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Testing gravity on kiloparsec scales with strong gravitational lenses

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Tristan L. Smith (UC Berkeley)

Cosmology and Nongalactic Astrophysics · Submitted 28 Jul 2009 · 63 references

Pith's verdict: An honest, useful extension of the SLACS lensing test: the new mass- and redshift-dependence bounds are the real contribution, and the p–γ_PPN degeneracy is acknowledged but not fully propagated.

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arXiv ID0907.4829 (version 2)
Pith IDVYEW6TD6, Pith's permanent record of this paper and its review
CitationTristan L. Smith (UC Berkeley). "Testing gravity on kiloparsec scales with strong gravitational lenses." arXiv:0907.4829 (2009). https://pith.science/paper/VYEW6TD6
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The paper

The paper claims

The SLACS lens sample shows no detectable variation of the lensing-to-dynamical mass ratio with lens mass or redshift, bounding such variation to under 50% and 40% respectively at 68% confidence.

The reading

General relativity predicts that the mass you infer from how light bends around a galaxy (the lensing mass) should equal the mass you infer from how fast its stars move (the dynamical mass). Many modified gravity theories break this equality, and some predict that the breaking should change with the galaxy's mass or its distance from us. This paper takes 53 strong gravitational lenses from the Sloan Lens ACS survey, measures both masses for each, and asks whether the ratio between them drifts across the sample. It does not: the data are consistent with a constant ratio, and the allowed drift is bounded at roughly the 50% level across two decades in mass and 40% across the survey's redshift range. The author then translates that null result into limits on three specific frameworks: scalar-tensor gravity, f(R) gravity with its chameleon screening mechanism, and a generic 'gravitational slip' parameterization. The f(R) bound is about a factor of ten weaker than the existing solar-system constraint, and the scalar-tensor bound is a lower limit on the cosmological constant energy density. The paper is careful about a known degeneracy between the slope of the galaxy's total mass profile and the gravity parameter, and it handles that degeneracy by marginalizing over the sample mean rather than quoting a universal value. The universal fit itself lands 2.4 sigma away from general relativity, which the author attributes to a mismatch between the low-redshift slope prior and the SLACS galaxies.
Extended reading notes

Core claim

The SLACS data constrain the variation of gamma_PPN (the ratio of lensing to dynamical mass) with lens mass and redshift to be less than about 50% over 10^12 to 10^14 solar masses and less than about 40% over 0.06 < z < 0.36 at 68% confidence, and this null result translates into Omega_V > 0.3, |f'(R0)|(z=0) < 1.8e-6 for n=1, and slip parameter w0 = 0.25 +0.22/-0.27.

Load-bearing premise

The central claim rests on the assumption, stated around Eq. (42), that the degeneracy between the total mass-profile slope p and gamma_PPN is a pure multiplicative constant across the sample, absorbed by the amplitude A marginalized over the hand-chosen range [0.8, 1.2]. The author justifies this by calling the degeneracy 'nearly linear' (Fig. 4). If the p-gamma_PPN relation has any residual mass or redshift dependence, that residual leaks directly into the quoted bounds on m_z and m_M, because the amplitude marginalization removes only the constant part of the bias.

