Induced gravity (or Emergent gravity) is an idea in quantum gravity that space-time background emerges as a mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics approximation of Bose–Einstein condensates. The concept was originally proposed by Andrei Sakharov in 1967.
Sakharov observed that many condensed matter systems give rise to emergent phenomena which are identical to general relativity quantitatively. Crystal defects can look like torsion, for example. His idea was to start with an arbitrary background pseudo-Riemannian manifold (in modern treatments, possibly with torsion) and introduce quantum fields (matter) on it but not introduce any gravitational dynamics explicitly. This gives rise to an effective action which to one-loop order contains the Einstein-Hilbert action with a cosmological constant. In other words, general relativity arises as an emergent property of matter fields and is not put in by hand. On the other hand, such models typically predict huge cosmological constants.
The particular models proposed by Sakharov and others have been proven impossible by the Weinberg-Witten theorem. However, models with emergent gravity are possible as long as other things, such as spacetime dimensions, emerge together with gravity. Developments in AdS/CFT correspondence after 1997 suggest that the microphysical degrees of freedom in induced gravity might be radically different. The bulk space-time arises as an emergent phenomenon of the quantum degrees of freedom that live in the boundary of the space-time.
- A.D. Sakharov, VACUUM QUANTUM FLUCTUATIONS IN CURVED SPACE AND THE THEORY OF GRAVITATION, 1967.
- Carlos Barcelo, Stefano Liberati, Matt Visser, Living Rev.Rel. 8:12, 2005.
- D. Berenstein, Emergent Gravity from CFT, online lecture.
- C. J. Hogan Quantum Indeterminacy of Emergent Spacetime, preprint
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