REVIEW
Is Cosmic Speed-Up Due to New Gravitational Physics?
Astrophysics · Submitted 22 Jun 2003 · 34 references
Pith's verdict: A clean, honest first pass at 1/R gravity as a dark-energy alternative: the vacuum solutions are right, but the matter-era argument that carries the 'no dark energy' claim does not hold up as written.
T0 · AI review
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Referee report
The paper
The paper claims
A tiny correction to Einstein's gravity, of the form $-1/R$, might make the universe accelerate on its own, removing the need for dark energy.
The reading
What carries the argument
The load-bearing device is a conformal transformation. Writing $p equiv exp(sqrt{2/3},varphi/M_P) equiv 1 + mu^4/R^2$ and rescaling the metric to $tilde g_{mu nu} = p,g_{mu nu}$ turns the fourth-order $f(R)$ theory into ordinary Einstein gravity plus a scalar field $varphi$ with potential $V(varphi) = mu^2 M_P^2 (sqrt{p}-1)/p^2$, which vanishes at $varphi to 0$ and $varphi to infty$ and peaks at $p = 4/3$. The original frame's complicated $ddot H$ equations become a standard roll-down problem, and the three cosmic futures are read off from whether the field undershoots, hits, or overshoots the top of that potential. The matter-frame Hubble parameter is recovered through $H = sqrt{p},(tilde H - varphi'/M_Psqrt{6})$, and the general $n$ case gives the potential in Eq. (17) and the equation-of-state formula in Eq. (19). The authors also note that static spherically symmetric solutions are Schwarzschild-(anti) de Sitter, so solar-system tests are safe provided $mu$ is small enough.
Extended reading notes
Core claim
The central claim is that cosmic acceleration can arise from a very small correction to the gravitational action of the form $R^n$ with $n<0$, so that dark energy is not required. Working with $S = int d^4x sqrt{-g},(M_P^2/2)(R - mu^4/R) + S_M$, the authors show that the constant-curvature vacuum solutions satisfy $R = pm sqrt{3},mu^2$: increasing $mu$ from zero splits the unique Minkowski vacuum into a de Sitter and an anti-de Sitter branch. The de Sitter solution is unstable, with a long decay time $tau sim mu^{-1}$, but nearby trajectories give genuine late-time acceleration. In vacuum there are three outcomes depending on the initial scalar velocity: eternal de Sitter (requires tuning), power-law acceleration with $a(t) propto t^2$ and $w_{rm eff} = -2/3$, or a future curvature singularity in which $H$ stays finite while $dot H$ diverges. The authors argue the same three futures survive when matter is included, and they generalise to $-mu^{2(n+1)}/R^n$ with $n>1$, obtaining $a(t) propto t^q$ with $q = (2n+1)(n+1)/(n+2)$ and an effective equation of state approaching $-1$ as $n to infty$, which fits current observational bounds on $w_{rm DE}$.
Load-bearing premise
The load-bearing premise is that the single new scale $mu$ can be set by hand to about $10^{-33}$ eV so that the correction becomes important exactly at the present epoch, and that the resulting transition from matter domination to self-acceleration yields an expansion history that matches observations; the authors state they have merely chosen $mu$ to achieve this end and explicitly defer a quantitative analysis of the transition, which they treat only through approximate equations that drop the potential gradient.
Editorial extensions
If this is right
- If the mechanism holds, the dark energy budget of the universe is zero and the acceleration is a geometric effect of a $1/R$ term in the gravitational action with $mu sim 10^{-33}$ eV.
- The generic prediction is an effective equation of state between $-1$ and $-2/3$, with the exact value set by the power $n$ of the correction, so measurements of $w_{rm DE}$ discriminate among members of this family.
- Because a positive-power curvature term $m^{-2}R^2$ drives Starobinsky inflation, the same gravitational sector can account for both the early and late accelerating phases, with General Relativity valid only in between.
- Astrophysical tests of the Schwarzschild solution are unaffected as long as $mu^4$ is small, since the static spherically symmetric solutions become Schwarzschild-(anti) de Sitter and deviate only on horizon-sized scales.
- The de Sitter vacuum branch is unstable on a timescale $tau sim mu^{-1}$, so a universe sitting exactly at the potential maximum is a tuned, transient state rather than a generic outcome.
Reading between the lines
- The clearest observational handle is not the background expansion alone but the growth of structure: a gravity-only explanation of acceleration generally predicts a different growth rate and a different slip between the two gravitational potentials than a cosmological constant does, so joint fits to expansion and weak-lensing growth would separate the two pictures.
- Because the matter-era behaviour is governed by the approximate Eqs. (15)-(16), which drop the potential gradient, the model's viability likely hinges on whether the transition epoch produces a smooth, non-oscillatory join between matter domination and self-acceleration; a numerical integration of the full fourth-order system would settle this quickly.
- The same $1/R$ term changes the inner dynamics of compact objects and the early universe at high curvature, so a bound from big-bang nucleosynthesis or from the cosmic microwave background's acoustic scale would constrain $mu$ independently of the local acceleration measurement.
- The family indexed by $n$ is a one-parameter ladder interpolating between $w_{rm eff} = -2/3$ and $-1$, which makes it a natural target for forthcoming dark-energy equation-of-state constraints rather than a single fixed hypothesis.
