Probing Newton's Constant on Vast Scales: DGP Gravity, Cosmic Acceleration and Large Scale Structure

Arthur Lue; Glenn D. Starkman; Roman Scoccimarro

REVIEW

Probing Newton's Constant on Vast Scales: DGP Gravity, Cosmic Acceleration and Large Scale Structure

Arthur Lue, Roman Scoccimarro, Glenn D. Starkman

Astrophysics · Submitted 23 Jan 2004 · 37 references

Pith's verdict: The force-law derivation is solid and worth citing; the sigma_8 tension is real in direction but softer in magnitude than the abstract's 'two sigma' framing suggests.

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CitationArthur Lue, Glenn D. Starkman, Roman Scoccimarro. "Probing Newton's Constant on Vast Scales: DGP Gravity, Cosmic Acceleration and Large Scale Structure." arXiv:astro-ph/0401515 (2004). https://pith.science/paper/3P23VOMS

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Two things to take away. The force-law derivation in Sec. II.C is the real contribution: they extend their static de Sitter result to an evolving matter-dominated background and get Eqs. 2.16-2.19, with G_eff = G(1 + 1/(3beta)) and beta negative and time-dependent. That is genuine work, and the point that DGP does not obey Birkhoff's law — the force law depends on the background expansion — is well made. The headline sigma_8 <= 0.8 at two sigma is softer than the abstract implies, and the softness is in the observational chain, not the derivation. What holds up: the growth suppression follows cleanly from Eq. 3.3; f(Omega_m) ~ Omega_m^{2/3} is a nice, checkable contrast with Omega_m^{5/9}; the ISW cancellation (the graviscalar does not couple to photons, so subhorizon ISW is unchanged) is clean and non-obvious; and the spherical-collapse result that the nu_n are nearly unchanged is a useful practical point for bias calibration. The paper is explicit about its approximations in Sec. II.D. On the stress-test's transfer-function worry: I think it mostly dissolves. The formula is G_eff = G(1 + 1/(3beta)), not G(1 + beta/3) — both the reader and the stress-test misread the OCR. As beta -> -infinity at high z, 1/(3beta) -> 0, so G_eff -> G and the high-z modes really do evolve standardly. The paper should have shown this rather than asserting it, but the physics supports them. The real soft spots are the ones the reader named: the bias conversion (sigma_8^* = 0.89 -> 1.00 with only a 10% systematic) and holding the WMAP normalization fixed while varying Omega_m. The 'two-sigma' framing is a reasonable summary of a chain with several 10-15% steps, not a sharp result. Who it is for: anyone working on infrared modifications of gravity or using growth as a dark-energy discriminator. The derivation is worth citing; the sigma_8 number should be cited with caveats attached. Recommendation: send it out. The derivation is solid and the qualitative conclusion — DGP growth is suppressed relative to LambdaCDM — is robust even if the exact sigma_8 shifts. A referee should push on the normalization chain, not the force law.

Referee report

Significance

The force-law derivation in an evolving background (Sec. II.C) is a genuine technical advance over the static case, and the algebra is internally consistent: I verified that Eqs. (2.18), (3.1), (3.2), (3.4) and (3.5) follow from one another and from the Friedmann equation (2.8), and that the effective equation of state w_eff = -1/(1+Omega_m) is correct. The cancellation in Eq. (3.11) is a clean and falsifiable statement: the DGP scalar couples to the trace of the matter energy-momentum tensor but not to photons, so ISW and lensing are unaffected at subhorizon scales and the only large-scale-structure signature is the growth rate. The prediction f ~ Omega_m^{2/3} versus the LambdaCDM value Omega_m^{5/9} is a roughly 10% discriminant that is independent of the primordial normalization, and the authors are right to flag it as the cleanest future test. The approximations (quasistatic sources, rH << 1, v << 1, compact support well inside the horizon) are stated explicitly in Sec. II.D, which is good practice. If the quantitative conclusion holds, it is a significant constraint on a leading modified-gravity explanation of acceleration.

Major objections (2)

[Sec. III.B, Eq. (3.3), and Sec. IV, Fig. 3] The sigma_8 calculation applies a single scale-independent growth factor D+(z) from Eq. (3.3), which is derived under the weak-brane condition r >> r*. Footnote 2 states that for 1-sigma fluctuations of scale r = 10-100 Mpc/h the transition scale is r* = 5-15 Mpc/h, so at the low end of that range r and r* are comparable rather than well separated. Since sigma_8 is defined at 8 h^{-1} Mpc, the defining scale sits essentially at r*, where the force law is crossing over between the Einstein phase (Eq. 2.21) and the weak-brane phase (Eq. 2.23). In the Einstein phase the fractional deviation from Newtonian gravity scales as (r/r*)^{3/2} and is therefore smaller than the weak-brane value 1/(3 beta) used in Eq. (3.3). Applying the weak-brane G_eff at all scales therefore overestimates the suppression precisely where sigma_8 is measured, and it also makes the growth scale-independent when the crossover inevitably makes it scale-dependent, changing the shape as well as the amplitude of P(k). A concrete test is to recompute sigma_8 with a growth factor that interpolates between Eqs. (2.21) and (2.23) as a function of scale, and to report how much the curve in Fig. 3 moves. The correction goes in the direction of raising sigma_8 and weakening the quoted two-sigma tension, so this bears directly on the headline number in abstract:s5.
[Sec. IV, paragraph comparing to SDSS] The 'two-sigma' characterization rests on a chain that is not fully propagated into the quoted significance. The measured sigma_8^* = 0.89 +/- 0.02 at z = 0.1 is converted to a dark matter value sigma_8 = 1.00 +/- 0.11 using b = 1.04 +/- 0.11 at L ~ 1.9 L* from the 2dF bispectrum and the Norberg scaling b/b* = 0.85 + 0.15(L/L*); the paper then allows 'another 10% systematic uncertainty' without folding it into the error bar. In addition, the WMAP primordial normalization is held fixed as Omega_0m is varied away from 0.3, which is an approximation that affects the shape of the sigma_8(Omega_0m) curve in Fig. 3, and the SDSS value itself was derived under the assumption of Einstein gravity. Since the headline claim is a significance statement, the report should give the full error budget explicitly and recompute the separation with the systematic included, rather than quoting 'about two sigma' from the statistical error alone. The qualitative conclusion is likely to survive because the modified expansion history and the repulsive force law both suppress growth, but the quantitative significance should be stated with the systematics it actually carries.

