Cosmological Constant  

In General > s.a. cosmological-constant phenomenology; cosmological-constant problem; dark-energy models; mach's principle; vacuum.
* History: Introduced by Einstein in 1917 to obtain static universes.
$ Def: A constant Λ representing a vacuum energy density, introduced in the action of general relativity or the Einstein equation, respectively,

M (R − 2Λ) dv,       Rab − \(1\over2\)R gab + Λ gab = 8πG Tab .

* In quantum field theory: Usually considered to be due to zero-point energy (as pointed out by Zel'dovich in 1968), but in some proposals arises from its fluctuations; Required by symmetry breaking in the early universe, Hawking's picture of spacetime foam, or the gauged SO(n) of extended supergravity.
* In quantum gravity: The ground state for a spacetime with non-zero Λ, to the extent that it is understood, is (Anti-)de Sitter spacetime; A common handwaving argument for the natural value of Λ in quantum gravity is that dimensional considerations lead to lP−2, but arguments of the fluctuation type can also be made assuming that each spacetime element contributes an amount lP−2 to the Lagrangian density but with a fluctuating sign.

Variable Cosmological Constant, Λ as a Field > s.a. non-commutative gravity; unimodular gravity; newton's gravitational constant.
@ General references: Gasperini PLB(87), CQG(88) [thermal approach]; McGuigan PRD(90) [quantum, from t = (det q)1/2]; van Putten gq/98 [consequences]; Burdyuzha et al ap/99; Novello et al CQG(01)ht/00; Elizalde PLB(01), Caldwell ap/02 [from Casimir effect]; Donoghue JHEP(03) [gradients]; Shapiro et al PLB(03); Ahmed et al PRD(04)ap/02, Ahmed IJMPA(05)-proc [causal sets and statistical fluctuations], comment Volovik JETPL(04)gq and Barrow PRD(07)gq/06; Hsu & Zee MPLA(05) [Planck mass and size of universe]; Barceló JETPL(07)gq/06; Antoniadis et al NJP(07)gq/06 [dynamical screening by quantum field theory effects]; Xu et al a0905, PLB(10)-a0905; Yoon a0906; Ahmed & Sorkin PRD(13)-a1201; Mäkelä PRD(13); Solà IJMPD(15)-a1505-GRF [and cosmological entropy]; Smolin CQG(16)-a1507 [as conjugate variable to Newton's constant]; Chernyavsky & Hajian CQG(18)-a1710 [as a conserved charge, thermodynamic approach]; Cree et al PRD(18)-a1805; Alexander et al a1807 [conjugate to Chern-Simons invariant]; > s.a. special relativity [de Sitter version].
