Cosmological Constant| 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].
@ Self-tuning: Kim & Lee PLB(04)ht/03;
Kim JPCS(10)-a1009;
Sobral-Blanco & Lombriser PRD(20)-a2003 [local mechanism].
@ Relaxation: Brown & Teitelboim PLB(87) [dynamical neutralization];
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 the 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];
Viaggiu a2102 [quantum fluctuations and renormalization].
@ 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,
PS(19)-a1908;
> 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(11)-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 PiP(18)-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];
Manfredi GRG(21)-a2102 [as an eigenvalue];
> s.a. modified general relativity; unimodular gravity.
@ Other origin: Lee et al JCAP(07)ht [entanglement energy];
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 PDU(18)-a1709 [from small exotic \({\mathbb R}^4\)s];
Le Delliou & Lorca PDU(20)-a1906 [topological];
Gaztañaga MNRAS(21)-a2101 [boundary term in the action];
Perez & Sudarsky GRG(21)-a1911 [energy momentum diffusion in discrete spacetime];
> 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 PLB(18)-a1801 [superpositions];
Perez et al IJMPD(18)-a1804 [in terms of noisy diffusion of energy to Planck scale];
Cremaschini & Tessarotto Symm(18)-a1807;
Zhang et al a2101 [lqg, regularization];
Koberinski FP(21)-a2101 [regularization];
> 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"];
Romano et al EPL(14)-a1311 [effect of primordial curvature perturbations];
Davidson & Rubin PRD(14)-a1401 [Λ = 0 in normalized general relativity];
> s.a. category theory; emergent gravity.
> Online resources:
see Wikipedia page.
main page
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