Minor objections (10)

[Sec. III.B, after Eq. (3.2)] The text notes that beta approaches minus infinity at high redshift, which reads as an alarmingly large correction, but does not state the fact that actually matters: the fractional correction entering G_eff is 1/(3 beta), which goes to zero as beta diverges, so G_eff returns to G at high redshift. This is exactly what licenses the use of an Einstein-gravity transfer function in Sec. IV. One sentence making the high-z limit explicit would remove the apparent tension and would also answer the natural objection that the transfer function shape might be altered.
[Sec. IV, transfer function paragraph] The statement that modes contributing to sigma_8 'entered the Hubble radius at redshifts high enough that they evolve in the standard fashion' is correct but asserted rather than shown. A short quantitative estimate, for example evaluating 1/(3 beta) at z ~ 10^3-10^4 and showing it is of order 10^{-4}, would make the argument self-contained.
[Sec. III.B, first paragraph] The phrase 'one is always in the weak-brane regime, 2r >> r*' appears to contain a stray factor of two; the condition should presumably read r >> r*. Please check the typesetting.
[Eqs. (2.18) and (3.1)] The nested radical in Eq. (2.18) and the corresponding bracket in Eq. (3.1) are difficult to parse as set. Rewriting the expression in terms of epsilon alone, with the definition displayed separately, would help the reader verify the algebra.
[Fig. 1 caption] The caption describes 'the upper line' and 'the lower one' but does not state unambiguously which curve corresponds to which Omega_0m in each panel, nor which curves are DGP and which are dark energy. Labelling the curves directly in the figure would remove the ambiguity.
[Fig. 3 and surrounding text] The predicted sigma_8 at the supernova best-fit value Omega_0m = 0.18 is shown only graphically. Quoting the number in the text, together with the corresponding value at Omega_0m = 0.3, would let the reader judge the tension without reading it off the figure.
[Sec. III.D, final paragraph] The text says 'we ignore the fact that the ISW effect at low multipoles can be different in DGP gravity', but Sec. III.D has just argued that the ISW effect is identical to the dark-energy case at subhorizon scales. The caveat should be stated as applying only to scales comparable to the horizon, where the approximation of Sec. II.D breaks down, so that it does not appear to contradict the result of Eq. (3.11).
[Sec. III.C] The quoted difference between delta_c = 1.656 and 1.689 is small; stating the fractional difference and comparing it to the intrinsic accuracy of the spherical-collapse approximation would make clear that this is a null result rather than a marginal one.
[Sec. IV, first paragraph] The DGP parameter fit of Ref. [21] is pre-WMAP while the normalization is taken from the WMAP analysis of Ref. [33]. A sentence noting that the two are consistent for the parameters relevant to large-scale structure, as the text already implies, would make the mixed provenance explicit.
[Sec. III.E] The superposition argument for the linear regime is sound, but the nonlinear case is dismissed with the observation that nonlinearities develop late. Since the bias-independence argument in Sec. IV leans on the higher-order moments being close to LambdaCDM, a brief statement of the expected size of the correction from second-order perturbation theory would strengthen that link.

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The paper

The paper claims

The paper argues that if cosmic acceleration comes from gravity leaking into a fifth dimension rather than from dark energy, the growth of large-scale structure is suppressed enough to conflict with observed galaxy clustering at roughly the

The reading

The paper asks whether the accelerated expansion of the universe could be a signal of modified gravity rather than a dark energy fluid, and whether that idea can be told apart from dark energy using the growth of cosmic structure. In the Dvali–Gabadadze–Porrati (DGP) braneworld, gravity is four-dimensional at short distances but leaks into a fifth dimension beyond a crossover scale $r_0$, and choosing $r_0$ close to today's Hubble radius $H_0^{-1}$ makes the expansion accelerate now without any dark energy. The authors derive the gravitational field of a spherical overdensity in an expanding DGP background and show that well inside the horizon the force law is Newtonian with a shifted, time-dependent coupling $G_{eff} = G(1+1/3)$-style correction, $G_{eff}=G(1+1/3)$, where $ = - (1+_m)/(1-_m)$ divided by two is negative and of order unity today, so the effective Newton constant is smaller than in general relativity. Because this extra repulsion suppresses the growth of density and velocity perturbations, fitting the supernova-preferred matter density pushes the present amplitude $_8$ down to about 0.7 to 0.8, while galaxy surveys indicate a value near 1.0. The payoff is a concrete, testable tension: DGP can explain the acceleration or the observed structure, but not obviously both.