@ Relaxation: Brown & Teitelboim PLB(87) [dynamical neutralization]; Kim & Lee PLB(04)ht/03, Kim JPCS(10)-a1009 [self-tuning]; Štefančić PLB(09)-a0807 [from inhomogeneous equation of state]; Porto & Zee CQG(10)-a0910, MPLA(10)-a1007-proc [extreme ultra-IR]; Bauer et al PLB(09)-a0902, PLB(10)-a0912, Bauer et al CQG(10) [perturbations], JCAP(10)-a1006, Alberte et al JHEP(16)-a1608 [dynamical relaxation].
@ And cosmology: Novello et al CQG(02) [from chiral anomaly]; Aldrovandi et al G&C(05)gq/03; Shapiro & Solà ap/04-talk; Borges & Carneiro GRG(05)gq [decaying vacuum density]; Ma NPB(08)-a0708 [and constraints]; Basilakos et al PRD(09)-a0907 [expansion and structure formation]; Xu MPLA(10) [varying in time, from renormalization group]; Barrow & Shaw PRL(11)-a1007, GRG(11)-a1105-GRF, Solà JPCS(11)-a1102 [and sthe cosmological-constant problem]; Romano & Chen JCAP(11)-a1104-GRF [corrections from local inhomogeneities]; Biswas et al a1105-conf [beginning with Λ < 0]; Bisabr IJMPD(18)-a1803 [decay from gravitational coupling and expansion of the universe].
@ Running, scale dependence: Kosower MPLA(89); Bhattacharya et al PLB(00); Bonanno & Reuter JCAP(07) [from renormalization group, and cosmology]; Foot et al PLB(08)-a0712 [does not run with renormalization scale]; Shapiro & Solà a0808, PLB(09)-a0910 [it may run]; Capozziello & Funkhouser MPLA(09)-a0812 [scaling law]; Velasquez-Toribio IJMPD(12)-a0907 [and perturbations]; Ward MPLA(10) [in quantum gravity]; Hamber & Toriumi IJMPD(13)-a1301 [running would be inconsistent with general covariance]; Markkanen PRD-a1412 [curvature-induced]; Solodukhin PLB(16)-a1509 [and UV divergences in quantum gravity].
@ From fluctuations: Sorkin IJTP(97)gq; Gurzadyan & Xue MPLA(03)ap/01; Padmanabhan CQG(02)gq, CQG(05)ht/04 [and quantum gravity]; Volovik JLTP(01)gq, in(03)gq; in Dreyer ht/04; Jejjala & Minic IJMPA(07)ht/06; Elizalde JPA(07) [non-trivial topology and braneworld boundary conditions]; Sorkin AIP(07)-a0710 [causal set discreteness]; Wang et al a0806 [quantum fluctuations of spacetime]; Santos a0902, PLA(09)-a0912; Katti et al CQG(09)-a0904 [analogy with surface tension of a fluid membrane]; Broda & Szanecki AdP(10)-a0910-proc; Maggiore PRD(11)-a1004; Santos ASS(11)-a1006; de Cesare et al PLB(16)-a1603 [stochastic fluctuations of Newton's constant]; Hoga a1804-GRF [from first principles]; Viaggiu CQG(18)-a1810; > s.a. cosmic acceleration.
@ From condensate: Dymnikova & Khlopov MPLA(00) [evaporating Bose condensate]; Alexander & Vaid ht/06, ht/07 [chiral fermions in FLRW spacetime]; Finazzi et al a1204-proc [analog-gravity point of view]; Das & Bhaduri a1812 [ultralight bosons].

