The Cosmological-Constant Problem  

In General > s.a. boundaries in field theory; branes; quintessence; vacuum.
* Idea: The current formulation of the problem is, Why is the observed value of the cosmological constant so small (e.g., after so many phase transitions)? [Before 1997-1998, the question usually was, Why is its observed value zero?]
* Second problem: The coincidence between the epoch of galaxy formation tgal and the epoch of Λ-domination tcc; > s.a. Coincidence Problem.
@ Reviews: Adler et al AJP(95)jul; Dolgov ap/97-proc; Weinberg ap/00-conf; Straumann ap/00-conf, ap/02-conf, gq/02-conf; Brax CP(04); Banks PT(04)mar; Nobbenhuis PhD(06)gq [approaches]; Solà JPCS(13)-a1306 [pedagogical]; Burgess a1309-ln [the naturalness problem and microphysics]; Padilla a1502-ln; Ng a1706-proc [approaches].
@ And the equivalence principle: Bertolami IJMPD(09) [violation]; Ginat a2105-GRF [the equivalence principle helps].

Higher-Dimensional Proposed Solutions
* Idea: Many proposals have been made; 2000, recent ones include large extra dimensions (> see brane cosmology).
@ Strings / M-theory: Witten MPLA(95)ht, Kane et al PLB(05) [string vacua]; McGuigan ht/06, ht/06 [seesaw]; Hawking & Hertog PRD(06) + pn(06)jun; de Alwis PLB(07)ht/06; Bousso ht/06-talk [local values and the landscape]; Barvinsky PRL(07); Kiefer et al CQG(11)-a1010 [landscape-motivated]; Avilán & Roldán a1011; Bousso a1203-proc [and the string theory landscape]; Sumitomo & Tye JCAP(12)-a1204 [simple stringy mechanism]; > s.a. string phenomenology.
@ Brane world: Burgess et al PLB(00); Förste et al JHEP(00); Chen et al JHEP(00); Arkani-Hamed et al PLB(00)ht; Kakushadze PLB(00)ht, PLB(00)ht, PLB(00)ht; de Alwis NPB(01); Flanagan et al PRD(01) [and hierarchy]; Tye & Wasserman PRL(01); Nojiri et al RMF(02)ht/01; Corradini et al MPLA(03), IJMPA(03)ht/02; Sorkin BJP(05)gq-proc [the value of Λ would be too small]; Ellwanger MPLA(05); Steinhard & Turok Sci(06)ap + pw(06)may [cyclic universe with decreasing cosmological constant], comment Vilenkin Sci(06)ap; Diakonos & Saridakis JCAP(09)-a0708; Shao & Chen PRD(10)-a1005.
@ Other higher-dimensional: Wesson & Liu IJMPD(01)gq [Kaluza-Klein theory]; Erdem JPA(07)gq/06-conf, JPA(08)-a0712 [symmetries]; Hertzberg & Masoumi JCAP(16)-a1509.

Quantum Gravity and Modified-Gravity Solutions > s.a. modified general relativity; time in quantum theory.
* Conformal gravity: The theory naturally quenches the amount by which the cosmological constant gravitates, rather than its value.
@ Quantum cosmology: Hawking PLB(84); Weiss PLB(87), Duff PLB(89) [criticism]; Wu PLB(08)-a0709; Shaw & Barrow PRD(11)-a1010 [value depends on observation time]; Larsen et al PRD(11)-a1107 [in the quantum multiverse]; Jalalzadeh et al PDU-a1709 [q-deformed]; > s.a. quantum gravity phenomenology [including wormholes, baby universes].
@ Lattice-type approaches: Vergeles ht/04 [lattice quantum gravity]; Loll et al NPB(06) [2D causal, with topology change].
@ And discrete spacetime: Mok ap/01; Trout a1208, a1208; Miković & Vojinović EPL(15)-a1407 [quantum Regge calculus approach].
@ Other quantum gravity: Özer NPB(91) [third quantization]; Alexander & Calcagni PLB(09)-a0806 [superconducting lqg]; Mannheim MPLA(11)-a1005-conf [intrinsically quantum-mechanical gravity]; Miao & Zhao IJMPD(14)-a1312 [and gup]; Moffat a1407-proc [finite, unitary non-local formulation]; Carlip PRL(19)-a1809, comment Wang & Unruh a1911, reply Carlip a1911, comment Piattella a2007 [high curvature at Planck scales, hidden at observable scales]; Hogan a2003 [gravitational drag from coherent energy flows]; > s.a. approaches to quantum gravity [gravity as condensate]; non-commutative cosmology.
@ Related proposals: Linde PLB(88) [two universes]; Özer gq/00 [from gravity + electromagnetism unification]; Sundrum PRD(04)ht/03 [fat gravitons]; Alexander et al ht/04 [vacuum gravitational instability]; Novello PoS-ap/05 [and graviton mass]; Prokopec gq/06 [semiclassical general relativity + matter]; Nojiri et al PLB(11)-a1010 [non-local gravity]; García-Aspeitia a1011 [2D spacetime and Planck scale]; Aslanbeigi et al PRD(11)-a1106, Wondrak a1705-conf [gravitational aether]; Wilson JModP(13)-a1111; Finazzi et al PRL(12) + news at(12)feb, PhysOrg(12)mar [analog gravity and BECs]; Mannheim a1703-GRF [fully quantum-mechanically consistent conformal gravity]; Carroll & Remmen PRD(17)-a1703 [non-local constraint on the action]; Vasak et al a1802 [covariant canonical gauge theory of gravity]; Xiong a1805; Appleby & Linder a2009 [well tempering]; > s.a. Übergravity.