What carries the argument

The load-bearing object is the ratio $(r)$ defined in Eq. (2.18), built from the parameter $ = (1 2r_0 H + 2r_0^2 H^2)/(1 2r_0 H)$ (lower signs for the self-accelerating branch), which interpolates the metric of a spherical overdensity between an Einstein phase at small radii and a weak-brane phase at large radii. Its argument is $8r_0^2 R_g/9^2 r^3$, with $R_g$ the effective Schwarzschild radius of the overdensity, so the crossover radius $r_* = (r_0^2 R_g/^2)^{1/3}$ is where the extra scalar switches on. Because $ $ contains the Hubble rate, the force law inherits the expansion history; this is what makes DGP distinguishable from a dark energy model with the same $H(z)$, and it is also why the suppression of growth is roughly twice what a Birkhoff-obeying modification would give. In linear theory the whole effect collapses to the single replacement $G G(1+1/3)$, which feeds directly into the growth equation and into the velocity growth rate $f d D_+/d a$.

Extended reading notes

Core claim

The central claim is that DGP gravity does not obey Birkhoff's law: the force law around an isolated mass depends on the background cosmological expansion, because the brane's extrinsic curvature controls the strength of the scalar gravitational mode. Generalizing an earlier static de Sitter calculation to an expanding matter-dominated background, the authors find two regimes separated by a new scale $r_* = (r_0^2 R_g/^2)^{1/3}$. Inside $r_*$ the metric reduces to the Einstein phase with a small $1/r^{3/2}$ correction; outside it the weak-brane phase sets in and the two gravitational potentials acquire different effective Newton constants, with the Newtonian one becoming $G_{eff} = G(1+1/3)$. Since $ $ is negative and grows in magnitude with time, gravity becomes effectively weaker than Einstein gravity as the universe ages, and linear growth is suppressed relative to a dark energy model engineered to produce the identical expansion history. The suppression is about twice as large as in modified-gravity models that do obey Birkhoff's law. Combined with the supernova-preferred matter density, this drives the present normalization to $_8 0.8$ at roughly two $\sigma$, against a dark-matter value near 1.0 inferred from SDSS galaxy clustering. The authors also show that $^2(-)$ for linear perturbations is exactly the four-dimensional Einstein expression, so the late-time integrated Sachs–Wolfe effect and weak lensing at subhorizon scales are unchanged from a dark energy model with the same expansion history. They are explicit that the treatment is restricted to subhorizon, quasistatic, spherical perturbations, and that a fully consistent linear and second-order treatment, plus the horizon-scale ISW calculation, remains to be done.

Load-bearing premise

The claimed tension rests on turning the measured L* galaxy clustering amplitude into a dark-matter $_8$ through an empirical luminosity-bias relation, and on holding the primordial fluctuation normalization fixed as $_m$ is varied, a chain to which the paper allows only about 10% systematic uncertainty.

Editorial extensions

If this is right

If DGP is right, the linear growth rate behaves as $f _m^{2/3}$ rather than the $_m^{5/9}$ of a flat cosmological constant model, a difference of at least 10% for $_m$ between 0.2 and 0.3 that redshift-space distortion surveys can reach.
Because the extra gravitational scalar does not couple to photons, the late-time integrated Sachs–Wolfe effect and weak lensing at subhorizon scales look exactly like a dark energy model with the same expansion history; only the growth rate and the geometrical distances carry the DGP signature.
Spherical collapse happens later in DGP (redshift 0.35 rather than 0.66 for the same initial perturbation) but the linearly extrapolated threshold changes only from 1.689 to 1.656, and the hierarchical moments such as the skewness shift by less than a percent, so nonlinear growth can still be used to calibrate galaxy bias as in standard cosmology.
Fitting the supernova acceleration inside DGP drives $_m$ to about 0.18, where the predicted $_8$ falls to 0.7 or below at one sigma, so sharper supernova evidence for an effective equation of state near $-1$ would deepen the tension rather than relieve it.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The cleanest discriminator suggested by this machinery is a joint measurement of the growth rate and the expansion history at the same redshift: a DGP fit that matches supernovae but predicts a lower $f$ at fixed $_m$ would be separable from a dark energy model with matching $w(z)$.
Because the paper finds $^2(-)$ unchanged, gravitational-slip measurements, a standard probe of modified gravity, would be blind to this particular modification at subhorizon scales; the signal lives in the growth rate and in distances instead.
The crossover radius scales as $R_g^{1/3}$, so the Einstein-to-weak-brane transition sits at a few megaparsecs for galaxy-scale masses and moves only weakly with mass; if the null lensing result survives for aspherical lenses, a stacked lensing analysis could in principle map that transition directly.
The two-sigma tension is only as firm as the conversion of an L* galaxy clustering amplitude into a dark-matter amplitude; a bias-independent $_8$ from cluster counts or cosmic microwave background lensing at $_m$ near 0.2 would settle whether the conflict is real.

