Emergent Gravity and the Dark Universe

TL;DR

This work proposes that spacetime and gravity are emergent from quantum entanglement, with de Sitter space exhibiting a volume-law contribution to entropy that alters gravity at cosmological scales. By treating matter as creating a local entropy displacement within a dark-energy medium, the theory maps the gravitational response to an elastic memory effect, producing an additional dark gravity force that accounts for galaxy and cluster phenomenology without invoking particle dark matter. A central result is a Milgrom-like scaling, with $g_D=\sqrt{g_B a_M}$ and $a_M = a_0/6$ in $d=4$, derived from an elastic-energy balance and a Tully–Fisher–type relation for apparent dark matter density. The framework connects holographic ideas, tensor-network descriptions, and thermodynamic gravity to observational scaling relations, offering a conceptual alternative to ΛCDM while highlighting open cosmological questions and the role of the acceleration scale $a_0$.

Abstract

Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional `dark' gravitational force describing the `elastic' response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale a_0 =cH_0, and provide evidence for the fact that this additional `dark gravity~force' explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

Figures (5)

• Figure 1: Two possible quantum entanglement patterns of de Sitter space with a one-sided horizon. The entanglement between EPR pairs is represented pictorially by tiny ER-bridges. The entanglement is long range and connects bulk excitations that carry the positive dark energy either with the states on the horizon (left) or primarily with each other (right). Both situations leads to a thermal volume law contribution to the entanglement entropy.
• Figure 2: In AdS (left) the entanglement entropy obeys a strict area law and all information is stored on the boundary. In dS (right) the information delocalizes into the bulk volume. Only in dS the matter creates a memory effect in the dark energy medium by removing the entropy from an inclusion region.
• Figure 3: The Penrose diagram of global de Sitter space with a mass in the center of the static patch. The global solution requires that an equal mass is put at the anti-podal point.
• Figure 4: The one-sided perspective on de Sitter space with a mass $M$ in the center. The entropy associated with the horizon area is contained in delocalized states that occupy the bulk. The mass $M$ removes part of, and therefore displaces, the entropy content in the interior.
• Figure 5: When a certain amount of volume $V_0^*$ is being removed from an incompressible elastic medium it leads to a displacement $\ u(r) = -V_0^*/A(r)$.