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Modified gravity, Dark Energy and MOND
General Relativity and Quantum Cosmology · Submitted 20 Dec 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that for some choices of these invariants the models are ghost free and modify Newtonian gravity below a characteristic acceleration scale given by a_0 = c\mu, where c is the speed of light and \mu is a parameter of the model that also determines the late-time Hubble constant: H_0 \sim \mu.
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The abstract, sentence by sentence
We propose a class of actions for the spacetime metric that introduce corrections to the Einstein-Hilbert Lagrangian depending on the logarithm of some curvature scalars. We show that for some choices of these invariants the models are ghost free and modify Newtonian gravity below a characteristic acceleration scale given by a_0 = c\mu, where c is the speed of light and \mu is a parameter of the model that also determines the late-time Hubble constant: H_0 \sim \mu. In these models, besides the massless spin two graviton, there is a scalar excitation of the spacetime metric whose mass depends on the background curvature. This dependence is such that this scalar, although almost massless in vacuum, becomes massive and effectively decouples when one gets close to any source and we recover an acceptable weak field limit at short distances. There is also a (classical) ``running'' of Newton's constant with the distance to the sources and gravity is easily enhanced at large distances by a large ratio. We comment on the possibility of building a model with a MOND-like Newtonian limit that could explain the rotation curves of galaxies without introducing Dark Matter using this kind of actions. We also explore briefly the characteristic gravitational phenomenology that these models imply: besides a long distance modification of gravity they also predict deviations from Newton's law at short distances. This short distance scale depends on the local background curvature of spacetime, and we find that for experiments on the Earth surface it is of order \sim 0.1mm, while this distance would be bigger in space where the local curvature is significantly lower.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a class of actions for the spacetime metric that introduce corrections to the Einstein-Hilbert Lagrangian depending on the logarithm of some curvature scalars. | contribution 0.96 | 0.88 | 0.09 | asserted 0.90 |
| s1 | We show that for some choices of these invariants the models are ghost free and modify Newtonian gravity below a characteristic acceleration scale given by a_0 = c\mu, where c is the speed of light and \mu is a parameter of the model that also determines the late-time Hubble constant: H_0 \sim \mu. | result 0.93 | 0.94 | 0.42 | asserted 0.99 |
| s2 | In these models, besides the massless spin two graviton, there is a scalar excitation of the spacetime metric whose mass depends on the background curvature. | result 0.90 | 0.75 | 0.11 | asserted 1.00 |
| s3 | This dependence is such that this scalar, although almost massless in vacuum, becomes massive and effectively decouples when one gets close to any source and we recover an acceptable weak field limit at short distances. | result 0.80 | 0.82 | 0.13 | asserted 1.00 |
| s4 | There is also a (classical) ``running'' of Newton's constant with the distance to the sources and gravity is easily enhanced at large distances by a large ratio. | result 0.97 | 0.78 | 0.13 | asserted 0.97 |
| s5 | We comment on the possibility of building a model with a MOND-like Newtonian limit that could explain the rotation curves of galaxies without introducing Dark Matter using this kind of actions. | interpretation 0.42 | 0.36 | 0.26 | hedged possibility 0.99 |
| s6 | We also explore briefly the characteristic gravitational phenomenology that these models imply: besides a long distance modification of gravity they also predict deviations from Newton's law at short distances. | contribution 0.60 | 0.80 | 0.11 | asserted 0.89 |
| s7 | This short distance scale depends on the local background curvature of spacetime, and we find that for experiments on the Earth surface it is of order \sim 0.1mm, while this distance would be bigger in space where the local curvature is significantly lower. | result 0.99 | 0.92 | 0.07 | asserted 1.00 |
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The paper
Original abstract
We propose a class of actions for the spacetime metric that introduce corrections to the Einstein-Hilbert Lagrangian depending on the logarithm of some curvature scalars. We show that for some choices of these invariants the models are ghost free and modify Newtonian gravity below a characteristic acceleration scale given by a_0 = c\mu, where c is the speed of light and \mu is a parameter of the model that also determines the late-time Hubble constant: H_0 \sim \mu. In these models, besides the massless spin two graviton, there is a scalar excitation of the spacetime metric whose mass depends on the background curvature. This dependence is such that this scalar, although almost massless in vacuum, becomes massive and effectively decouples when one gets close to any source and we recover an acceptable weak field limit at short distances. There is also a (classical) ``running'' of Newton's constant with the distance to the sources and gravity is easily enhanced at large distances by a large ratio. We comment on the possibility of building a model with a MOND-like Newtonian limit that could explain the rotation curves of galaxies without introducing Dark Matter using this kind of actions. We also explore briefly the characteristic gravitational phenomenology that these models imply: besides a long distance modification of gravity they also predict deviations from Newton's law at short distances. This short distance scale depends on the local background curvature of spacetime, and we find that for experiments on the Earth surface it is of order \sim 0.1mm, while this distance would be bigger in space where the local curvature is significantly lower.
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9 arXiv papers cite this in 9 sentences
Papers citing it · 4 sentences without a confident label
Compares with it 1 paper
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Since now the mass grows at short distance this condition means that the force would only appear at $long$ distances, $r>r_c$, where $r_c$, defined as GM/r_c^2 ≡Λ, corresponds to a fixed gravitational acceleration[This dependence of the mass with the distance yielding a fixed Newtonian acceleration as the threshold for the appearance of new effects is the same one finds for the scalar mode of the metric in the purely gravitational model of [ref] .] $a_c= Λ$.
Dark Energy, scalar-curvature couplings and a critical acceleration scale · Introduction · 0.99
Cites it as background 4 papers
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A number of proposals [ref] have been put forward for extensions to General Relativity that recover Eq.([ref]) - or variations thereof - in appropriate limits.
Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory · Introduction · 0.87
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The viable f(R)-gravity models replacing the dark energy have been considered [ref] .
Modified Starobinsky Inflation · Introduction · 0.85
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[ref] and for examples of $f(R)$ inflationary models, check [ref] and the references therein.
A viable logarithmic f(R) model for inflation · A new logarithmic model · 0.97
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