Original abstract

The nature of the fuel that drives today's cosmic acceleration is an open and tantalizing mystery. The braneworld theory of Dvali, Gabadadze, and Porrati (DGP) provides a context where late-time acceleration is driven not by some energy-momentum component (dark energy), but rather is the manifestation of the excruciatingly slow leakage of gravity off our four-dimensional world into an extra dimension. At the same time, DGP gravity alters the gravitational force law in a specific and dramatic way at cosmologically accessible scales. We derive the DGP gravitational force law in a cosmological setting for spherical perturbations at subhorizon scales and compute the growth of large-scale structure. We find that a residual repulsive force at large distances gives rise to a suppression of the growth of density and velocity perturbations. Explaining the cosmic acceleration in this framework leads to a present day fluctuation power spectrum normalization sigma_8 <= 0.8 at about the two-sigma level, in contrast with observations. We discuss further theoretical work necessary to go beyond our approximations to confirm these results.

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.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,678 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.96 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.54 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The nature of the fuel that drives today's cosmic acceleration is an open and tantalizing mystery. The braneworld theory of Dvali, Gabadadze, and Porrati (DGP) provides a context where late-time acceleration is driven not by some energy-momentum component (dark energy), but rather is the manifestation of the excruciatingly slow leakage of gravity off our four-dimensional world into an extra dimension. At the same time, DGP gravity alters the gravitational force law in a specific and dramatic way at cosmologically accessible scales. We derive the DGP gravitational force law in a cosmological setting for spherical perturbations at subhorizon scales and compute the growth of large-scale structure. We find that a residual repulsive force at large distances gives rise to a suppression of the growth of density and velocity perturbations. Explaining the cosmic acceleration in this framework leads to a present day fluctuation power spectrum normalization sigma_8 <= 0.8 at about the two-sigma level, in contrast with observations. We discuss further theoretical work necessary to go beyond our approximations to confirm these results.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The nature of the fuel that drives today's cosmic acceleration is an open and tantalizing mystery.	background 0.91	0.04	0.02	asserted 1.00
s1	The braneworld theory of Dvali, Gabadadze, and Porrati (DGP) provides a context where late-time acceleration is driven not by some energy-momentum component (dark energy), but rather is the manifestation of the excruciatingly slow leakage of gravity off our four-dimensional world into an extra dimension.	background 1.00	0.05	0.06	asserted 0.97
s2	At the same time, DGP gravity alters the gravitational force law in a specific and dramatic way at cosmologically accessible scales.	background 0.99	0.08	0.03	asserted 1.00
s3	We derive the DGP gravitational force law in a cosmological setting for spherical perturbations at subhorizon scales and compute the growth of large-scale structure.	contribution 0.54	0.97	0.04	asserted 0.95
s4	We find that a residual repulsive force at large distances gives rise to a suppression of the growth of density and velocity perturbations.	result 0.94	0.95	0.20	asserted 1.00
s5	Explaining the cosmic acceleration in this framework leads to a present day fluctuation power spectrum normalization sigma_8 <= 0.8 at about the two-sigma level, in contrast with observations.	result 0.93	0.89	0.77	asserted 0.91
s6	We discuss further theoretical work necessary to go beyond our approximations to confirm these results.	future work 0.85	0.14	0.03	unclear 0.72

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1. The top panel shows the ratio of the growth factors

**Figure 2.** FIG. 2. Numerical solution of the spherical collapse. The le

**Figure 3.** FIG. 3. The linear power spectrum normalization,

Figures reproduced from arXiv:astro-ph/0401515 by the authors.

References

Works cited (37)

[1]

S. Perlmutter et al. [Supernova Cosmology Project Collaboration], Astrophys. J. 517, 565 (1999)

View on Pith 1999
[2]

A. G. Riess et al. [Supernova Search Team Collaboration], Astron. J. 116, 1009 (1998)

View on Pith 1998
[3]

C. Deﬀayet, Phys. Lett. B 502, 199 (2001)

View on Pith 2001
[4]

C. Deﬀayet, G. R. Dvali and G. Gabadadze, Phys. Rev. D 65, 044023 (2002)

View on Pith 2002
[5]

T. Damour, I. I. Kogan and A. Papazoglou, Phys. Rev. D 66, 104025 (2002)

View on Pith 2002
[6]

K. Freese and M. Lewis, Phys. Lett. B 540, 1 (2002)

View on Pith 2002
[7]

K. Freese, Nucl. Phys. Proc. Suppl. 124, 50 (2003)

View on Pith 2003
[8]

G. Dvali and M. S. Turner, arXiv:astro-ph/0301510

View on Pith Pith review arXiv
[9]

Capozziello S., Carloni S., Troisi A., arXiv:astro-ph/0303041

View on Pith Pith review arXiv
[10]

S. M. Carroll, V. Duvvuri, M. Trodden and M. S. Turner, arXiv:as tro-ph/0306438

View on Pith
[11]

S. Capozziello, V. F. Cardone, S. Carloni, A. Troisi., arXiv:astro- ph/0307018

View on Pith
[12]

S. Nojiri and S. D. Odintsov, Phys. Rev. D 68, 123512 (2003)

View on Pith 2003
[13]

J. Khoury and A. Weltman, arXiv:astro-ph/0309300

View on Pith Pith review arXiv
[14]

J. Khoury and A. Weltman, arXiv:astro-ph/0309411

View on Pith Pith review arXiv
[15]

A. Lue, R. Scoccimarro and G. Starkman, arXiv:astro-ph/030 7034

View on Pith
[16]

T. Multamaki, E. Gaztanaga and M. Manera, Mon. Not. Roy. Ast ron. Soc. 344, 761 (2003)

View on Pith 2003
[17]

G. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485, 208 (2000)

View on Pith 2000
[18]

