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Degravitation and the relaxed Einstein equations
General Relativity and Quantum Cosmology · Submitted 20 Apr 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We observe that at any step of computation we recover in the limit of vanishing modification parameters the corresponding general relativistic result.
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The abstract, sentence by sentence
The general idea to modify Einstein's field equations by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$ was apparently outlined for the first time in [12-15]. The modification itself originates from the quest of finding a mechanism which is able to degravitate the vacuum energy on cosmological scales. We present in this article 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 particular theory of gravity we work out the effective relaxed Einstein equations as well as the effective 1.5 post-Newtonian total near-zone mass of a many body system. We observe that at any step of computation we recover in the limit of vanishing modification parameters the corresponding general relativistic result.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The general idea to modify Einstein's field equations by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$ was apparently outlined for the first time in [12-15]. | background 1.00 | 0.04 | 0.03 | hedged possibility 0.62 |
| s1 | The modification itself originates from the quest of finding a mechanism which is able to degravitate the vacuum energy on cosmological scales. | background 1.00 | 0.06 | 0.04 | asserted 0.99 |
| s2 | We present in this article a precise covariant coupling model which acts like a high-pass filter with a macroscopic distance filter scale $\sqrt{\Lambda}$. | contribution 0.84 | 0.93 | 0.29 | asserted 1.00 |
| s3 | In the context of this particular theory of gravity we work out the effective relaxed Einstein equations as well as the effective 1.5 post-Newtonian total near-zone mass of a many body system. | contribution 0.95 | 0.96 | 0.15 | asserted 1.00 |
| s4 | We observe that at any step of computation we recover in the limit of vanishing modification parameters the corresponding general relativistic result. | result 0.97 | 0.95 | 0.24 | asserted 1.00 |
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The paper
Original abstract
The general idea to modify Einstein's field equations by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$ was apparently outlined for the first time in [12-15]. The modification itself originates from the quest of finding a mechanism which is able to degravitate the vacuum energy on cosmological scales. We present in this article 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 particular theory of gravity we work out the effective relaxed Einstein equations as well as the effective 1.5 post-Newtonian total near-zone mass of a many body system. We observe that at any step of computation we recover in the limit of vanishing modification parameters the corresponding general relativistic result.
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How the literature uses it
3 arXiv papers cite this in 50 sentences
Papers citing it · 44 sentences without a confident label
Uses its method or tool 1 paper
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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
Compares with it 1 paper
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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, Orbital Dynamics and the Effective Barycentre · The effective Newtonian potential: · 0.97
Cites it as background 1 paper
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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, Orbital Dynamics and the Effective Barycentre · The nonlocally modified Einstein field equations: · 0.82
What it cites · 125 sentences without a confident label
Uses the method or tool of 12 papers
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In order to obtain the leading term of $S_NL$, the equation above can be functionally integrated with the aid of the covariant curvature expansion technique presented in [ref] .
On covariant long-distance modifications of Einstein theory and strong coupling problem · The nonlocally modified Einstein equations: · 1.00
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In order to obtain the leading term of $S_NL$, the equation above can be functionally integrated with the aid of the covariant curvature expansion technique presented in [ref] .
The basis of nonlocal curvature invariants in quantum gravity theory · The nonlocally modified Einstein equations: · 1.00
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In order to obtain the leading term of $S_NL$, the equation above can be functionally integrated with the aid of the covariant curvature expansion technique presented in [ref] .
Nonlocal action for long-distance modifications of gravity theory · The nonlocally modified Einstein equations: · 1.00
Uses data or values from 3 papers
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Although there is some freedom in the precise computation of the vacuum energy, the most reasonable estimates range around a value of $ρ_th≈10^111 J/m^3$ [ref] .
The Cosmological Constant · Degravitation of the vacuum energy: · 0.96
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Experimental results [ref] from deviation measurements of the Newtonian law at small length scales ($∼25 μm$) suggest that the dimensionless correction constant needs to be of the order $σ≲10^-4$.
New Experimental Constraints on Non-Newtonian Forces below 100 microns · The nonlocally modified wave equation: · 0.81
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Experimental results [ref] from deviation measurements of the Newtonian law at small length scales ($∼25 μm$) suggest that the dimensionless correction constant needs to be of the order $σ≲10^-4$.
Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale · The nonlocally modified wave equation: · 0.81
Cites as support 3 papers
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However they can be discarded as they will cancel out with their wave zone counterparts as was shown in [ref] .
Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations · The effective total mass: · 0.98
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Although the nonlocal equations of motion are themselves generally covariant, they cannot (for nontrivial $G_Λ(_g)$) be presented as a metric variational derivative of a diffeomorphism invariant action unless you assume that they are only a first, linear in the curvature, approximation for the complete equations of motion [ref] .
Nonlocal action for long-distance modifications of gravity theory · Conclusion: · 0.96
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Although the nonlocal equations of motion are themselves generally covariant, they cannot (for nontrivial $G_Λ(_g)$) be presented as a metric variational derivative of a diffeomorphism invariant action unless you assume that they are only a first, linear in the curvature, approximation for the complete equations of motion [ref] .
On covariant long-distance modifications of Einstein theory and strong coupling problem · Conclusion: · 0.96
Cites as background 35 papers
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The general idea of a differential coupling was apparently formulated for the first time in [ref] in order to address the cosmological constant problem [ref] .
Degravitation of the Cosmological Constant and Graviton Width · Conclusion: · 0.91
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The general idea of a differential coupling was apparently formulated for the first time in [ref] in order to address the cosmological constant problem [ref] .
Non-Local Modification of Gravity and the Cosmological Constant Problem · Conclusion: · 0.91
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The general idea of a differential coupling was apparently formulated for the first time in [ref] in order to address the cosmological constant problem [ref] .
On covariant long-distance modifications of Einstein theory and strong coupling problem · Conclusion: · 0.91
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