Modifications
of Newtonian Gravity |

**In General** > s.a. newtonian
gravity / covariant quantum gravity; graviton.

* __Motivation__:
1740s, Clairaut experiments with adding a 1/*r*^{
3} term to the force to explain quantitatively the Moon's
apsidal motion; 1905, The realization that Newtonian gravitation was
incompatible with special relativity; Poincaré made the first attempt to
modify the theory; 2001, Interest has increased recently because of
proposed higher-dimensional models with 4D spacetime as brane, and to some
extent because of possible alternative to dark matter in explanations of
galactic dynamics.

* __Radial dependence__:
The only corrections to the potential consistent with relativistic field
theory are Yukawa-type,

*U*(*r*) = –(*G* *mm*'/*r*)
(1 + *α * exp{–*r*/*λ*}) ,

where the range *λ* is related to the graviton mass by *m*_{g}
= \(\hbar\)/*λc*.

@ __General articles__: Shelupsky AJP(85)dec
[and light bending]; Cook CP(87);
Milgrom Rech(88)feb; Parker &
Zumberge Nat(89)nov;
Onofrio MPLA(98)
[motivation and tests]; Mostepanenko proc(04)gq/03 [Casimir force]; Cannella PhD-a1103
[effective field theory approach and tests of gravity].

@ __Early work on non-Newtonian effects__: Heaviside 1894
[gravitomagnetism]; Forward PIRE(61);
in Bodenmann PT(10)jan
[Clairaut].

@ __Phenomenology__: Marinoni & Piazza ap/03/ApJL
[GraS];
Dvali ht/04-conf
[infrared];
> s.a. MOND; Yilmaz
Theory.

> __Phenomenology__:
see newtonian orbits; phenomenology
of gravity [PN approximation]; Sagnac
Effect; tests of general
relativity; tests of
newtonian gravity.

**Sources of Corrections** > s.a. brane
phenomenology; fifth force; higher-dimensional
gravity; modified gravity [non-local
theory].

* __Astrophysics__: The
Newtonian description of stars does not take into account all pressure
effects and therefore can not be used in strong field regimes.

@ __General relativistic__: Iorio GJI(06)gq
[on Earth, and possible measurement]; Brannen IJMPD(09)
[and graviton interactions]; Van den Bleeken a1703 [twistless torsion from large-*c* expansion, for strong gravitational time dilation]; Bailey a1706 [velocity-dependent inverse cubic force correction].

@ __Quantum mechanical__: Donoghue PRL(94);
Kazakov CQG(01);
Kirilin & Khriplovich JETP(02)gq;
Kirillov & Turaev G&C(03)ht/01
[spacetime foam]; Ward IJMPA(05)
[resummed quantum gravity]; Bailey & Kostelecký PRD(06)gq
[with Lorentz symmetry violation]; Akhundov & Shiekh EJTP(08)-gq/06
[rev]; Faller PRD(08)-a0708
[from effective quantum gravity and scalar QED]; Caldwell & Grin PRL(08)
[modifications below 0.05 mm and cosmology]; Modesto & Randono a1003
[and modifications to the entropy-area relation]; Wu et al a1607 [gravitational interaction between polarizable objects].

@ __With 3D spatial curvature, enhanced Newtonian gravity__:
Abramowicz et al GRG(14)-a1303
[perihelion advance and light bending].

@ __Other sources__: Antoniadis hp/99-conf;
Zinoviev a1201
[causality, and planet motion]; Floratos & Leontaris JCAP(12)-a1202
[non-trivial spatial topology]; Gorbatsievich & Schmutzer IJMPE(12)-a1203
[projective unified field theory]; Diósi EPJwc(14)-a1406
[delay time]; > s.a. quantum-gravity
effects; string phenomenology.

**Parametrized Post-Newtonian (PPN) Formalism** > s.a. gravitational
phenomenology; tests of general
relativity.

* __Idea__: A framework
for comparing general relativity with other metric theories, using 10
parameters which can be experimentally determined; It includes the PN
approximation of (nearly) every metric theory, but only treats
conservative aspects and does not include radiation; Some parameter-value
ranges correspond to Lorentz-symmetry violating theories and overlap with
the Standard Model Extension framework.

* __Rem__: Some
modified-gravity theories, such as massive scalar-tensor theories, have no
PPN expansion.

* __Interpretation__:
For an isolated, spherical object, if *β* represents the
non-linearity in gravitational attraction, and *γ* the amount of
curvature produced by a body,

*g*_{00} = –1 + 2*U*
, *g*_{ij}
= (1 + 2*γ* *M*/*R*) δ_{ij}
+ ... , where *U* = *M*/*R*
– *β* (*M*/*R*)^{2} +
...

* __Status, parameter values__:
2004, From Cassini data, *β*–1 = (1.2 ± 1.1) × 10^{–4};
2006, Bounds on *β* and *γ* are 10^{–4}–10^{–5},
various missions to improving limits by several orders of magnitude
(LATOR, ASTROD, BepiColombo, GAIA) under consideration; 2006, on galactic
scales, *γ* = 0.98 ± 0.07 (68% cl); 2010, The
data that currently provide the tightest constrains on the parameterized
post-Einsteinian framework come from the orbital period decay of binary
pulsars; 2016, Using a 0.4-ns giant pulse from the Crab pulsar, \(\Delta\gamma < 8\times 10^{-16}\).

@ __General references__: in Eddington 22;
Robertson in(62);
Schiff SIAM(62),
in(67); Nordtvedt PR(68),
PR(68),
PR(69);
Will ApJ(71);
Will & Nordtvedt ApJ(72);
in Misner et al 73, Ch39; Rendall PRS(92);
Kopeikin & Vlasov PRP(04)
[reference frames, scalar-tensor theory]; Blanchet et al PRD(05)gq
[structure, near zone]; Allemandi et al GRG(05)gq
[alternative theories]; Hwang et al a1012
[cosmologically-motivated].

@ __Specific theories__: Alexander & Yunes PRD(07),
PRL(07)ht
[for Chern-Simons gravity]; Hohmann et al a1607 [multiscalar-tensor
gravity, parameter *γ*]; > s.a. bimetric
gravity; brans-dicke theory; higher-order
theories; lorentz-symmetry
phenomenology; newton-cartan
theory; theories of gravity [C-theory].

@ __Constraints on values__: Arminjon in(03)gq
[new method]; Bolton et al PRD(06)ap
[*γ* on galactic scales]; Yunes & Hughes PRD(10)-a1007
[constraints from binary pulsars]; Yang & Zhang a1608 [Crab pulsar].

@ __Effects__: Rama & Ghosh PLB(96),
same as PLB(96)
[values for repulsive gravity]; Schröder & Treder FP(02)
[Earth-Moon system]; Arminjon PRD(05)gq,
in(06)gq/05
[corrections to equations of motion and new self-acceleration].

@ __Variations__: Xu & Ma PLB(07)
[for
5D gravity, and tests of Kaluza-Klein theory]; Clifton PRD(08)-a0801
[for fourth-order theories].

@ __Experiments__: Gai et al EA(12)-a1203
[GAME mission]; Verma et al ApJ-a1707 [determining *β* using asteroid radar astronomy].

> __Related topics__:
see cosmological models
[post-Friedmann framework]; motion of
test particles and orbits in
newtonian gravity and relativistic
gravity; self-force; sources
of gravitational waves; dark
matter.

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send feedback and suggestions to bombelli at olemiss.edu – modified 27 jul
2017