G. R. Dvali, G. Gabadadze, M. Kolanovic and F. Nitti, Phys. Rev. D 64, 084004 (2001)

View on Pith 2001
[19]

G. R. Dvali, G. Gabadadze, M. Kolanovic and F. Nitti, Phys. Rev. D 65, 024031 (2002)

View on Pith 2002
[20]

P. P. Avelino and C. J. A. Martins, Astrophys. J. 565, 661 (2002); C. Deﬀayet, G. R. Dvali and G. Gabadadze, arXiv:astro-ph/0106449

View on Pith Pith review arXiv 2002
[21]

C. Deﬀayet, S. J. Landau, J. Raux, M. Zaldarriaga and P. Astie r, Phys. Rev. D 66, 024019 (2002)

View on Pith 2002
[22]

J. S. Alcaniz, Phys. Rev. D 65, 123514 (2002); D. Jain, A. Dev and J. S. Alcaniz, Phys. Rev. D 66, 083511 (2002); J. S. Alcaniz, D. Jain and A. Dev, Phys. Rev. D 66, 067301 (2002)

View on Pith 2002
[23]

C. Deﬀayet, G. R. Dvali, G. Gabadadze and A. I. Vainshtein, Phy s. Rev. D 65, 044026 (2002)

View on Pith 2002
[24]

A. Lue, Phys. Rev. D 66, 043509 (2002)

View on Pith 2002
[25]

A. Gruzinov, arXiv:astro-ph/0112246

View on Pith Pith review arXiv
[26]

M. Porrati, Phys. Lett. B 534, 209 (2002)

View on Pith 2002
[27]

A. Lue and G. Starkman, Phys. Rev. D 67, 064002 (2003)

View on Pith 2003
[28]

G. Dvali, A. Gruzinov and M. Zaldarriaga, Phys. Rev. D 68, 024012 (2003)

View on Pith 2003
[29]

A. Lue, Phys. Rev. D 67, 064004 (2003). 19

View on Pith 2003
[30]

C. Deﬀayet, Phys. Rev. D 66, 103504 (2002)

View on Pith 2002
[31]

M. A. Luty, M. Porrati and R. Rattazzi, JHEP 0309, 029 (2003)

View on Pith 2003
[32]

F. Bernardeau, Ap. J. 392, 1 (1992)

View on Pith 1992
[33]

D. N. Spergel et al., Ap. J. S. 148, 175 (2003)

View on Pith 2003
[34]

G. Hinshaw et al., Ap. J. S. 148, 135 (2003)

View on Pith 2003
[35]

M. Tegmark, et al., arXiv:astro-ph/0310725

View on Pith Pith review arXiv
[36]

L. Verde, et al., MNRAS 335, 432 (2002)

View on Pith 2002
[37]

P. Norberg, MNRAS 328, 64 (2001) 20

View on Pith 2001

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Symmetron Cosmology
astro-ph.CO 2011-07 accept novelty 6.0 of 10

The symmetron scalar reaches its symmetry-breaking vacuum by today for a wide range of initial conditions, but its simplest quartic potential is too shallow to act as dark energy.
Dynamical Masses in Modified Gravity
astro-ph.CO 2010-03 accept novelty 6.0 of 10

Spherically symmetric semi-analytic models reproduce the modified-gravity force enhancement measured in f(R) and DGP N-body simulations, yielding a calibrated dynamical-to-lensing mass ratio that depends on mass, radi...
Spherical Collapse and the Halo Model in Braneworld Gravity
astro-ph.CO 2009-11 accept novelty 6.0 of 10

The brane-bending mode's constant interior field breaks energy-conservation-based virial estimates, and a force-based virial condition plus a closed-form field profile reproduces DGP simulation trends in the halo mass...
Cosmological Simulations of Normal-Branch Braneworld Gravity
astro-ph.CO 2009-10 conditional novelty 6.0 of 10

In normal-branch DGP with a tuned dark energy component, N-body simulations show a matter power spectrum enhanced by up to a factor of two near k = 0.7 h/Mpc and a strongly enhanced abundance of massive halos.
Galileon Cosmology
hep-th 2009-05 conditional novelty 6.0 of 10

Covariantizing the DGP decoupling lagrangian yields a 4D galileon cosmology whose self-interactions screen the scalar at early times, whose expansion history tracks DGP, and which requires a crossover scale above abou...
N-Body Simulations of DGP and Degravitation Theories
astro-ph.CO 2009-03 conditional novelty 6.0 of 10

N-body simulations of DGP and cascading/degravitation gravity show enhanced clustering relative to standard cosmology, with the standard halofit formula overpredicting the boost on nonlinear scales and a retuned versi...
Observational Evidence for Cosmological-Scale Extra Dimensions
astro-ph 2008-12 conditional novelty 6.0 of 10

A single extra scalar force from cosmological-scale extra dimensions, with a crossover length of 300 to 600 Mpc, is argued to explain four independent two-sigma excesses in structure growth and the missing large-angle...
Challenges to the DGP Model from Horizon-Scale Growth and Geometry
astro-ph 2008-08 accept novelty 6.0 of 10

The self-accelerating DGP braneworld is disfavored at roughly 5 sigma relative to Lambda CDM once CMB growth effects at horizon scales are combined with distance measures.
Non-linear evolution of f(R) cosmologies II: power spectrum
astro-ph 2008-07 accept novelty 6.0 of 10

