In General > s.a. newtonian gravity and modifications; gravitational phenomenology.
* History, I: The first systematic studies were carried out by Galileo (XVI century), or maybe by Riccioli; Hooke suggested that gravity plays a role in celestial motions, but the first precise description is Newton's (1665).
* History, II: 1915, The equivalence principle, Einstein's theory of general relativity, gravity as geometry; 1920s, Cartan analyzed the geometric structure of Newtonian gravity (in terms of a degenerate non-dynamical metric) and general relativity, and introduced the concept of torsion; A general framework is Ehler's Frame Theory; Alternative gravity theories.
* History, III: Various precursors are XX century proposals of higher-dimensional gravity, discrete theories, etc; 1990s, Beginning of a systematic study of phenomenology of higher-dimensional models; Quantum gravity?
* Strength: When we jump off a ledge, gravity takes over, but what happens when we hit the ground below?
* Motivation to look for new theories: Galactic rotation curves (unless explained by dark matter) and cosmological expansion acceleration (unless explained by dark energy); Eötvös-type experiments; Search for theory of quantum gravity and quantum corrections to classical gravity; (Anomalous spacecraft acceleration is now considered to have other explainations).
@ Intros and textbooks: Schutz 03 [II]; Olmo a1112-ch [intro]; Gasperini 13 [II, and other interactions]; Girifalco 14 [I]; Fleury a1902-ln [IIb].
@ General references: Cartan ENS(23), ENS(24), ENS(25); Mann gq/98-GR15; Aguirre et al CQG(01)hp [and astrophysics]; Deser IJMPA(02)ht/01 [rev]; Sotiriou et al IJMPD(08)-a0707 [no-progress report]; Krasnov MPLA(07)-a0711 [non-metric theories]; Sotiriou PhD(07)-a0712 [theory and phenomenology]; Zee IJMPA(08)-a0805-conf [rambling talk]; Padmanabhan FP(08) [and the equivalence principle]; Percacci PoS-a0910 [particle-physics perspective, gauge and renormalization]; Ananth IJMPD(10) [and Yang-Mills theory]; Bertolami a1112-talk; Starkman PTRS(11)-a1201 [and cosmology]; Frampton & Karl a1304 [at very short distances]; Trippe ZfN(14)-a1401 [the missing mass problem and the need for a new theory]; Papini MPLA(14) [covariance and gauge invariance]; Capozziello & Lambiase a1409-conf [open problems]; Lobo JPCS(15)-a1412 [dark matter, dark energy and modified gravity]; Strominger a1703-ln [infrared structure].
@ History: Synge et al PRS(62), Hoyle et al PRS(62) [status]; Gondhalekar 01; Kumar & Suresh gq/06; Graney PT(12)sep [Riccioli]; Pitts a1907-ch; > s.a. history of relativistic physics.
@ Speculations, origin of gravity: Mazur APPB(96)ht; Wootters FP(03) [from simple assumptions]; Amelino-Camelia et al IJMPD(15)-a1505-GRF [breakdown of conformal invariance]; Sels & Wouters JPCS(17)-a1602 [from mutual information in many-body quantum systems]; Altamirano et al NJP(17)-a1605 [from repeated quantum measurements]; Khosravi PRD(16)-a1606 [from ensenble average of all theoretically consistent models]; > s.a. emergent gravity; entropic gravity; phenomenology of entanglement; dynamical wave-function collapse.
@ Gravity as a universal force: Dieks Syn(87) [Reichenbach and Grünbaum]; Dadhich gq/04, gq/04-proc [universality??].
@ Gravity as geometry: Giesel et al PRD(12)-a1202 [based tensorial geometries other than Lorentzian geometries]; Capozziello et al IJGMP(12)-a1202 [physical foundations, Ehlers-Pirani-Schild approach]; Capozziello et al IJGMP(14)-a1401 [symmetries and affine structure]; Ximenes & Biezuner a1912 [obstructions].
> And other areas of physics: see modified quantum theory.
> Online resources: see Internet Encyclopedia of Science pages; Verlinde, Wilczek and Mersini-Houghton debate.

