Scalar-Tensor
Theories of Gravity| Scalar-Tensor
Theories of Gravity |
In General > s.a. gravity; higher-order
theories; mass.
* Idea: Theories of gravitation
which include, besides the metric,
a scalar field 
,
often called an inflaton, and possibly other fields, with an action of the form
S[g, ]
=
dv [
f() R – 
()
gac 
a c
– V()]
,
where f() > 0
so that Geff = (8
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 (dilaton), supergravity
(partner of spin- particle),
Kaluza-Klein, 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].
@ 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 a0712-JPC;
Salgado et al a0801-PRD
[hyperbolicity].
@ Related topics: Wiaux CQG(99)
[gauge freedom]; Salgado gq/02/PRD
[weak field]; Agarwal & Bean a0708 [dynamical
stability].
Conformal Frames > s.a. brans-dicke.
* Jordan/Pauli frame:
The equivalence principle is satisfied, but hab =
gab – 
ab is
not the spin-2 massless graviton, and violates the WEP
(in fact, the energy density is not bounded from below, not
acceptable
classically).
* Einstein frame: Used
in inflationary models because equations are easier;
The
perturbation hab = gab– 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
are conformally related, gabE =
2 gabJ;
The S-matrices are
equivalent, since the transformation
is local, from Chisholm's theorem.
@ Jordan vs Einstein frame: Cho PRL(92), CQG(97);
Magnano & Sokolowski
PRD(94)gq/93;
Capozziello et al CQG(97),
CQG(97);
in Brans gq/97-in;
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]; Bhadra et al MPLA(07)gq/06
[Brans-Dicke, light deflection]; Faraoni & Nadeau PRD(07)gq/06;
Järv et al PRD(07)-a0705 [and
general relativity limit]; Roberts a0706.
Cosmology > s.a. bianchi
I; brans-dicke; chaos; cmb; cosmology; inflationary
models; perturbations.
* Remark: In many cases,
the late-time evolution is difficult to distinguish from that predicted by
general relativity.
@ General references: Faraoni 04; Faraoni AP(05)gq [phase
space
structure]; Catena et al PRD(07)ap/06
[frame-invariant approach]; Demianski et al a0711-A&A
[models].
@ Cosmic acceleration: Boisseau et al PRL(00)gq;
Esposito-Farèse & Polarski
PRD(01);
del Campo & Salgado CQG(03)ap;
Demianski et al A&A(06)ap;
Barenboim & Lykken a0711.
@ Singularities: Kaloper & Olive PRD(98) [FRW]; Faraoni PRD(04)gq;
Gunzig & Saa IJTP(04) [removal by CabcdCabcd].
@ Other classical cosmology: Santiago et al PRD(98)
[late evolution]; Coley
GRG(99)ap [solutions];
Billyard et al PRD(99), JMP(00)gq [cyclic,
heteroclinic];
Bezerra
et al BJP(04)ht/03 [vacuum
solutions]; Coc et al PRD(06)ap [nucleosynthesis];
Faraoni et al CQG(06)
[non-chaotic]; Carloni et al CQG(08)gq/07 [FRW
+ non-minimal scalar]; > s.a. dark
energy.
@ Quantum cosmology: Fabris et al CQG(99)
[non-minimal coupling], & Reuter
GRG(00);
Chakraborty
NCB(01) [in Ashtekar variables]; > s.a. FRW
models, minisuperspace
quantum cosmology [Bergmann-Wagoner theory].
Other Phenomenology > s.a. Birkhoff Theorem; lensing; (post-)newtonian
gravity;
wormholes.
* Gravitational waves:
Linearized gravitational waves in Brans-Dicke and scalar-tensor theories carry
negative energy.
@ General references: Esposito-Farèse gq/04-in
[test, rev].
@ Gravitational waves: Scharre & Will PRD(02),
Will & Yunes CQG(04)
[LISA, waveforms]; Sotani & Kokkotas PRD(04)gq [neutron
star seismology]; Faraoni PRD(04)
[stability of Minkowski]; > s.a. gravitational wave
background.
@ Other solutions: Moffat gq/07 [spherically symmetric, non-singular].
@ Other effects: Faraoni & Gunzig A&A(98)
[light amplification];
Shojai
et al MPLA(98), MPLA(98)
[quantum gravity]; Jacobson PRL(99)ap [primordial
black holes]; Bezerra et al PRD(05)ht/04 [Lorentz
violations, with torsion]; Burton et al a0711 [spinning
particles]; > s.a. astrophysics [Buchdahl
inequality], gravitational
constant [variation]; Q-Stars.
Specific Theories > s.a. bianchi
models; brans-dicke; dilaton;
quintessence; unified
theories [Weyl-Dirac].
* Jordan theory: A generalization
of Brans-Dicke; > s.a. kaluza-klein theory.
* Other examples: Bergmann-Wagoner
theory, quintessence.
@ From large extra dimensions: Giudice et al NPB(01)
[curvature-Higgs mixing].
@ Other theories: Graf PRD(03)gq/02, gq/06 [metric
+ volume element, Ricci
flow gravity].
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
27 jun 2008