Cosmological
Constant| Cosmological
Constant |
In General > s.a. cosmological
constant problem; mach's
principle; vacuum.
* History: Introduced
by Einstein in 1917 to obtain static universes.
$ Def: A constant 
representing
a vacuum energy density,
introduced in the action of general relativity or in the Einstein equation,
respectively,
M (R – 2)
dv, Rab– 
R gab+ gab =
8
G 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 nonzero ,
to the extent that it is understood, is (Anti-)de Sitter spacetime; A common
handwaving argument for the natural value of in
quantum gravity is that dimensional considerations lead to lP–2,
but arguments of the fluctuation type can also be made assuming that each st
element contributes an amount lP–2 to
the lagrangian density but with a fluctuating sign.
Consequences and Observation > s.a. black
hole radiation; cosmological
models; dark
energy; quintessence.
* Value: From small
clusters of galaxies, |
vacuum|
= ||
/ 8 < 10–57 cm–2;
From the fact that the radius of curvature
of
the observable universe is basically infinite, < 10–122 lP–2;
From 2001 cosmological model, 2.036 
10–35
s–2; 2003, WMAP results indicate = LU–2,
LU = 2.85 
0.25
Mpc, or equivalent amount of dark energy.
@ Measurement: Phillips MNRAS(94); Balaguera-Antolinez
et al IJMPD(05)gq/04 [astrophysical
bounds]; Vanderveld et al PRD(07)-a0706 [corrections
from inhomogeneities]; Chiba & Nakamura a0708-PTP
[null test].
@ And lensing: Kochanek ApJ(96)ap/95 [ < 0.66,
flat cosmology]; Cheng & Krauss IJMPA(00)ap/98 [0.25 < < 0.55,
flat cosmology].
@ And cosmology: in Visser 95 [geometry]; Krauss ap/96 [ < 0],
ApJ(98)ap/97,
hp/98-in
[age of galaxies]; Ishak et al a0710 [lensing].
@ And other astronomy: Sereno & Jetzer PRD(06)ap [solar
and stellar systems]; Iorio IJMPD(06),
a0710 [solar
system]; Erni & Tammann ap/06 [nearby
supernovas]; Jetzer & Sereno NCB(07)-a0711-in
[solar system].
@ The case for non-zero cosmological constant: Efstathiou et al Nat(90);
Krisciunas JRASC(93)ap;
Krauss & Turner
GRG(95);
Ostriker & Steinhardt Nat(95);
Roos & Harun-or-Rashid A&A(98)ap/97;
Neupane gq/98;
Zehavi & Dekel
Nat(99)ap;
Frampton ap/99-in;
Lineweaver ap/99 [obs];
Mannheim ap/99-in, ap/99-in,
ApJ(01)ap/99 [conformal
gravity]; Carmeli & Kuzmenko ap/01-in,
IJTP(02)ap/01 [cosmological
model]; Trotta et al PRD(03)ap/02 [Bayesian
vs frequentist]; Böhmer ap/05-wd.
@ Consequences of non-zero cosmological constant: Cohn ASS(98)ap;
Whitehouse & Kraniotis
ap/99 [rotation
curves]; Axenides et al MPLA(00)ap [modified
motion]; Banks ht/00,
GRG(03)ht [susy
breaking]; Miguel & Pereira IJMPD(01)gq/00 [speed
of light]; Dyson
et al JHEP(02)ht [and
holography]; Böhmer & Harko PLB(05)
[minimum mass]; Balaguera-Antolinez et al CQG(06)gq/95;
Nowakowski & Balaguera-Antolinez ap/06-in
[in astrophysics]; Peirani & De Freitas A&A-a0806 [galaxy groups].
> Effects: see cosmic
acceleration; energy [virial
theorem]; galaxy distribution;
gravitational phenomenology [PN]; tests
of general relativity.
Variable Cosmological Constant > s.a. non-commutative
gravity; unimodular
gravity; variation
of constants.
@ 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].
@ And cosmology: Novello et al CQG(02)
[from chiral anomaly]; Aldrovandi et al G&C(05)gq/03;
Shapiro & Sola ap/04-in;
Borges & Carneiro GRG(05)gq [decaying
vacuum density]; Ma a0708 [and constraints].
@ 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].
@ 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;
Ahmed
et al PRD(04)ap/02,
Ahmed IJMPA(05)in
[causal sets and statistical fluctuations], comment Volovik JETPL(04)gq and
Barrow PRD(07)gq/06;
Jejjala & Minic IJMPA(07)ht/06;
Elizalde JPA(07)
[non-trivial topology and braneworld boundary conditions]; Sorkin a0710-in
[causal set discreteness]; Wang et al a0806 [quantum
fluctuations of spacetime]; > s.a. cosmic
acceleration.
@ From condensate: Dymnikova & Khlopov MPLA(00)
[evaporating Bose condensate]; Alexander & Vaid ht/06,
ht/07 [chiral
fermions in FRW spacetime].
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-in
[and dilatonic gravity]; Earman SHPMP(03)
[conceptual]; Aldrovandi et al IJMPD(04)gq [and
fundamental physics]; Bousso a0709-ln.
@ History: Harvey PT(07)apr
[Schrödinger and Einstein]; Calder & Lahav a0712 [early
precursors, Newton].
@ Reviews: Bernstein & Feinberg ed-89; Weinberg RMP(89),
ap/96;
Sahni & Starobinsky
IJMPD(00)ap/99;
Harvey & Schücking AJP(00)
[Einstein]; Carroll LRR(01)ap/00;
Peebles & Ratra RMP(03)ap/02;
Padmanabhan PRP(03)ht/02;
Bousso a0708-ln.
@ 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-in;
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 [as
zero-point energy]; > s.a. brans-dicke, standard
model;
wormholes.
@ As integration constant: Padmanabhan IJMPD(06)gq; > s.a. modified
general relativity, unimodular gravity.
@ Other origin: Jackson & Hogan ht/07 [unconventional
quantum spin-statistics]; Pankovic et al a0712 [holography, surface energy
density].
@ And higher dimensions: Wesson FPL(06)gq/04 [vacuum
instability]; Bauer ht/06-PhD [discrete extra dimensions].
@ And quantum cosmology, Wheeler-DeWitt equation: Garattini gq/04 [as
Sturm-Liouville eigenvalue]; Capozziello & Garattini CQG(07)gq [as
eigenvalue of Wheeler-DeWitt equation
for f(R) theory]; Garattini a0712-in.
@ 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 =
0?]; Datta IJMPD(96)
[non-gravitating]; Aldrovandi & Barbosa
gq/02 [and
Lorentz group
Casimir]; Aldrovandi et al FP(03)
[ → 
];
Mersini-Houghton gq/06 [arrow
of time forbids
> 0]; Mazur ap/07 [from "gravitational
atoms"]; Lee et al JCAP(07)ht [from
entanglement energy].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
11 jul 2008