Scalar-Tensor Theories of Gravity |
In General
> s.a. gravitation; higher-order theories
and types [equivalence]; mass;
phenomenology; 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.
@ Reviews, history: Fujii & Maeda 03;
Brans gq/05 [overview];
Goenner GRG(12) [history 1941–1962, Scherrer, Jordan, Thiry];
Quirós IJMPD(19)-a1901.
@ General references:
Bergmann IJTP(68);
Harrison PRD(72),
Serna et al CQG(02)gq [and general relativity];
Charmousis et al PRL(11)-a1106 [with consistent self-tuning mechanism];
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];
Kovacs & Reall a2003
[effective field theory, well-posed initial value formulation];
> s.a. affine connections [non-metricity formulation].
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;
non-local theories; 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 GRG(16)-a1503 [with an external scalar];
Crisostomi et al JCAP(16)-a1602 [extended];
Ezquiaga et al PRD(16)-a1603 [most general];
Quiros et al a1905 [issue with classification];
Borowiec & Kozak a2003 [hybrid metric-Palatini theories].
> Other theories:
see Bergmann-Wagoner Theory;
brans-dicke theory; dilaton;
Horndeski Action [including generalizations];
quintessence.
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send feedback and suggestions to bombelli at olemiss.edu – modified 11 mar 2020