First cosmological simulations with the chameleon mechanism show it suppresses f(R) power spectrum enhancements at small scales by up to a factor of four, while leaving measurable signals at intermediate scales.
Parameterized Beyond-Einstein Growth
astro-ph 2007-01 accept novelty 6.0 of 10

A single growth-index parameter, derived analytically, separates the effect of cosmic expansion from the effect of modified gravity on how structure grows.
Cosmological solutions and growth index of matter perturbations in $f(Q)$ gravity
gr-qc 2021-03 conditional novelty 5.0 of 10

For the power-law f(Q) = Q + αQ^n model, the background expansion mimics ΛCDM when |n|<1, but the growth index of matter perturbations differs, providing an observational signature to test the theory.
Signatures of $f(Q)$-gravity in cosmology
astro-ph.CO 2021-01 conditional novelty 5.0 of 10

A modified-gravity model with an exactly standard expansion history produces measurable, sign-dependent signatures in matter clustering, CMB lensing, and the integrated Sachs-Wolfe tail, and future gravitational-wave ...
Phenomenology of the generalized cubic covariant Galileon model and cosmological bounds
astro-ph.CO 2019-12 conditional novelty 5.0 of 10

Adding two free parameters to the cubic covariant Galileon model lets CMB-only data accommodate a higher local Hubble constant, but model selection against LambdaCDM remains inconclusive.
Interpreting cosmological tensions from the effective field theory of torsional gravity
astro-ph.CO 2019-09 conditional novelty 5.0 of 10

A reconstructed f(T) torsional gravity model can simultaneously fit the local Hubble constant and the amplitude of matter clustering, easing both cosmological tensions, though the fit is partly built in by construction.
The road ahead of Horndeski: cosmology of surviving scalar-tensor theories
astro-ph.CO 2018-10 conditional novelty 5.0 of 10

After the GW170817 speed limit, the surviving Horndeski class is constrained with current data and forecast for future surveys, and one EFT function is shown to be unconstrainable by cosmology while still deciding whi...
Towards Precision Constraints on Gravity with the Effective Field Theory of Large-Scale Structure
astro-ph.CO 2018-02 conditional novelty 5.0 of 10

The difference in the EFTofLSS speed-of-sound counterterm between Lambda-CDM and nDGP gravity is measured to about 13% precision from simulation ratios and scales linearly with the modified Poisson coupling.
A Perturbative Approach to the Redshift Space Power Spectrum: Beyond the Standard Model
astro-ph.CO 2016-06 conditional novelty 5.0 of 10

A numerical perturbation-theory code computes the one-loop redshift-space power spectrum and its multipoles for a broad class of modified gravity models, checked against analytic results and against N-body simulations...
Cosmic expansion and growth histories in Galileon scalar-tensor models of dark energy
astro-ph.CO 2010-03 conditional novelty 5.0 of 10

In Galileon scalar-tensor cosmology with a power-law coupling, the asymptotic growth index of matter perturbations is 9/16 and falls to about 0.4 today, distinct from ΛCDM and DGP even when the expansion history matches.
Current constraints on the cosmic growth history
astro-ph.CO 2010-02 conditional novelty 5.0 of 10

Joint cosmological data constrain phenomenological modifications to gravity to within about 3 percent at recombination, but allow order-unity late-time deviations in the growth of structure.
Cosmological Constraints on DGP Braneworld Gravity with Brane Tension
astro-ph.CO 2009-05 conditional novelty 5.0 of 10

Joint CMB, supernova, H0 and galaxy-ISW data show no preference for DGP braneworld gravity on either branch, requiring H0 r_c > 3 at 95% confidence.
Parametrized Post-Friedmann Signatures of Acceleration in the CMB
astro-ph 2008-01 accept novelty 5.0 of 10

The parametrized post-Friedmann formalism is generalized to multicomponent universes with curvature, and WMAP data constrain the metric ratio parameter to geff = -0.12 +/- 0.27 at z ~ 0.7 and k ~ 10^-3 Mpc^-1.
Structure formation in the DGP cosmological model
astro-ph 2005-11 accept novelty 5.0 of 10

Setting the bulk Weyl perturbations to zero in DGP violates the four-dimensional Bianchi identity; the correct linear growth equation follows from five-dimensional bulk regularity and matches the Lue-Scoccimarro-Stark...
Cosmology with HI Intensity Mapping
astro-ph.CO 2026-07 accept novelty 4.0 of 10

SKAO HI intensity mapping forecasts yield competitive LambdaCDM constraints (e.g. H0 to ~0.3 km/s/Mpc optimistic) via power spectrum, BAO, bispectrum and stacking, complementary to CMB and optical surveys.
Late Time Phenomena in $f(T,\mathcal{T})$ Gravity Framework: Role of $H_0$ Priors
gr-qc 2024-11 conditional novelty 4.0 of 10

An f(T,T) gravity model fitted to Pantheon+, BAO, and cosmic chronometer data yields a range of H0 posteriors that track the input priors, and predicts a growth rate about 9-11% below ΛCDM for two data combinations.
Bayesian analysis of $f(T)$ gravity using $f\sigma_8$ data
astro-ph.CO 2019-07 conditional novelty 4.0 of 10

Three f(T) gravity models fit combined supernova, cosmic-chronometer, CMB-shift and growth-rate data about as well as ΛCDM, with the exponential model marginally preferred by the Deviance Information Criterion.
Selected topics in scalar-tensor theories and beyond
gr-qc 2019-01 accept novelty 4.0 of 10

