|Scalar-Tensor Theories of Gravity|
In General > s.a. gravitation;
higher-order theories and types [equivalence];
scalar fields [scalar components of gravity].
* Idea: Theories of gravitation which include, besides the metric, one or more scalar fields φi, often called inflatons, and possibly other fields, with an action of the form
S[gab, φ] = ∫ dv [\(1\over2\)f(φ) R − \(1\over2\)ω(φ) gac ∂a φ ∂c φ − V(φ) + (possible higher-order terms in derivatives of the φi)] ,
where f(φ) > 0 so that Geff
= (8π f)−1 > 0,
gravity is attractive and the graviton carries positive energy.
* Motivation: Slows down the expansion rate in extended and hyperextended inflation, and allows bubble nucleation; The scalar field, and others, appears naturally in low-energy effective actions and dimensional reductions of most hep-inspired unified theories, including string theory (as dilaton), supergravity (as partner of a spin-\(1\over2\) particle), Kaluza-Klein theory, higher-derivative theories.
@ General references: Bergmann IJTP(68); Harrison PRD(72), Serna et al CQG(02)gq [and general relativity]; Fujii & Maeda 03; Brans gq/05 [overview]; Charmousis et al PRL(11)-a1106 [with consistent self-tuning mechanism]; Goenner GRG(12) [history 1941-1962, Scherrer, Jordan, Thiry]; Padilla & Sivanesan JHEP(12)-a1206 [boundary terms and junction conditions]; Zhou et al PRD(13)-a1211 [first-order action]; Bloomfield JCAP(13)-a1304 [simplified approach based on Horndeski's theory]; Gao PRD(14)-a1406, Ezquiaga et al PRD(16)-a1603 [unifying frameworks]; Kozak a1710-MS [Palatini approach].
@ Cauchy problem, evolution: Teyssandier & Tourrenc JMP(83); Damour & Esposito-Farèse CQG(92); Damour & Nordtvedt PRL(93), PRD(93) [general relativity as attractor]; Salgado CQG(06)gq/05; Salgado & Martínez-del Río JPC(07)-a0712; Salgado et al PRD(08)-a0801 [hyperbolicity]; Faraoni & Lanahan-Tremblay PRD(08)-a0808.
@ Hamiltonian approach: Lin a1702 [Ostrogradski ghost issue].
@ Related topics: Wiaux CQG(99) [gauge freedom]; Salgado gq/02/PRD [weak field]; Agarwal & Bean CQG(08)-a0708 [dynamical stability]; Carloni & Dunsby GRG(16)-a1306 [1+1+2 formalism]; Vilson AACA(15)-a1509 [invariant quantities].
Conformal Frames > s.a. brans-dicke
theory; conformal structures.
* Jordan / Pauli frame: Defined by f(φ) = φ in the general form of the action; The weak equivalence principle is satisfied, but hab = gab − ηab is not the spin-2 massless graviton, and the φR term can become negative so the energy density is not bounded from below, which is not acceptable classically.
* Einstein frame: Defined by f(φ) = 1 in the general form of the action; It is used in inflationary models because equations are easier to work with; The perturbation hab = gab − ηab represents the spin-2 massless graviton and is used for quantization, but the WEP is not satisfied (weakly, ok with tests).
* Relationships: The metrics in the two frames are conformally related, gabE = Ω2 gabJ, and the dilatons are related by φJ = 1/GA2(φE); Since the transformation is local Chisholm's theorem implies that the S-matrices are equivalent; The scalar-field transformation shows that the Einstein-frame theory can be considered as a sector of the Jordan-frame one, and in this sector there is no instability.
@ General references: Carloni et al GRG(10)-a0907 [conformal transformations in cosmology]; Järv et al JPCS(14)-a1501 [parametrizations and general relativity limit].
@ Jordan vs Einstein frame: Cho PRL(92), CQG(97); Magnano & Sokołowski PRD(94)gq/93; Capozziello et al CQG(97), CQG(97); in Brans gq/97-fs; in Faraoni et al FCP(99)gq/98; Faraoni & Gunzig IJTP(99)ap; Quirós gq/99, PRD(00)gq/99, et al PRD(00)gq/99 [and singularities]; Gong gq/00; Macías & García GRG(01) [inequivalent]; Casadio & Gruppuso IJMPD(02)gq/01 [and boundary terms]; Álvarez & Conde MPLA(02)gq/01; Flanagan CQG(04)gq [including higher-order theories]; Bhadra et al MPLA(07)gq/06 [Brans-Dicke theory, light deflection]; Faraoni & Nadeau PRD(07)gq/06; Järv et al PRD(07)-a0705 [and general relativity limit]; Roberts a0706; Capozziello et al PLB(10)-a1003 [higher-order gravity, inequivalent]; Corda APP(11)-a1010 [and gravitational-wave astronomy]; Xu & Zhao a1106-wd [inequivalent]; Kozyrev & Daishev a1207; Postma & Volponi PRD(14)-a1407 [equivalent; action written in terms of conformally invariant quantities].
@ Quantum aspects: Kamenshchik & Steinwachs PRD(15)-a1408; Banerjee & Majumder PLB(16)-a1601; Pandey & Banerjee a1610 [equivalence]; > s.a modified approaches to quantum gravity.
Specific Theories > s.a. bianchi models;
bimetric theories; higher-dimensional gravity;
unified theories [Weyl-Dirac].
* Jordan theory: A generalization of Brans-Dicke theory; > s.a. kaluza-klein theory.
@ From large extra dimensions: Giudice et al NPB(01) [curvature-Higgs mixing].
@ Other theories: Graf PRD(03)gq/02, PMCPA(07)gq/06 [metric + volume element, Ricci flow gravity]; Scholz et al FP(09) [scale-covariant field]; Babichev et al IJMPD(09) [with infrared screening]; Minotti a1106 [with enhanced gravitational effects]; Zumalcárregui & García-Bellido PRD(14)-a1308 [derivative couplings]; Chavineau et al a1503 [with an external scalar]; Crisostomi et al JCAP(16)-a1602 [extended]; Ezquiaga et al PRD(16)-a1603 [most general].
> Other theories: see Bergmann-Wagoner Theory; brans-dicke theory; dilaton; Horndeski Action [including generalizations]; quintessence.
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