived from a general $f(R,\Lm)$ theory by imposing a single requirement: the theory must admit all solutions of General Relativity without a cosmological constant whenever $\Lm = T \neq 0$ on-shell, though not necessarily only those solutions. An important consequence is that all vacuum solutions of General Relativity without a cosmological constant are limits of solutions of Entangled Relativity when the matter fields tend to zero. In addition, we introduce a broader class of theories featuring an \textit{intrinsic decoupling}, which, however, do not generally admit the solutions of General Relativity.