Original abstract
We show that cosmic acceleration can arise due to very tiny corrections to the usual gravitational action of General Relativity of the form $R^n$, with $n<0$. This eliminates the need for dark energy, though it does not address the cosmological constant problem. Since a modification to the Einstein-Hilbert action of the form $R^n$, with $n>0$, can lead to early-time inflation, our proposal provides a unified and purely gravitational origin for the early and late time accelerating phases of the Universe.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We show that cosmic acceleration can arise due to very tiny corrections to the usual gravitational action of General Relativity of the form $R^n$, with $n<0$. This eliminates the need for dark energy, though it does not address the cosmological constant problem. Since a modification to the Einstein-Hilbert action of the form $R^n$, with $n>0$, can lead to early-time inflation, our proposal provides a unified and purely gravitational origin for the early and late time accelerating phases of the Universe.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that cosmic acceleration can arise due to very tiny corrections to the usual gravitational action of General Relativity of the form $R^n$, with $n<0$. | result 0.87 | 0.90 | 0.86 | asserted 0.98 |
| s1 | This eliminates the need for dark energy, though it does not address the cosmological constant problem. | limitation 0.86 | 0.55 | 0.15 | asserted 1.00 |
| s2 | Since a modification to the Einstein-Hilbert action of the form $R^n$, with $n>0$, can lead to early-time inflation, our proposal provides a unified and purely gravitational origin for the early and late time accelerating phases of the Universe. | interpretation 0.95 | 0.43 | 0.35 | asserted 0.75 |
What was examined, and what was not
- arXiv listing abstract v2
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- P abstract
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Figures
Figures reproduced from arXiv:astro-ph/0306438 by the authors.
References
How later papers used it
320 later papers cite it
2 later papers by other authors are listed below: 2 compared their own results with it.
Compares with it 2 of 6 papers with this label
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Obtained, for n=1, m=2, and Λ_1=Λ_2=0 in another work's equation at small curvature, the solution of this paper's equation, â ∝t^2.
Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models (2010) · 0.89 · paraphrased: the licence does not allow quoting
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Expanding for small $κ$, we find [equation] The leading Kaniadakis correction on the de Sitter branch is precisely the $1/R$ modification proposed by Carroll, Duvvuri, Trodden and Turner as a geometric origin of late-time acceleration [ref] , with the inverse-curvature scale fixed by the deformation parameter as $κ^2σ^2/6$.
Reconstructing $f(R)$ gravity from generalized entropies: exact Lagrangians (2026) · Exact Lagrangians · 0.87
How the literature uses it
248 arXiv papers cite this in 311 sentences
Papers citing it · 130 sentences without a confident label
Contests it 2 papers
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Chiba concluded that the model was ruled out by Solar System data, contradicting the original claims of [ref] based on the assumption that the Schwarzschild solution should hold as a vacuum solution.
Stellar structure models in modified theories of gravity: lessons and challenges · Weak-field limit, PPN formalism, and matching to the exterior solution · contest 0.80
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The simple model in Ref. [ref] was shortly found to have an instability [ref] .
Beyond Special and General Relativity. Neutrinos and Cosmology · Review on alternative models to explain the accelerated expansion · contest 0.81
Builds on it 3 papers
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It is natural to consider generalizing the action of [ref] to include other curvature invariants [ref] .
Cosmic acceleration and the challenge of modifying gravity · Extensions: Higher-Order Curvature Invariants · 0.86
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It is natural to consider generalizing the action of [ref] to include other curvature invariants [ref] .
Some Adventures in the Search for a Modified Gravity Explanation for Cosmic Acceleration · Extensions: Higher-Order Curvature Invariants · 0.90
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It is natural to consider generalizing the action of [ref] to include other curvature invariants [ref] .
Dark Energy and Cosmology · Extensions: Higher-Order Curvature Invariants · 0.90
Compares with it 6 papers
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Expanding for small $κ$, we find [equation] The leading Kaniadakis correction on the de Sitter branch is precisely the $1/R$ modification proposed by Carroll, Duvvuri, Trodden and Turner as a geometric origin of late-time acceleration [ref] , with the inverse-curvature scale fixed by the deformation parameter as $κ^2σ^2/6$.
Reconstructing $f(R)$ gravity from generalized entropies: exact Lagrangians · Exact Lagrangians · 0.87
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When $n=1$, $m=2$, and $Λ_1=Λ_2=0$ in ([ref]) and the curvature is small, we obtain the solution of ([ref]): $â ∝t^2$, which is consistent with the result in [ref] .
Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models · Unified theories without a flat space solution · 0.89
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The $π$ behavior instead closely resembles that of the $f(R)$ scalar field [ref] under the chameleon mechanism [ref] .
N-Body Simulations of DGP and Degravitation Theories · Fundamentals · 0.92
Cites it as background 152 papers
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In this paper, we will study three different modified gravity scenarios, focusing on their predictions for lensing observables: (i) $$ gravity [ref] ; (ii) the Dvali-Gabadadze-Porrati (DGP) model [ref] ; and (iii) Tensor-Vector-Scalar theory (TeVeS) [ref] .
Weak Lensing Probes of Modified Gravity · Introduction · 0.82
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These modifications must become important at late times in order to explain the fact that the universe has started to accelerate only recently, and so much attention has been focused on actions with inverse powers of curvature invariants, mainly squares of the Ricci scalar $R$, the Ricci tensor $R_μν$, and the Riemann tensor $R_μνρσ$ [ref] .
Unsuccessful cosmology with Modified Gravity Models · Introduction · 0.90
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We focus here on thin-shell screening, as our specific emphasis will be $f(R)$ gravity which screens by the chameleon mechanism [ref] .
Galaxy morphology rules out astrophysically relevant Hu-Sawicki $f(R)$ gravity · Introduction · 0.89
Discussion
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