Spacetime Foam  

In General > s.a. cell complex [froth]; equivalence principle [violations].
* Idea: A version of quantum spacetime, modeled as a differentiable manifold with fluctuating small-scale topology; Introduced by Wheeler, could lead to consider particle phenomenology as a "chemistry of geometry"; To make this more precise, we must understand the quantum gravity vacuum and its fluctuations; Some versions of spacetime foam can be seen as a "sea of virtual black holes".
* Conditions: It requires a cosmological constant (at least in Hawking's picture).
@ General: Wheeler AP(57), 62 pp 71-83; Hawking NPB(78), in(79); Crane & Smolin GRG(85), NPB(86); Friedman et al NPB(88) [and fermions]; Kirillov & Turaev G&C(03)ht/01 [Coulomb & Newton V]; Ng gq/04-MGX, LNP(05)gq/04 [and information]; Frenkel a1011 ["spacetime foam formulas"]; Ng a1102-proc.
@ Phenomenological description: Amelino-Camelia gq/01.

Models > s.a. finsler geometry; kaluza-klein theory; spin foam; string phenomenology.
* Strings and branes: The foamy structures are provided by lower-dimensional background brane defects in a D3-brane Universe, whose density is a free parameter to be constrained phenomenologically.
@ Algebraic approach: Baez pr(84); Heller & Sasin IJTP(97) [classical model]; Raptis & Zapatrin CQG(01)gq.
@ Gas / superposition of wormholes: Preparata et al GRG(00)gq/98 [quantum gravity ground state]; Garattini PLB(99)ht/98 [semiclassical wormholes], ZN(01)gq/00-proc, JOB(02)gq/01-proc, IJMPA(02)gq/01, IJTGN(02)gq [Reissner-Nordström wormholes]; Cacciatori et al PLB(98)ht/97; Requardt a0910 [non-local correlations and black-hole entropy, holography, entanglement].
@ Strings and branes: Ellis et al PRD(01)ht/00 [interactions and GZK cutoff]; Iqbal et al JHEP(08)ht/03 [topological strings]; Hartnoll & Policastro ATMP(06)ht/04 [twistor string theory]; Mavromatos AIP(09)-a0909, IJMPA(10)-a1010, JPCS(11)-a1010 [phenomenology]; Mavromatos et al PLB(11) [and Finsler metrics]; > s.a. phenomenology of cosmological perturbations [structure formation].
@ Other models: Alberty PLB(89) [2D]; Seriu PLB(93); Redmount & Suen PRD(93), PRD(94)gq/93; Nergiz & Saclioglu PRD(96)ht/95 [quasi-periodic Gibbons-Hawking metric]; Zizzi IJTP(99) [and de Sitter space]; Dzhunushaliev IJMPD(02)gq/00, gq/00-conf, FP(02)gq/01 [dielectric]; Braden & Nekrasov CMP(04) [non-commutative instantons]; Bernadotte & Klinkhamer PRD(07) [classical model with defects in Minkowski]; Ng PLB(97)gq, Ent(08)-a0801, a1001-conf [holographic]; Queiruga a1912 [non-metricity tensor]; > s.a. quantum spacetime models; topology change; wormholes [gas].

Consequences > s.a. black-hole entropy; quantum-gravity phenomenology; gravitational thermodynamics.
@ Gravity: Hawking PRD(96) [virtual black holes, black-hole evaporation]; Garattini MPLA(98)gq, IJMPA(99)gq/98, ht/99-TX19 [black-hole pair production]; Garattini NPPS(00)gq/99 [black-hole entropy, cosmological constant], IJMPD(02)gq/00 [cosmological constant]; Dzhunushaliev IJMPD(02)gq/00, gq/00-conf [polarization by wormhole]; Mäkelä & Peltola PRD(04)gq/03 [Schwarzschild horizon]; Schulz FdP(18)-a1810 [cosmological constant, problem of time].
@ Cosmology: Liu et al PRD(95) [entropy and flatness without inflation]; Kirillov ap/07/MNRAS [dark energy, dark matter, etc]; Arzano et al PLB(07) [holographic foam]; Ng AIP(09)-a0808, a1910 [holographic foam and dark energy]; > s.a. dark energy.
@ Thermal properties: Garay PRL(98)gq, PRD(98)gq; Rosales gq/99 [electroweak coupling]; Liu & Ma IJMP(00)gq/99; Agnese & La Camera NCB(01)gq/00 [black hole horizons]; Garattini PLB(99)ht, Ent(00)gq, IJMPA(02)gq/01 [entropy].
@ Field propagation, matter: Hawking PRD(96) [loss of coherence, Higgs particle, θQCD]; Garay IJMPA(99)gq; Kirillov ht/00-proc [quantum field theory]; Kirillov & Savelova a0806 [path integral and cutoff], a0808 [behavior of bosonic systems], G&C(08) [astrophysical effects]; Mavromatos & Sarkar NJP(08) [model of flavour vacua]; Kirillov et al PLB(08)-a0802 [cosmic-ray propagation]; Sarkar FP(10) [neutral-kaon entanglement correlations]; Savelova GRG(16)-a1405 [anisotropy in the vacuum speed of light, and dispersion]; Oniga & Wang PRD(16)-a1603 [bosonic fields]; > s.a. field theory phenomenology; matter phenomenology; photon phenomenology.

"When I hear that spacetime becomes a foam at the Planck scale, I don't reach for my gun. (I haven't any.)
But I do wonder what that foam has to do with the macroscopic events that spacetime was constructed
to represent and the macroscopic means we use to locate events. — N D Mermin

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