Historical research guide · 0443 · 2017
Emergent Gravity and the Dark Universe
Erik P. Verlinde
In one minute
Erik Verlinde argues that gravity is not fundamental. Spacetime, in this picture, is the pattern of quantum entanglement in a deeper microscopic state, and gravity is what a change in that pattern looks like when matter is present. The derivation works cleanly in a universe with negative curvature; this paper carries it into a universe like ours, one with positive dark energy and a cosmological horizon. Verlinde’s proposal is that the horizon’s enormous entropy is not stuck on the horizon but spread through the volume, carried by slowly thermalising states that we measure as dark energy. Matter displaces some of that entropy, and the medium pushes back — an elastic response which, to an astronomer, looks exactly like extra gravity from unseen matter. The push-back becomes noticeable precisely where the observed missing mass appears, below a surface density set by the Hubble acceleration scale, and it reproduces the baryonic Tully-Fisher relation of spiral galaxies with no adjustable parameter.
Connection
This is chapter 3’s argument — that gravity is induced rather than fundamental — carried all the way to an observational prediction, and chapter 5’s picture of the vacuum as a medium with a mechanical response, written in the language of entanglement rather than fluid dynamics. It is also chapter 13’s move in its purest form: dark energy and dark matter stop being two mysteries and become one property of spacetime.
From the source
Spacetime geometry represents the entanglement structure of an underlying microscopic quantum state, and gravity emerges as the description of the change in entanglement caused by matter; in Anti-de Sitter space this has been carried far enough that the linearised Einstein equations follow from general quantum-information principles.Section 1.1, Emergent spacetime and gravity from quantum information
De Sitter space corresponds microscopically to an ensemble of metastable quantum states that together carry the Bekenstein-Hawking entropy of the cosmological horizon, and the thermal excitations responsible for that entropy constitute the positive dark energy — so dark energy and the accelerated expansion are caused by the slow thermalisation of emergent spacetime.Section 1.2, Emergent gravity in de Sitter space; hypothesis of section 2
The phenomena attributed to dark matter — flattened rotation curves, weak-lensing excess — appear only when the surface mass density falls below a universal value set by the Hubble acceleration scale divided by eight pi times Newton’s constant, which is equivalently the statement that the entropy change caused by adding the mass stays below the entropy of a black hole that would fit inside the same region.Section 1.3, Equations (3) and (4)
The volume-law contribution to the entanglement entropy turns the otherwise stiff geometry of spacetime into an elastic medium whose response is an extra dark gravitational force; in four dimensions the resulting scaling relation between the apparent dark and baryonic accelerations is the baryonic Tully-Fisher relation, with the Milgrom acceleration coming out as the Hubble acceleration scale divided by six — and Verlinde is explicit that this is an estimate of the strength of the extra force, not a new law of gravity or of inertia.Section 1.4, Equations (5) to (7); Section 7.2, Equations (102) and (103)
The paper’s central formula relates the apparent dark matter mass to the baryonic mass distribution for approximately spherical, isolated, non-dynamical systems with no freely adjustable parameters, and because cluster gas is extended rather than central it yields between 1.5 and 3.5 times more apparent dark matter than modified Newtonian dynamics, significantly reducing and possibly removing the cluster missing-mass problem.Section 7.2, Equations (99) and (106)
Whether emergent gravity can reproduce the acoustic peaks of the cosmic microwave background, structure formation and the cosmological evolution of the universe is left open: the analysis is static and assumes dark-energy domination, so the verdict against the particle dark-matter paradigm at early times waits on that work.Section 8.2, Emergent gravity and apparent dark matter in cosmological scenarios
The way in
https://doi.org/10.21468/SciPostPhys.2.3.016How to cite it
Erik P. Verlinde (2017) Emergent Gravity and the Dark Universe doi:10.21468/SciPostPhys.2.3.016