A survey of scalar-tensor and Horndeski gravity that organizes the field and argues, against earlier work, that the general-relativistic de Sitter phase is not a generic attractor of Brans-Dicke cosmology.
Conjoined constraints on modified gravity from the expansion history and cosmic growth
astro-ph.CO 2017-05 conditional novelty 4.0 of 10

A joint H(z)-fσ8(z) figure of merit ranks nine cosmological models and separates ΛCDM from DGP and f(T) modified gravity, though the ranking carries no stated uncertainty.
The phenomenological approach to modeling the dark energy
astro-ph.CO 2012-04 accept novelty 4.0 of 10

Dark energy and modified gravity can be described by one background quantity and two perturbation quantities, and this review shows how existing models and observational constraints fit that framework.
The Paths of Quintessence
astro-ph 2006-01 conditional novelty 4.0 of 10

The w-w' phase plane of dark energy is organized by friction versus potential steepness, and the resulting freezing and thawing regions show that quintessence is generically not a slow-roll phenomenon.
Effective Field Theory of Dark Energy: a Review
astro-ph.CO 2019-07 accept novelty 3.0 of 10

The review consolidates the effective field theory of dark energy: its action, its mapping onto known gravity theories, its stability conditions, and the cosmological constraints and forecasts obtained with it.
Brane-World Gravity
hep-th 2010-04 accept novelty 3.0 of 10

Brane-world models recover four-dimensional gravity at low energies while predicting calculable, testable corrections at high energies, and this review consolidates their geometry, cosmology, and observational status.
Dark Energy and Modified Gravity
astro-ph 2008-11 accept novelty 3.0 of 10

The two simplest infrared modifications of general relativity, f(R) and DGP, both fail current theoretical and observational tests, leaving the cosmological constant without a serious challenger.
Reconstructing Dark Energy
astro-ph 2006-10 accept novelty 3.0 of 10

Model-independent reconstruction of the cosmic expansion history from 2006-era data is consistent across parametric and non-parametric methods, and a plain cosmological constant still fits as well as any evolving dark energy.
Ghosts in the self-accelerating universe
hep-th 2007-09 conditional novelty 2.0 of 10

The self-accelerating DGP braneworld, the leading modified-gravity alternative to dark energy, carries a ghost that survives every simple repair attempted in the literature.
Dark Energy from Brane-world Gravity
astro-ph 2006-02 unverdicted novelty 1.0 of 10

A review of DGP brane-world gravity, which explains cosmic acceleration via gravity leakage without dark energy, including its perturbative growth equation and known open problems.

How the literature uses it

51 arXiv papers cite this in 76 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 · 44 sentences without a confident label

Builds on it 1 paper

Here we propose a phenomenological extension of these results valid for general $α$ theories, which reduce to the equations of [ref] in the DGP case.

N-Body Simulations of DGP and Degravitation Theories · Cosmological Perturbations · 0.99

Uses its method or tool 3 papers

One is the spherically symmetric solution (vainshtein), which can be used in modeling a spherical collapse of dark matter halos in DGP [ref] .

Self-Consistent Cosmological Simulations of DGP Braneworld Gravity · Brane bending mode and Vainshtein effect · 0.85
In this limit, we solve the ordinary differential equation [ref] [equation] for the linear matter density perturbation $Δ_m$.

Cosmological Constraints on DGP Braneworld Gravity with Brane Tension · gISW cross correlations · 0.94
We begin by reviewing the techniques introduced in Ref. [ref] for the brane bending field but pay special attention to the matching of the various solutions as well as derive a closed form expression for the global field profile.

Spherical Collapse and the Halo Model in Braneworld Gravity · Top-Hat Overdensity in DGP · 0.86

Compares with it 4 papers

* The above results all agree with [ref] for the DGP case $α=1/2$, with one exception: we have taken into account the modified propagator ([ref]) in the right-hand side of ([ref]).

N-Body Simulations of DGP and Degravitation Theories · Cosmological Perturbations · 0.96
As another quick check, letting $β→β_DGP$ and setting $D=5$, this agrees with explicit cosmological results in DGP [ref] .

Enhanced Peculiar Velocities in Brane-Induced Gravity · Massive/Resonance Gravity · 0.95
For comparison, the linearized perturbation equation derived for the full DGP model, derived in [ref] for spherical top-hat perturbations, takes on an identical form to ([ref]), with $β$ in this case given by

Galileon Cosmology · Growth of Density Perturbations · 0.99

Cites it as support 2 papers

Observations based on structure formation provide further evidence of the difference between DGP and LCDM, since the two models suppress the growth of density perturbations in different ways [ref] .

Dark Energy and Modified Gravity · BRANE-WORLD MODELS · 0.98
Observations based on structure formation provide further evidence of the difference between DGP and LCDM, since the two models suppress the growth of density perturbations in different ways [ref] .

Brane-World Gravity · `Self-accelerating' DGP · 0.96

Cites it as background 21 papers

A first study of spherical perturbations in the context of DGP was undertaken in [ref] .

Spherical Collapse and the Halo Model in Braneworld Gravity · Introduction · 0.84
The cosmology and phenomenology of DGP was first derived in [ref] (see also [ref] ).

Massive Gravity · Phenomenology of DGP · 0.95
The Vainshtein mechanism occurs not only in modern incarnations of Boulware-Deser [ref] ghost-free massive gravity [ref] but also in galileon cosmology [ref] and braneworld models [ref] .

