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); 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; Mäkelä PRD(13); Smolin CQG(16)-a1507 [as conjugate variable to Newton's constant]; Chernyavsky & Hajian CQG(18)-a1710 [as a conserved charge, thermodynamic approach]; Alexander et al a1807 [conjugate to Chern-Simons invariant].
@ 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]; Štefančić PLB(09)-a0807 [relaxation, from inhomogeneous equation of state]; Basilakos et al PRD(09)-a0907 [expansion and structure formation]; Porto & Zee CQG(10)-a0910, MPLA(10)-a1007-proc [relaxation, extreme ultra-IR]; 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].

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; > 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 [as a topological invariant, from small exotic \({\mathbb R}^4\)s]; > 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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