Brans-Dicke Theory of Gravity  

In General > s.a. scalar-tensor theories.
* Idea: A scalar-tensor theory of gravity containing an arbitrary "Dicke coupling constant" .
* In the Jordan frame: The action, if K (K0) is the trace of the extrinsic curvature induced by g () on M and including a cosmological constant, is

SJ[g, , ...] = (1/16) M dv [ (R – 2) – gab –1a b] + 2 bdry(M) (K– 0K0) ds + Smatter ;

The field equations, in units in which G = 1, are

= {8/3 + 2) T ,     Gab = (8–1)Tab + (–2) (,a,b – gab ,m,m) + –1 (;ab – gab ) .

* In the Einstein frame: The action is

SE[g, , ...] = (1/16) M dv [R – ( + 3/2) ,a,a] + M dv exp{–2}m ;

The field equations are

Gab = 8 (,a,b – gab gmn ,m,n) .

* History: Perfectly viable in 1971, was neglected for some years, then revived since the 1980s because it (with other matter fields) arises in Kaluza-Klein theories, and as an effective theory in the low-energy limit of string theory.

Phenomenology > s.a. cosmic acceleration; early-universe cosmology; gravitomagnetism; monopoles; wormhole solutions.
* Properties: The massless is to be thought of as corresponding to a "varying gravitational constant G –1"; It incorporates the weak form of the equivalence principle, not the strong one; The local special relativistic laws are valid as usual; The field interacts with matter only indirectly, through the metric.
* Bounds: 1973, needed > 5 for reasonable agreement with experiment; 1987, There are much stronger lower bounds, and it does not seem very natural (the → limit of the theory is general relativity, if Taa 0).
* And PPN parameters: Cosmological models predict a departure from the general relativity value of |1–| between 10–5 and 10–7.
@ Tests, effects: Dereli & Tucker MPLA(02)gq/01 [precession and torsion]; Barros & Romero MPLA(03) [time delay & Lense-Thirring effect]; Psaltis ap/05/ApJ [msec pulsars]; Carneiro & Montenegro BJP(05)gq-in [and cosmic coincidence].
@ Gravitational waves: Scharre & Will PRD(02)gq/01 [waveforms]; Sahoo & Singh MPLA(04)gq; Will & Yunes CQG(04)gq [and LISA]; Faraoni PRD(04)gq [negative energy, stability of Minkowski]; > s.a. gravitational-wave background; scalar-tensor theories.
@ Topological defects: Barros & Romero PRD(97) [monopoles], MPLA(01) [gravitational forces]; Dahia & Romero PRD(99)gq/98 [lines]; Delice PRD(06)gq, PRD(06) [cosmic strings, with cosmological constant].
@ Black holes: Campanelli & Loustó IJMPD(93)gq; Beesham MPLA(98) [parameter interpretation]; Tamaki et al PRD(98)gq/97 [non-abelian], PRD(99)gq [monopole]; Kim PRD(99) [Kerr-Newman type]; Agnese & La Camera NCB(01)gq/00 [black hole metric fluctuations]; Sakai & Barrow CQG(01)gq [evolution]; Kozyrev gq/02 [static, spherical]; Sheykhi & Alavirad IJMPD-a0809 [Brans-Dicke-Maxwell]; Avelino et al PRD(09)-a0904 [mass inflation].
@ Bianchi models: Guzman PLB(97) [cosmic no-hair theorem]; Cervantes-Cota & Nahmad GRG(01)gq/00 [I-V-IX, solutions and isotropization]; Núñez-Yépez GRG(01) [VII]; > s.a. bianchi models; chaos in bianchi models; inflationary models.
@ Inflation: Gong PRD(99)gq/98; del Campo et al JCAP(07) [emergence from past-eternal static spacetime]; Berman & Trevisan IJTP(09)gq/01.
@ Other FRW cosmology: Wetterich NPB(88) [varying G]; Gong gq/98; Quirós et al PRD(00) [singularity]; Arik & Çalik MPLA(06)gq/05 [dark energy and dark matter]; Arik et al IJMPD(08)gq/06 [Friedmann equation]; Berman gq/06/ASS; Montenegro & Carneiro CQG(07)gq/06 [decaying vacuum density].
@ Other cosmology: Krori et al PLA(81) [stationary axisymmetric Brans-Dicke-Maxwell]; Pimentel PRD(96), MPLA(97); Park & Sin JKPS(99)gq; Chen et al IJTP(05)gq/03 [and Higgs mechanism]; Acquaviva & Verde JCAP(07)-a0709 [and cosmological parameters]; Smolyakov a0711 [and small cosmological constant]; del Campo et al JCAP(09) [static universe, stability]; > s.a. NUT Space; singularities.

References > s.a. 3D gravity; gravitational constant; quantum cosmology; quintessence.
@ General: Brans & Dicke PR(61); Dicke PR(62); in Dicke 64; Jackiw NC(68).
@ Summaries: in Misner et al 73, 1070ff; Will in(79).
@ → limit: Banerjee & Sen PRD(97); Faraoni PLA(98)gq, PRD(99)gq; Quirós gq/99/PLA; Bhadra & Nandi PRD(01)gq/04 [scalar field]; Chauvineau CQG(03).
@ → 0 limit: Punzi et al PLB(08)-a0804 [geometrical structure].
@ Quantum theory: Cho CQG(97) [and equivalence principle]; Zhu et al MPLA(98) [quantum cosmology and cosmological constant]; Pimentel & Mora PLA(01)gq/00 [3rd quantization]; Ohkuwa NCB(03) [WKB time]; > s.a. renormalization of quantum gravity.
@ Generalizations, extensions: Chakraborty & Ghosh PS(03); Catena PRD(07)ht/06 [minimal supersymmetric extension]; Amendola et al PRD(08)-a0801 [with Gauss-Bonnet term, and Solar System tests]; Smolyakov a0907 [non-linear, Born-Infeld-like]; Qiang et al PLB(09) [5D, and cosmology].
@ Related topics: Arazi & Simeone MPLA(00)gq [linearized, strings]; Miyazaki gq/00/PRD [and general relativity]; Bhadra et al MPLA(07) [Jordan vs Einstein frame]; Rador PLB(07) [Brans-Dicke type higher-order gravity]; Chernodub & Niemi PRD(08)-a0709 [and electroweak theory]; Faraoni CQG(09)-a0906 [mass and range of scalar field]; > s.a. spherical general relativity.

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