Original abstract

Modifications to GR generically predict time and scale-dependent effects which may be probed by observations of strong lensing by galaxies. Measurements of the stellar velocity dispersion determine the dynamical mass whereas measurements of the Einstein radius determine the lensing mass. In GR these two masses are equal; in alternative gravity theories they may not be. Using measurements of the stellar velocity dispersion and strong lensing around galaxies from the Sloan Lens ACS (SLACS) survey we place constraints on lensing in modified gravity theories and extend previous studies by applying this data to explore its dependence on various properties of the lens such as the lens redshift or mass and thereby constrain scalar-tensor, f(R) gravity theories, and generic parameterizations of deviations from GR. Besides applying the observations to these specific gravity theories, the data places a constraint on a generic dependence of modifications to GR on the lens mass and redshift. At the 68% confidence level we find that the ratio between the lensing and dynamical masses can only vary by less then 50% over a mass range for the lens galaxies of 1E12 < M/Msun < 1E14 and less than 40% over the redshift range 0.06 < z < 0.36.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,124 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.35 · human participants 0.02 · controlled comparison 0.21 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.46 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Modifications to GR generically predict time and scale-dependent effects which may be probed by observations of strong lensing by galaxies. Measurements of the stellar velocity dispersion determine the dynamical mass whereas measurements of the Einstein radius determine the lensing mass. In GR these two masses are equal; in alternative gravity theories they may not be. Using measurements of the stellar velocity dispersion and strong lensing around galaxies from the Sloan Lens ACS (SLACS) survey we place constraints on lensing in modified gravity theories and extend previous studies by applying this data to explore its dependence on various properties of the lens such as the lens redshift or mass and thereby constrain scalar-tensor, f(R) gravity theories, and generic parameterizations of deviations from GR. Besides applying the observations to these specific gravity theories, the data places a constraint on a generic dependence of modifications to GR on the lens mass and redshift. At the 68% confidence level we find that the ratio between the lensing and dynamical masses can only vary by less then 50% over a mass range for the lens galaxies of 1E12 < M/Msun < 1E14 and less than 40% over the redshift range 0.06 < z < 0.36.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Modifications to GR generically predict time and scale-dependent effects which may be probed by observations of strong lensing by galaxies. background 1.00 0.05 0.04 hedged possibility 0.97
s1 Measurements of the stellar velocity dispersion determine the dynamical mass whereas measurements of the Einstein radius determine the lensing mass. background 0.82 0.10 0.03 asserted 1.00
s2 In GR these two masses are equal; in alternative gravity theories they may not be. background 1.00 0.05 0.04 hedged possibility 0.53
s3 Using measurements of the stellar velocity dispersion and strong lensing around galaxies from the Sloan Lens ACS (SLACS) survey we place constraints on lensing in modified gravity theories and extend previous studies by applying this data to explore its dependence on various properties of the lens such as the lens redshift or mass and thereby constrain scalar-tensor, f(R) gravity theories, and generic parameterizations of deviations from GR. contribution 0.94 0.95 0.13 asserted 1.00
s4 Besides applying the observations to these specific gravity theories, the data places a constraint on a generic dependence of modifications to GR on the lens mass and redshift. contribution 0.80 0.89 0.11 asserted 0.99
s5 At the 68% confidence level we find that the ratio between the lensing and dynamical masses can only vary by less then 50% over a mass range for the lens galaxies of 1E12 < M/Msun < 1E14 and less than 40% over the redshift range 0.06 < z < 0.36. result 1.00 0.96 0.83 asserted 1.00

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from analysis of existing data 1.00.

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 evolution of
Figure 2. FIG. 2: The combination
Figure 3. FIG. 3: The minimum mass for a halo to be screened given
Figure 4. it is clear there is a degeneracy between the slope of the density profile, p, and γPPN. In order to make progress in measuring γPPN a prior must be placed on p. It is important that any approach taken to place this prior be independent of the theory of gravity. One ap￾proach, discussed in Ref. [48], uses an assumed scaling law (related to the fundamental plane [49]) that relates the power-law slope, p, to the luminosity, Einstein radius, and effective radius is used to estimate the average value for p within a population of lenses. In this approach a universal value for γPPN would…
Figure 5. FIG. 5: The mean (
Figure 7. FIG. 7: The measurement of
Figure 8. FIG. 8: Constraints to modified gravity theories and paramet

Showing 7 of the paper's 8 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:0907.4829 by the authors.

References
How the literature uses it

32 arXiv papers cite this in 53 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 · 39 sentences without a confident label

Builds on it 1 paper
Uses its data or values 2 papers
  • Reference [ref] has performed such a test for a sample of galaxies from the Sloan Lens ACS (SLACS) survey and find a constraint $f_R0<2.5×10^-6$.

    Tests of Chameleon Gravity · Strong Gravitational Lensing · 0.80

  • In specific, Smith [ref] derived an upper bound of $<2.5×10^-6$ on the Hu-Sawicki $f(R)$ model ($α=0.5$), assuming that environmental effects that may shield gravitational force modifications can be neglected.

    Constraining chameleon models with cosmology · Observational constraints · 0.92

Compares with it 4 papers
Cites it as support 1 paper
  • All current constraints on $f(R)$ models [ref] indicate that our use of this approximation scheme is justified, however we are also careful to check retrospectively that any parameter constraints we project for these models respect the assumption $M^2 ≫H^2_background$.

    Modified Gravity: the CMB, Weak Lensing and General Parameterisations · The Field Equations and Scalaron Mass Parameterisation · 0.96

Cites it as background 6 papers

What it cites · 3 sentences without a confident label

Uses the method or tool of 1 paper
Uses data or values from 1 paper
Compares with 1 paper
Cites as background 2 papers

Discussion

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