Brans-Dicke Theory of Gravity| Brans-Dicke Theory of Gravity |
In General
> s.a. gravitational constant; scalar-tensor
theories; types of higher-order theories [equivalence].
* Idea: A scalar-tensor
theory of gravity containing an arbitrary "Dicke coupling constant"
ω and, in the generalized form, a mass m; It amounts to
effectively introducing a dynamics for the gravitational coupling G.
* In the Jordan frame:
The action, if K (K0) is
the trace of the extrinsic curvature induced by g (η)
on ∂M and including a cosmological constant, is
SJ[g, Φ, ...] = \(1\over16\pi\) ∫M dv [Φ (R − 2Λ) − ω gab Φ−1 ∇aΦ ∇bΦ] + 2 ∫∂M (ΦK− Φ0K0) ds + Smatter ;
The field equations, in units in which G = 1, are
\(\square\)Φ = (\(8\pi\over3\)+ 2ω) T , Gab = (8π Φ−1)Tab + (ωΦ−2) (Φ,aΦ,b − \(1\over2\)gab Φ,mΦ,m) + Φ−1 (Φ;ab − gab \(\square\)Φ) .
* In the Einstein frame: The action is
SE[g, Φ, ...] = \(1\over16\pi\) ∫M dv [R − (ω + 3/2) Φ,a Φ,a] + ∫M dv exp{−2Φ}\(\cal L\)m ;
The field equations are
Gab = 8π (Φ,aΦ,b − \(1\over2\)gab gmn Φ,m Φ,n) .
* History: Perfectly viable in
1971, it 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; 2016, There is still
interest in the theory, despite the fact that Solar System tests impose strong
constraints on it, rendering it indistinguishable from general relativity.
@ General references:
Brans & Dicke PR(61);
Dicke PR(62);
in Dicke 64;
Jackiw NC(68);
Miyazaki gq/00/PRD [and general relativity];
Jackiw & Pi a1511-fs [reasons for current interest];
Fabris et al a1603-fs [new perspectives];
Brando et al IJMPD(19)-a1810 [and general relativity].
@ Summaries: in Misner et al 73, 1070ff;
Will in(79).
@ Jordan vs Einstein frame:
Bhadra et al MPLA(07);
Artymowski et al PRD(13)-a1309 [in quantization à la lqc];
Gionti PRD-a2003 [canonical analysis].
@ Related topics: Chernodub & Niemi PRD(08)-a0709 [and electroweak theory];
Faraoni CQG(09)-a0906 [mass and range of scalar field];
Lobo IJGMP(18)-a1610 [non-metricity];
> s.a. brans-dicke phenomenology [including solutions and cosmology];
gravitational thermodynamics; spherical general relativity.
> Online resources:
see Wikipedia page.
Variations and Generalizations
> s.a. 3D gravity; quantum cosmology [third quantization];
quantum cosmology models; quintessence.
@ ω → ∞ 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).
@ ω → 0 limit: Punzi et al PLB(08)-a0804 [geometrical structure].
@ Massive: Alsing et al PRD(12)-a1112 [radiation from compact binaries].
@ 3-dimensional: Alonso et al PRD(03);
do Prado et al a1012 [and cosmological acceleration].
@ 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];
Pal PRD(16)-a1608 [canonical quantization, FRW model, phase transition];
Frion & Almeida PRD(19)-a1810 [affine quantisation];
> s.a. renormalization of quantum gravity.
@ Lqg / lqc quantization:
Zhang & Ma JPCS(12);
Zhang at al PRD(13)-a1211,
Jin et al JCAP(19)-a1808;
Song et al a2004 [alternative Hamiltonian constraint]
@ 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 IJMPA(10)-a0907 [non-linear, Born-Infeld-like];
Qiang et al PLB(09) [5D, and cosmology];
Ponce de León CQG(10)-a0912,
JCAP(10)
[5D, effective 4D theory and cosmological acceleration];
De Felice & Tsujikawa JCAP(10)-a1005;
Wu & Wang PRD(12) [with torsion, in Riemann-Cartan spacetime];
Rasouli et al CQG(14)-a1405 [in arbitray dimensions];
Caramês et al EPJC(14)-a1409 [Brans-Dicke-Rastall theory, with violation of conservation laws];
> s.a. hořava gravity; lovelock gravity.
@ Related topics: Arazi & Simeone MPLA(00)gq [linearized, strings];
Rador PLB(07) [Brans-Dicke type higher-order gravity];
Chang-Young et al CQG(12)-a1105 [as an entropic phenomenon];
Roshan & Shojai CQG(11)-a1106 [post-Newtonian limit];
Almeida et al PRD(14)-a1311 [geometrical scalar-tensor theory];
Kofinas AP-a1510 [complete theory].
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