Phenomenology of Higher-Order Gravity Theories  

In General > s.a. cosmology in higher-order theories.
* Key features: On cosmological scales modified-gravity theories deviate from general relativity in that they can cause cosmic acceleration without a physical, negative-pressure fluid, a gravitational slip between the two metric potentials, and a propagation speed for gravitational waves that differs from that of light.
Stability: Certain f(R) theories can stabilize solutions which are unstable in general relativity, such as the Einstein static universe.
* Viability: Only the f(R) models which have a built-in chameleon screening mechanism are viable.
@ Reviews and general references: Capozziello & Francaviglia GRG(08); Sotiriou JPCS(09)-a0810; de la Cruz-Dombriz & Sáez-Gómez Ent(12)-a1207.
@ Stability: Schmidt PRD(94); Ezawa et al CQG(99) [higher-dimensional, semiclassical]; Dolgov & Kawasaki ap/03 [R–1 theories]; De Felice et al JCAP(06)ap [superluminal mode propagation]; Faraoni PRD(06)ap, Sotiriou PLB(07)gq/06, Sawicki & Hu PRD(07)ap [f(R) theories]; Sokołowski CQG(07)gq [interpretation and viability]; Böhmer et al PRD(07)-a0706 [Einstein static universe]; Lee a0710; Bertolami & Carvalho Sequeira PRD(09) [and energy conditions]; Saltas & Kunz PRD(11)-a1012 [and anisotropic stress]; > s.a. types of theories [Hamiltonian perturbation theory].
@ R–1 theories: Flanagan PRL(04)ap/03, Vollick CQG(04)gq/03, Kremer & Alves PRD(04)gq [Palatini form]; Soussa & Woodard GRG(04)ap/03 [force of gravity]; Vollick PRD(05)gq/04 [with Dirac field]; Shao et al PLB(06)gq/05 [as correction term].
@ Other theories: Clifton & Barrow PRD(05)gq [R1+a Lagrangian]; Navarro & Van Acoleyen JCAP(06)ap [ln f(R), dark energy and MOND]; Olmo AIP(10)-a0910 [general, esp 1/R and f(R) = R + R2/RP theories].
@ Non-local theories: Koivisto PRD(08)-a0807 [newtonian limit]; > s.a. theories of gravitation.

Solutions > s.a. Birkhoff's Theorem; black-hole solutions; Israel's Theorem; Lichnerowicz Theorem; schwarzschild spacetime.
* In general: All solutions of the ordinary Einstein equation still extremize S, and there are other solutions; However, if S does not include the usual R term, the ordinary solutions do not couple to positive-definite matter sources.
* Features: In some theories, torsion and its conjugate momentum play an important role.
* Results: Birkhoff's theorem in general is not valid, but it is in some cases; There is massive radiation (2 Yukawa potentials, 8 degrees of freedom, the usual spin-2 graviton, a massive one – negative energy – and one scalar field); It is claimed that in theories with purely quadratic terms in the action, the energy is identically zero, but this seems strange (RDS).
@ Gravitational waves: Campanelli & Loustó PRD(96)gq/95 [shock waves]; de Rey et al CQG(03)gq, CQG(03)gq, CQG(04)gq/03; Ananda et al PRD(08)-a0708 [4th-order gravity in FLRW models]; Corda a0710-proc [R–1 theory]; Capozziello et al PLB(08)-a0812 [massive, and LISA]; Kausar et al PRD-a1606, Liang et al a1701 [polarizations]; > s.a. gravitational waves and background.
@ Cosmological solutions: Clifton & Barrow PRD(05)gq [Gödel, Einstein and de Sitter], CQG(06) [Kasner-type], CQG(06)gq [cosmological, 4th-order theories]; Goswami et al PRD(08)-a0804 [Einstein universes, 4th-order theories]; Hindmarsh & Saltas PRD(12) [f(R) gravity from the renormalization group]; > s.a. types of spacetimes [Einstein static universe].
@ Axisymmetric: Capozziello et al CQG(10)-a0912; De Laurentis a1111; Suvorov & Melatos PRD(16)-a1608 [Ernst formulation, and applications].
@ Solutions with symmetries: Azadi et al PLB(08) [static cylindrically symmetric]; Sharif & Farasat Shamir MPLA(10) [plane-symmetric]; > s.a. spherical symmetry.
@ f(R) theories, gravitational collapse: Cembranos et al JCAP(12)-a1201 [dust collapse]; Borison et al PRD(12), Guo et al PRD(14)-a1312 [spherical scalar collapse]; Montes Núñez et al AIP(11)-a1210.
@ Other types of solutions: Campanelli et al PRD(94)gq [perturbative method]; Barraco & Hamity GRG(99) [asymptotically flat, and general relativity solutions]; Mazharimousavi et al EPJC(12)-a1110 [f(R) theory with an electromagnetic field]; > s.a. types of higher-order theories [3D]; gödel solution; wormhole solutions.