Types of Theories blue bullet s.a. theories of gravity [including higher-spin, vector, vector-tensor, ... theories].
* General idea: The first one in the modern sense was Newtonian gravity (originated in the 1660s, formulated in terms of action at a distance); The modern ones are usually geometrically formulated, as relativistic field theories; It can be fundamental or derived from other theories (induced gravity, AdS-cft, ...); Phenomenologically, the best motivated ones are scalar-tensor theories.
* Frameworks: The main ones in which various theories can be included and compared are the Dicke framework [@ in Dicke 64], and the PPN framework [which only treats conservative aspects, and does not include radiation]; There is also a Post-Keplerian framework, and Goldberger's & Rothstein's 2004 NRGR ("Non-Relativistic General Relativity", an unfortunate name) [this does include radiation].
* Results: General relativity (or another covariant gravity theory) is intrinsically non-linear because it must be self-interacting or "charged" if it is to interact consistently with matter via its stress tensors; This can be shown by bootstrapping the theory starting from any background; Of all the purely metrical theories, i.e., L = L(g, ∂g, ∂∂g, φ, ∂φ), only general relativity with arbitrary matter, i.e., L = |g|1/2 R + L(g, φ, ∂φ), gives second-order equations in g (and is linear in ∂∂g), and not fourth-order; A large class of these theories are "dynamically equivalent" to general relativity.
* Sources of corrections: A graviton mass gives corrections of order \((\lambda/\lambda^{~}_{\rm Compton})^2\), spacetime fluctuations corrections of order \((\lambda^{~}_{\rm fundam})^2/\lambda\).
@ General references: Weyl AJM(44) [as a linear field theory]; Deser GRG(70)gq/04 [need for non-linearity]; Ferraris & Kijowski GRG(82); Ferraris et al in-GR11; Ferraris et al CQG(88) + comment Brans CQG(88) + reply Ferraris et al CQG(90); Borowiec et al CQG(98)gq/96 [universality of Ricci-squared theories]; Knox SHPMP(11) [empirically equivalent theories and underdetermination]; Fabris & Velten a1501-proc [neo-Newtonian theories]; Licata et al IJGMP(17)-a1706 [approach based on the covariant derivative commutator algebra]; Clifton & Sanghai a1803 [parameterizations of alternative theories]; Alex & Reinhart PRD(20)-a1909 [guide for constructing alternative theories]; Velten & Caramês Univ(21)-a2102 [non-conserved energy-momentum]; Böhmer & Jensko a2103 [unified approach].
@ And matter: Pani et al PRD(13)-a1306 [auxiliary fields]; Gümrükçüoğlu & Namba PRD(19)-a1907, Feng & Carloni PRD(20)-a1910 [generalized coupling].
@ Non-relativistic theories: Kocharyan PRD(09)-a0905; Greenwald et al JCAP(10)-a1010 [compact objects and solar-system tests]; > s.a. hořava-lifshitz gravity; lorentz-symmetry violations; newtonian gravity.
@ As a spin-2 field theory in Minkowski space: Barceló et al PRD(14)-a1401, AP(18)-a1406 [graviton self-interactions and the cosmological constant]; Hertzberg & Sandora JHEP(17)-a1702 [general relativity from causality]; Blasi & Maggiore EPJC(17)-a1706 [and Fierz-Pauli theory]; > s.a. formulations of general relativity.
@ Other theories: Moffat EPJP(11)-a1008 [ultraviolet complete]; Letelier a1105 [non-covariant, with L = |g|ω R]; Greenberger FP(12) [Tic-Tac-Toe theory, negative masses and the equivalence principle]; Salvio & Strumia JHEP(14)-a1403 [agravity, theory without scales]; Markou et al CQG(19)-a1811 [vierbein, antisymmetric tensor]; Jokela et al JHEP(19)-a1901 [dual to a system of (2+1)-dimensional layers]; > s.a. differential geometry.
blue bullet General relativity and related theories: see general relativity, its formulations and variants [including infrared modifications].
blue bullet Modified theories: 2D and 3D theories; higher-dimensional gravity; higher-order theories; modified gravity; non-local theories.
blue bullet Other types: see ads-cft correspondence [gauge/gravity duality]; Constructive Gravity; Disformal Gravity; emergent gravity [including analog gravity]; entropic gravity; parity-violating theories; Projective Relativity; Screened Modified Gravity.

Phenomenology > s.a. Antigravity [repulsive component]; black holes; gravitational phenomenology; tests of general relativity.
@ References: Fischbach & Talmadge 99 [non-Newtonian]; Capozziello & Faraoni 11 [cosmology and astrophysics]; Linder JPCS(14)-a1201; Dupré a1403 [tidal acceleration and the structure of local gravity theories]; Di Virgilio et al proc(17)-a1702 [rev]; Albarran et al EPJC(18)-a1706 [gravity could become repulsive in the future]; Ezquiaga & Zumalacárregui a1710 [neutron-star merger GW170817].

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