References > s.a. general-relativity solutions; higher-order gravity.
@ General: Einstein SPAW(17); Hawking in(82), PTRS(83); Banks NPB(85); Coughlan et al NPB(89) [and dilatations]; Strominger NPB(89) [Lorentzian quantum cosmology]; Fiziev gq/00-talk [and dilatonic gravity]; Earman SHPMP(03) [conceptual]; Aldrovandi et al IJMPD(04)gq [and fundamental physics]; Beck PhyA(09) [axiomatic approach]; Dadhich Pra-a1006; Solà IJMPA(16)-a1612 [and dynamical vacuum energy].
@ History: Harvey PT(07)apr [Schrödinger and Einstein]; Calder & Lahav A&G(08)-a0712 [early precursors, Newton]; Kragh a1111/AHES [precursors]; Harvey a1211; Kragh & Overduin 14; Lahav fs(17)-a1704; O'Raifeartaigh et al EPJH(18)-a1711 [rev]; Novosyadlyj EPJH(18)-a1712; Cohen-Tannoudji Metr(18)-a1802-conf; O'Raifeartaigh & Mitton a1804; O'Raifeartaigh PT(18)oct.
@ Reviews: Bernstein & Feinberg ed-89; Weinberg RMP(89), ap/96; Sahni & Starobinsky IJMPD(00)ap/99; Harvey & Schücking AJP(00)aug [Einstein]; Carroll LRR(01)ap/00; Peebles & Ratra RMP(03)ap/02; Padmanabhan PRP(03)ht/02; Bousso GRG(08)-a0708-ln; Martin CRAS(12)-a1205.
@ I: Maddox Nat(89)feb; Mellor SP(89); Goldsmith 95; Krauss & Turner SA(04)sep.
@ And field theory: Schützhold PRL(02) [QCD trace anomaly]; Sundrum PRD(04)ht/03 ["fat" gravity and cosmological-constant suppression]; Moffat gq/03 [graviton as bound state], gq/03-proc; Mashhoon & Wesson CQG(04)gq [5D]; Mukohyama PRD(04) [radiative corrections and stability]; Blasone et al BJP(05)ht/04 [neutrino mixing]; Volovik JETPL(05)gq-in [from macroscopic parameters]; Mahajan et al PLB(06)ap [Casimir effect: not from zero-point energy]; Ram a0705, Demir FP(09)-a0910 [as zero-point energy]; Álvarez & Vidal a1007-wd [imaginary part]; Ziaeepour MPLA(12)-a1205; Garattini a1212-proc [effects of modified dispersion relations and non-commutative geometry]; > s.a. brans-dicke theory; de sitter space [stability]; standard model.
@ As integration constant: Padmanabhan IJMPD(06)gq; Cook a0810; Banks & Fischler a1811 [as an infrared boundary condition]; > s.a. modified general relativity; unimodular gravity.
@ Other origin: Jackson & Hogan IJMPD(08)ht/07 [unconventional quantum spin-statistics]; Panković et al a0712 [holography, surface energy density]; Dale et al a0906 [vector-tensor gravity, vector-field energy density]; Azri & Bounames GRG(12)-a1007 [from 8D hypercomplex manifold]; Capozziello & Luongo Entr(11)-a1010 [from entangled states]; Kiefer et al CQG(11)-a1010 [from scalar field decoherence]; Charmousis et al JHEP(17)-a1704 [holographic self-tuning]; Asselmeyer-Maluga & Król a1709 [from small exotic \({\mathbb R}^4\)s]; Le Delliou & Lorca a1906 [topological]; > s.a. cosmic acceleration; topology change.
@ And higher dimensions: Wesson FPL(06)gq/04 [vacuum instability]; Bauer PhD(06)ht [discrete extra dimensions]; Soni et al a1509 [compact dimensions].
@ And quantum gravity: Garattini gq/04, a0910-proc [as Sturm-Liouville eigenvalue]; Capozziello & Garattini CQG(07)gq [as eigenvalue of Wheeler-DeWitt equation for f(R) theory]; Garattini JPA(08)-a0712-conf; Garattini PRD(09)-a0912 [in Hořava gravity]; Yurov et al a1212 [as Sturm-Liouville eigenvalue]; Govaerts & Zonetti PRD(13)-a1212 [lessons from 2D dilaton gravity]; Miković & Vojinović a1407 [in a Regge state-sum model]; Majid & Tao a1412 [non-commutative geometry]; Dvali & Gómez a1412 [quantum exclusion of a positive cosmological constant]; Hamada & Matsuda PRD(16)-a1511 [two-loop corrections]; Padmanabhan IJMPD(16)-a1603, a1702-conf [microstructure of spacetime]; Ng a1706-proc [different methods]; Gryb & Thébault a1801 [superpositions]; Perez et al a1804 [in terms of noisy diffusion of energy to Planck scale]; Cremaschini & Tessarotto Symm(18)-a1807; > s.a. instantons; quantum gravity and cosmology [wormholes]; spacetime geometry in quantum gravity and spin-foam models.
@ Related topics: Zel'dovich JETPL(67) [and elementary particles]; Gasperini PLB(89) [and spacetime dimension]; Henneaux & Teitelboim PLB(89) [and time]; Louko CQG(91) [discontinuity at Λ = 0?]; Datta IJMPD(96) [non-gravitating]; Aldrovandi & Barbosa gq/02 [and Lorentz group Casimir]; Aldrovandi et al FP(03) [Λ → ∞]; Mersini-Houghton gq/06 [arrow of time forbids Λ > 0]; Mazur ap/07 [from "gravitational atoms"]; Lee et al JCAP(07)ht [from entanglement energy]; Romano et al EPL(14)-a1311 [effect of primordial curvature perturbations]; Davidson & Rubin PRD(14)-a1401 [Λ = 0 in normalized general relativity]; > s.a. emergent gravity.
> Online resources: see Wikipedia page.


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