Equivalence Principle Violation in Weakly Vainshtein-Screened Systems · Introduction · 0.94

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

S. Perlmutter et al. [Supernova Cosmology Project Collaboration], Astrophys. J. 517, 565 (1999)

View on Pith 1999

[2] [2]

A. G. Riess et al. [Supernova Search Team Collaboration], Astron. J. 116, 1009 (1998)

View on Pith 1998

[3] [3]

C. Deﬀayet, Phys. Lett. B 502, 199 (2001)

View on Pith 2001

[4] [4]

C. Deﬀayet, G. R. Dvali and G. Gabadadze, Phys. Rev. D 65, 044023 (2002)

View on Pith 2002

[5] [5]

T. Damour, I. I. Kogan and A. Papazoglou, Phys. Rev. D 66, 104025 (2002)

View on Pith 2002

[6] [6]

K. Freese and M. Lewis, Phys. Lett. B 540, 1 (2002)

View on Pith 2002

[7] [7]

K. Freese, Nucl. Phys. Proc. Suppl. 124, 50 (2003)

View on Pith 2003

[8] [8]

G. Dvali and M. S. Turner, arXiv:astro-ph/0301510

View on Pith Pith review arXiv

[9] [9]

Capozziello S., Carloni S., Troisi A., arXiv:astro-ph/0303041

View on Pith Pith review arXiv

[10] [10]

S. M. Carroll, V. Duvvuri, M. Trodden and M. S. Turner, arXiv:as tro-ph/0306438

View on Pith

[11] [11]

S. Capozziello, V. F. Cardone, S. Carloni, A. Troisi., arXiv:astro- ph/0307018

View on Pith

[12] [12]

S. Nojiri and S. D. Odintsov, Phys. Rev. D 68, 123512 (2003)

View on Pith 2003

[13] [13]

J. Khoury and A. Weltman, arXiv:astro-ph/0309300

View on Pith Pith review arXiv

[14] [14]

J. Khoury and A. Weltman, arXiv:astro-ph/0309411

View on Pith Pith review arXiv

[15] [15]

A. Lue, R. Scoccimarro and G. Starkman, arXiv:astro-ph/030 7034

View on Pith

[16] [16]

T. Multamaki, E. Gaztanaga and M. Manera, Mon. Not. Roy. Ast ron. Soc. 344, 761 (2003)

View on Pith 2003

[17] [17]

G. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485, 208 (2000)

View on Pith 2000

[18] [18]

G. R. Dvali, G. Gabadadze, M. Kolanovic and F. Nitti, Phys. Rev. D 64, 084004 (2001)

View on Pith 2001

[19] [19]

G. R. Dvali, G. Gabadadze, M. Kolanovic and F. Nitti, Phys. Rev. D 65, 024031 (2002)

View on Pith 2002

[20] [20]

P. P. Avelino and C. J. A. Martins, Astrophys. J. 565, 661 (2002); C. Deﬀayet, G. R. Dvali and G. Gabadadze, arXiv:astro-ph/0106449

View on Pith Pith review arXiv 2002

[21] [21]

C. Deﬀayet, S. J. Landau, J. Raux, M. Zaldarriaga and P. Astie r, Phys. Rev. D 66, 024019 (2002)

View on Pith 2002

[22] [22]

J. S. Alcaniz, Phys. Rev. D 65, 123514 (2002); D. Jain, A. Dev and J. S. Alcaniz, Phys. Rev. D 66, 083511 (2002); J. S. Alcaniz, D. Jain and A. Dev, Phys. Rev. D 66, 067301 (2002)

View on Pith 2002

[23] [23]

C. Deﬀayet, G. R. Dvali, G. Gabadadze and A. I. Vainshtein, Phy s. Rev. D 65, 044026 (2002)

View on Pith 2002

[24] [24]

A. Lue, Phys. Rev. D 66, 043509 (2002)

View on Pith 2002

[25] [25]

A. Gruzinov, arXiv:astro-ph/0112246

View on Pith Pith review arXiv

[26] [26]

M. Porrati, Phys. Lett. B 534, 209 (2002)

View on Pith 2002

[27] [27]

A. Lue and G. Starkman, Phys. Rev. D 67, 064002 (2003)

View on Pith 2003

[28] [28]

G. Dvali, A. Gruzinov and M. Zaldarriaga, Phys. Rev. D 68, 024012 (2003)

View on Pith 2003

[29] [29]

A. Lue, Phys. Rev. D 67, 064004 (2003). 19

View on Pith 2003

[30] [30]

C. Deﬀayet, Phys. Rev. D 66, 103504 (2002)

View on Pith 2002

[31] [31]

M. A. Luty, M. Porrati and R. Rattazzi, JHEP 0309, 029 (2003)

View on Pith 2003

[32] [32]

F. Bernardeau, Ap. J. 392, 1 (1992)

View on Pith 1992

[33] [33]

D. N. Spergel et al., Ap. J. S. 148, 175 (2003)

View on Pith 2003

[34] [34]

G. Hinshaw et al., Ap. J. S. 148, 135 (2003)

View on Pith 2003

[35] [35]

M. Tegmark, et al., arXiv:astro-ph/0310725

View on Pith Pith review arXiv

[36] [36]

L. Verde, et al., MNRAS 335, 432 (2002)

View on Pith 2002

[37] [37]

P. Norberg, MNRAS 328, 64 (2001) 20

View on Pith 2001