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 *φ*^{i},
often called inflatons, and possibly other fields, with an action of the
form

*S*[*g*_{ab},
*φ*] = ∫ d*v* [\(1\over2\)*f*(*φ*)
*R* – \(1\over2\)*ω*(*φ*) *g*^{ac}
∂_{a} *φ* ∂_{c
}*φ* – *V*(*φ*) + (possible
higher-order terms in derivatives of the *φ*^{i})]
,

where *f*(*φ*) > 0 so that *G*_{eff}
= (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-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 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 *h*_{ab}
= *g*_{ab} – *η*_{ab}
is not the spin-2 massless graviton, and the* φ**R* 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 *h*_{ab}
= *g*_{ab}– *η*_{ab}
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, *g*_{ab}^{E}
= Ω^{2} *g*_{ab}^{J},
and the dilatons are related by *φ*^{J}
= 1/*GA*^{2}(*φ*^{E});
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 a1603
[most general].

> __Other theories__:
see Bergmann-Wagoner Theory; brans-dicke
theory; dilaton; Horndeski
Action [including generalizations]; quintessence.

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