Newtonian Limit
* Remark: Its existence cannot work as a selection rule among metric f(R) theories, because it is implied by stability.
@ General references: Quandt & Schmidt AN(91)gq/01; Domínguez & Barraco PRD(04)gq [Palatini]; Capozziello gq/04-ch [rev]; Capozziello & Troisi PRD(05)ap [4th-order, PPN limit]; Sotiriou GRG(06)gq/05; Bertolami et al PRD(07)-a0704 [extra force]; Capozziello et al PRD(07)-a0708; Corda IJTP(08) [extra repulsive force]; Stabile PhD(08)-a0809; Sokołowski APPB(08)-a0810 [and stability]; Capozziello et al MPLA(09)-a0901 [presence of Yukawa correction]; Capozziello & Stabile CQG(09)-a0903 [quadratic Lagrangians], a1009 [fourth-order theories]; Capozziello et al PLB(10)-a1002 [compared to scalar-tensor gravity].
@ f(R) gravity: Stabile & Capozziello a1010-proc; Eingorn & Zhuk PRD(11)-a1104 [three and more spatial dimensions].
@ Newtonian limit, R–1: Dick GRG(04)gq/03; Rajaraman ap/03; Navarro & Van Acoleyen PLB(05)gq [and acceleration]; Cembranos PRD(06)gq/05 [as limit at intermediate energy]; Navarro & Van Acoleyen JCAP(06)gq/05 [large distance].
@ Post-Newtonian framework: Allemandi et al GRG(05); Capozziello et al MPLA(06)gq [and experimental constraints]; De Laurentis et al AdP(10)-a0911 [and cosmological gravitational waves]; Capozziello et al IJTP(10)-a1001 [post-Minkowskian limit].

Other Phenomenology > s.a. cosmology in higher-order theories [including cluster density profiles]; phenomenology of gravity; tests of general relativity.
@ Galaxy rotation curves: Capozziello et al PLA(04), AIP(05)ap/04; Frigerio & Salucci MNRAS(07)ap; Harko PRD(10)-a1004; Capozziello et al APP(13)-a1307 [hybrid metric-Palatini gravity]; Shojai & Shojai GRG(14) [f(R) gravity]; Salucci et al IJMPD(14)-a1405-GRF [Rn gravity].
@ Other galactic dynamics: Borka et al PRD(12) [Rn theories and precession of stellar orbits].
@ Solar system constraints: Olmo PRL(05)gq, PRD(05)gq + gq, Jin et al gq/06 [f(R)]; Faraoni PRD(06)gq; Ruggiero & Iorio JCAP(07)gq/06 [planetary orbits]; Chiba et al PRD(07)ap/06; Zakharov et al PRD(06); Faulkner et al PRD(07)ap/06, Saffari & Rahvar PRD(08)-a0708 [and cosmology]; Hu & Sawicki PRD(07)-a0705 [models that evade solar system tests]; Allemandi & Ruggiero GRG(07); Bertolami & Páramos PRD(08)-a0709; Iorio & Ruggiero SRE(08)-a0711; Capozziello & Tsujikawa PRD(08)-a0712; De Felice & Tsujikawa PRD(09)-a0907; Bisabr PLB(10)-a0907; Näf & Jetzer PRD(10)-a1004 [1/c expansion]; Bisabr G&C(10)-a1005 [power-law f(R) theories]; Faraoni PRD(11)-a1106 [Rn theories severely constrained]; Guo IJMPD(14)-a1306 [f(R) theories]; Xie & Deng MNRAS(13)-a1312 [f(R) theories]; Schärer et al PRD(14)-a1410 [tests in Earth orbit].
@ Solar system constraints, R–1: Erickcek et al PRD(06)ap [theory ruled out]; Exirifard a0810 [theory not ruled out].
@ Stars, astrophysics: Kainulainen et al PRD(07)-gq/06; Bustelo & Barraco CQG(07)gq/06; Henttunen et al PRD(08)-a0705; Capozziello et al PRD(11)-a1101 [f(R), hydrostatic equilibrium and stellar structure]; Goswami et al PRD(14)-a1409 [collapsing spherical stars]; > s.a. gravitating bodies; neutron stars.
@ Cosmological scales: Boubekeur et al PRD(14)-a1407 [clustering]; de Martino et al Univ(15)-a1507, Achitouv et al PRD(16)-a1511 [large-scale structure, halos].
@ Propagating degrees of freedom: Magnano & Sokołowski AP(03)gq/02 [massive spin-2 field generated]; Núñez & Solganik PLB(05)ht/04 [IR modifications not viable, ghosts or light gravity scalars]; Capozziello et al MPLA(07) [gravitational-wave background]; De Laurentis et al MPLA(12)-a1206 [massive ghost modes and gravitational Cherenkov radiation]; Myung a1608 [polarization modes of gravitational waves in f(R) gravity]; Bueno et al a1610.
@ Related topics: Accioly et al NCB(00), Accioly & Blas PRD(01)gq [light deflection, quadratic]; Gabadadze & Iglesias PLB(06) [precession]; Li et al CQG(09)-a0801 [indistinguishable macroscopic behavior]; Bisabr PLB(10)-a1003 [and time variation of α]; Morais et al JCAP(15)-a1507 [f(R) gravity and observed radiation]; Giacchini a1612-MG14 [R2 and Rab2 theories, short-range laboratory experiments].
> Related topics: see black-hole formation and laws; causality violation; Chameleon Field; energy [virial theorem]; energy conditions; equivalence principle; gravitational radiation; singularities and types of singularities [isotropic, naked]; thermodynamics.

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