Other Proposed Solutions > s.a. cosmological constant [scale dependence, variation, etc]; particle statistics [quons].
* Remark: Supersymmetry doesn't help, it is broken!
@ From vacuum fluctuations: Gurzadyan & Xue MPLA(03)ap/01, ap/05; Padmanabhan CQG(05)ht/04; Qi ht/05 [QED]; Samuel & Sinha PRL(06)cm [surface tension analog]; Beck & Mackey PhyA(07)ap/06 [measurability]; Doran & Jaeckel JCAP(06)ap [and measurements]; Maggiore PRD(11); Wang et al PRD(17)-a1703 [gravitating vacuum energy]; Wetterich PLB(17)-a1704 [graviton fluctuations]; Pejhan et al PLB(18)-a1808 [from the Krein-Gupta-Bleuler vacuum]; Brax & Valageas a1903 [cancellation mechanism]; Carlip a1905-GRF [hidden by spacetime foam]; Bengochea et al a1906 [problematic]; Viaggiu FP-a1910 [and metric averaging procedure]; Leonhardt a2001 [in Lifshitz theory]; Lozano & Mazzitelli a2008 [oscillating universe from random fluctuations].
@ Supersymmetric: Jejjala et al GRG(03)ht-GRF [holography and supersymmetry]; Froggatt et al NPB(06) [supergravity models].
@ And holography: Arzano et al PLB(07)gq/06; Carneiro IJMPD(03)gq-GRF; > s.a. holography.
@ Other fields: Barr et al PRD(06) [cancellation by cosmon]; Klinkhamer & Volovik JETPL(10)-a0907 [extension of standard model]; Popławski AdP(11)-a1105 [quarks and torsion]; Emelyanov & Klinkhamer PRD(12)-a1107, PRD(12)-a1109, Klinkhamer PRD(12) [two massless vector fields]; Padmanabhan & Padmanabhan IJMPD(13)-a1302 [inflation and particle physics parameters]; Nojiri MPLA(16)-a1601 [topological field theory]; Ahluwalia a2008 [spin-1/2 boson].
@ Other proposals: Duncan & Jensen NPB(90) [4-form dynamics]; Ghoroku CQG(91); Ng IJMPD(92); Squires PLA(92); Sivaram MPLA(99) [early-universe phase transition]; Nobbenhuis FP(06)gq/04; Jackiw et al PLA(05)ht [λφ4 field in AdS]; Triay IJMPD(05)gq; Nishino & Rajpoot MPLA(06) [Hodge duality]; Freese et al PLB(06) [devaluation]; 't Hooft & Nobbenhuis CQG(06)gq [complex transformations]; Shapiro & Solà JPA(07)gq/06-conf; Comelli IJMPA(08)-a0704 [modified Lagrangian]; O'Connell PLA(07) [causality-based]; Rodrigo CQG(07)-a0705 [void bubbles]; Andrianov et al PLB(07) [and spontaneous symmetry breaking]; Urban & Zhitnitsky JCAP(09)-a0906 [standard-model physics]; Linde & Vanchurin a1011 ["non-anthropic"]; Koksma & Prokopec a1105 [Lorentz invariance of the vacuum]; Maia IJMPcs(11)-a1107-talk [and spacetime deformation]; Darabi a1107; Astashenok & Del Popolo CQG(12)-a1203 [with volume averaging]; Jain et al IJMPA(15)-a1408 [conformal symmetry breaking]; Kourkoulou et al a2101 [non-trivial cancellations, analog model].

Other Proposed Solutions > s.a. dynamical wave-function collapse; Topos Theory.
* Anthropic approach: There is a probability distribution of values of the cosmological constant in different regions, and we live in one that is conducive to life.
@ Anthropic approach: in Barrow & Tipler 86, ch6; Weinberg PRL(87); Efstathiou MNRAS(95); Garriga et al PRD(00)ap/99; Donoghue JHEP(00); Förste et al PLB(00)gq; Garriga & Vilenkin PRD(00)ap/99, PRD(01)ht/00; Barrow et al PRD(02)ap/01; Banks et al JHEP(01); Vilenkin in(03)ht/01; Graesser et al PLB(04)ht; Garriga & Vilenkin PTPS(06)ht/05; Loeb JCAP(06)ap [observational test]; Starkman & Trotta PRL(06)ap, Trotta & Starkman AIP(06)ap [against]; Pogosian & Vilenkin JCAP(07)ap/06 [and WMAP-3 data]; Bousso et al PRD(07)ht [causal entropic principle]; Miralda-Escudé ap/07 [stryngbohtyk model]; Peacock MNRAS(07)-a0705; Olum & Schwartz-Perlov JCAP(07)-a0705 [in a large toy landscape]; Maor et al PRL(08)-a0709 [criticism]; Mersini-Houghton & Adams CQG(08)-a0810 [limitations]; Maia & Capistrano IJMPA(09)-a0905; Iorio MNRAS(10)-a0911 [the Sun's motion through the Milky Way]; Hong et al PRD(12)-a1110 [and primordial density perturbations]; Hartle & Hertog PRD(13)-a1309 [anthropic bounds from the no-boundary quantum state]; Berolami & Páramos GRG(20) [non-minimally coupled].
@ No zero-point energy contributions: Kimpton & Padilla JHEP(12)-a1112; Bernard & LeClair PRD(13)-a1211; Kaloper & Padilla PRL(14)-a1309, PRD(104)-a1406 [sequestering]; Fujii a1403; Balitsky & Kiselev PRD(14)-a1406 [vacuum energy suppression]; Barrow & Cotsakis a1907 [traceless f(R) gravity]; Yargic et al PRD-a2001 [only part of the stress-energy tensor gravitates]; Donoghue a2009 [in perturbation theory]; > s.a. canonical quantization [covariant].

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