Degravitation, Orbital Dynamics and the Effective Barycentre

Alain Dirkes

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Degravitation, Orbital Dynamics and the Effective Barycentre

Alain Dirkes

General Relativity and Quantum Cosmology · Submitted 14 Jul 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We notice that it is always possible to recover the corresponding general relativistic results in the limit of vanishing nonlocal modification parameters.

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What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.82 · mentions code or data availability 0.02.

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In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$. The general idea was obviously outlined for the first time in [13-16] and originates from the quest of finding a mechanism that is able to degravitate the vacuum energy on cosmological scales. We suggest in this manuscript a precise covariant coupling model which acts like a high-pass filter with a macroscopic distance filter scale $\sqrt{\Lambda}$. In the context of this specific theory of gravity we review some cosmological aspects before we briefly recall the effective relaxed Einstein equations outlined for the first time in [1]. We present a general procedure to determine the gravitational potentials for a far away wave zone field point. Moreover we work out the modified orbital dynamics of a binary-system as well as the effective 1.5 post-Newtonian barycentre for a generic $n$-body system. We notice that it is always possible to recover the corresponding general relativistic results in the limit of vanishing nonlocal modification parameters.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$.	contribution 0.93	0.82	0.07	asserted 0.99
s1	The general idea was obviously outlined for the first time in [13-16] and originates from the quest of finding a mechanism that is able to degravitate the vacuum energy on cosmological scales.	background 1.00	0.04	0.04	asserted 0.99
s2	We suggest in this manuscript a precise covariant coupling model which acts like a high-pass filter with a macroscopic distance filter scale $\sqrt{\Lambda}$.	contribution 0.56	0.86	0.17	hedged possibility 0.94
s3	In the context of this specific theory of gravity we review some cosmological aspects before we briefly recall the effective relaxed Einstein equations outlined for the first time in [1].	background 0.72	0.48	0.05	asserted 0.94
s4	We present a general procedure to determine the gravitational potentials for a far away wave zone field point.	method 0.73	0.91	0.06	asserted 1.00
s5	Moreover we work out the modified orbital dynamics of a binary-system as well as the effective 1.5 post-Newtonian barycentre for a generic $n$-body system.	contribution 0.95	0.95	0.18	asserted 1.00
s6	We notice that it is always possible to recover the corresponding general relativistic results in the limit of vanishing nonlocal modification parameters.	result 0.74	0.76	0.18	hedged possibility 0.61

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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Original abstract

In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$. The general idea was obviously outlined for the first time in [13-16] and originates from the quest of finding a mechanism that is able to degravitate the vacuum energy on cosmological scales. We suggest in this manuscript a precise covariant coupling model which acts like a high-pass filter with a macroscopic distance filter scale $\sqrt{\Lambda}$. In the context of this specific theory of gravity we review some cosmological aspects before we briefly recall the effective relaxed Einstein equations outlined for the first time in [1]. We present a general procedure to determine the gravitational potentials for a far away wave zone field point. Moreover we work out the modified orbital dynamics of a binary-system as well as the effective 1.5 post-Newtonian barycentre for a generic $n$-body system. We notice that it is always possible to recover the corresponding general relativistic results in the limit of vanishing nonlocal modification parameters.

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2 arXiv papers cite this in 10 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 8 sentences without a confident label

Uses its method or tool 1 paper

Following the usual procedure [ref] , presented in [ref] , we obtain the Green function in momentum space, [equation] It should be noticed that the first of these two contributions will eventually give rise to the usual Green function [ref] .

The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity · The nonlocal wave equation · 0.86

Uses its data or values 1 paper

We remind from [ref] that findings obtained in the framework of calculations performed previously in the context of possible deviations of the perihelion precession of Mercury led to a value for the dimensionless UV parameter, $|σ|≤9.3·10^-4$.

The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity · Conclusion · 0.93

What it cites · 187 sentences without a confident label

Uses the method or tool of 7 papers

Following the usual procedure [ref] we obtain the nonlocally modified Green function in momentum space, [equation] where we remind that by assumption we have $|σ|<1$.

Gravitational waves · The effective relaxed Einstein equations: · 0.93
In order to determine the precise form of the spatial components of the near zone potentials we need to expand the ratio inside the formal solution [ref] in terms of a power series, [equation] where $u=cτ$ and $τ=t-r/c$ is the retarded time.

The Confrontation between General Relativity and Experiment · A particular solution: · 0.84
In order to determine the precise form of the spatial components of the near zone potentials we need to expand the ratio inside the formal solution [ref] in terms of a power series, [equation] where $u=cτ$ and $τ=t-r/c$ is the retarded time.

Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations · A particular solution: · 0.84

Uses data or values from 4 papers

The latter (J0737-3039) is composed by two massive neutron stars orbiting their common center-of-mass on almost circular orbits ($e≈0.088$) [ref] .

Testing GR with the Double Pulsar: Recent Results · The energy released by a binary-system: · 0.96
The supernovae results in combination with the Cosmic Microwave Background data [ref] , interpreted in terms of the Standard Model of Cosmology ($Λ$CDM-model), allow for a precise determination of the vacuum energy density of the order of $ρ_ob∼10^-9 J/m^3$ as it is observed in the Universe.

Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters · The vacuum energy and the degravitation mechanism: · 0.81
Experimental results [ref] from deviation measurements of the Newtonian law at small length scales ($∼75 μm$) suggest that the dimensionless correction constant needs to be of the order $σ≲10^-3$.

New Experimental Constraints on Non-Newtonian Forces below 100 microns · The effective Newtonian potential: · 0.81

Compares with 3 papers

It should be mentioned that in [ref] we reduced the modified retarded Green function to the two leading order terms only and therefore obtained a slightly different result for the effective mass.

Degravitation and the relaxed Einstein equations · The effective Newtonian potential: · 0.97
It should be noticed that this result agrees with the $σ$-value inferred from Newtonian potential experiments designed to measure the Newtonian coupling parameter [ref] .

New Experimental Constraints on Non-Newtonian Forces below 100 microns · The perihelion precession of Mercury: · 0.95
It should be noticed that this result agrees with the $σ$-value inferred from Newtonian potential experiments designed to measure the Newtonian coupling parameter [ref] .

Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale · The perihelion precession of Mercury: · 0.95

Cites as support 2 papers

These terms will eventually cancel out with contributions coming from the wave zone as was shown in [ref] .

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. II. Two-body equations of motion to second post-Newtonian order, and radiation-reaction to 3.5 post-Newtonian order · A particular solution: · 0.96
These terms will eventually cancel out with contributions coming from the wave zone as was shown in [ref] .

Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations · A particular solution: · 0.96

Cites as background 37 papers

In this sense we will in the remaining part of this chapter briefly resume the nonlocally modified theory of gravity outlined for the first time in [ref] .

Degravitation and the relaxed Einstein equations · The nonlocally modified Einstein field equations: · 0.82
Further technical details, regarding this particular issue, can be withdrawn from [ref] .

The basis of nonlocal curvature invariants in quantum gravity theory · The nonlocally modified Einstein field equations: · 0.85
The parameter $κ$, although named differently, was encountered in the context of various nonlocal modified theories of gravity which originate from the pursuit of constructing a UV-complete theory of quantum gravity or coming from models of noncommutative geometry [ref] .

Gravitational Waves in the Spectral Action of Noncommutative Geometry · The nonlocally modified Einstein field equations: · 0.94

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