pith. sign in

arxiv: 2509.24622 · v2 · submitted 2025-09-29 · 🌀 gr-qc · hep-ph

Prospect on constraining environment-dependent dilaton model from gravitational redshift measurements

Li Hu , Rong-Gen Cai , Song He , Li-Fang Li , Tong Liu , Peng Xu , Shao-Jiang Wang This is my paper

Pith reviewed 2026-05-18 13:04 UTC · model grok-4.3

classification 🌀 gr-qc hep-ph
keywords environmentally dependent dilatongravitational redshiftatomic clocksscalar-tensor gravitymass density environmentsparameter constraintsmodified gravityconformal gravity
0
0 comments X

The pith

Atomic clock comparisons in different mass densities can constrain the environmentally dependent dilaton model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines the environmentally dependent dilaton model, a conformal scalar-tensor extension of general relativity, and identifies how future gravitational redshift measurements with atomic clocks could constrain its parameters. The scheme compares frequency shifts of clocks placed in environments of varying mass density, such as ultrahigh vacuum, water, or osmium, to isolate the scalar field's contribution to redshift. Modeling the mass distribution discretely in low-density settings goes beyond the usual continuous approximation and shows that substantial parameter space remains accessible. A sympathetic reader would care because these tests target relatively weak couplings and supply constraints that complement those from existing experiments.

Core claim

In the environmentally dependent dilaton model, the scalar field contributes to gravitational redshift in a density-dependent way. Placing atomic clocks in materials with different densities and comparing their frequency shifts probes this contribution. Discrete modeling of mass distributions in low-density environments extends beyond the continuous approximation and reveals that a significant portion of the parameter space stays accessible to high-precision experiments, mainly for weak couplings complementary to those already bounded by other tests.

What carries the argument

The environmentally dependent dilaton, a scalar field whose coupling to matter in conformal scalar-tensor gravity varies with local mass density and thereby modifies the effective gravitational redshift.

If this is right

  • High-precision gravitational redshift experiments can exclude significant regions of the parameter space.
  • The accessible regions are primarily sensitive to relatively weak couplings.
  • These constraints are complementary to those from existing tests.
  • Discrete representation of mass distribution in low-density environments improves the modeling beyond the continuous approximation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Null results from the proposed setups would tighten bounds specifically on weak dilaton couplings in low-density regimes.
  • The redshift comparison method could be adapted to probe other environment-dependent modifications to gravity.
  • Combining these laboratory measurements with astrophysical redshift data might further restrict viable parameter values.

Load-bearing premise

Differences in gravitational redshift between atomic clocks in environments of different mass densities can be attributed to the scalar field contribution in the dilaton model.

What would settle it

A null result showing no frequency shift difference beyond general relativity predictions when comparing clocks in osmium versus ultrahigh vacuum would exclude the accessible regions of the model's parameter space for weak couplings.

Figures

Figures reproduced from arXiv: 2509.24622 by Li-Fang Li, Li Hu, Peng Xu, Rong-Gen Cai, Shao-Jiang Wang, Song He, Tong Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic diagram of gravitational redshift repro [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Expected values of gravitational redshift for different density pairs in a model with a continuous mass distribution. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Expected values of gravitational redshift for different density pairs in the non-excluded region. Note that redshift [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Continuous vs. discrete modelings. In the continuous [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The distribution of the scalar field [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Expected values of gravitational redshift for different density pairs in a model with a discrete mass distribution. Here, [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Expected values of gravitational redshift for a den [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

Scalar-tensor gravity represents a natural extension of general relativity. This paper investigates a conformal scalar-tensor gravity, the environmentally dependent dilaton model, and identifies regions of its parameter space potentially constrained by future experiments using atomic clocks to measure gravitational redshift. We propose an experimental scheme in which atomic clocks are placed in environments of different mass densities, such as ultrahigh vacuum, water, or osmium, and their frequency shifts are compared to probe the scalar field contribution to gravitational redshift. By further modeling the mass distribution in low-density environments with a discrete representation, we go beyond the standard continuous approximation. Despite limitations inherent to specific experimental configurations, our analysis reveals that a significant portion of the parameter space remains accessible. Importantly, the accessible regions are complementary to those constrained by existing tests, as they are primarily sensitive to relatively weak couplings. Consequently, high-precision gravitational redshift experiments hold the potential to exclude significant regions of this parameter space in the future.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes using high-precision atomic clock comparisons of gravitational redshift in environments with different mass densities (ultrahigh vacuum, water, osmium) to constrain the parameter space of the environmentally dependent dilaton model within conformal scalar-tensor gravity. It introduces a discrete representation of mass distributions in low-density regimes as an improvement over the standard continuous approximation and argues that future experiments could exclude significant regions of parameter space, particularly for weak couplings, in a manner complementary to existing tests.

Significance. If the proposed scheme and modeling hold, the work identifies a potentially new experimental window for testing scalar-tensor theories via gravitational redshift, with emphasis on complementarity to current bounds and accessibility for relatively weak dilaton couplings. This could motivate targeted clock experiments in controlled density environments.

major comments (2)
  1. [Modeling section] Modeling section: the discrete particle representation of low-density mass distributions is presented as the key advance that yields a quantitatively different scalar profile than the continuous approximation, yet no explicit side-by-side comparison of the resulting scalar-field solutions or propagated frequency shifts is provided. Without this, it remains unclear whether the difference exceeds the projected clock precision (∼10^{-18}–10^{-19}) or is masked by environmental systematics on atomic transitions.
  2. [Parameter-space analysis] Parameter-space analysis: the central claim that accessible regions are primarily sensitive to relatively weak couplings and complementary to existing constraints relies on forward projections, but the manuscript lacks detailed quantitative scans, error budgets, or explicit mapping of the proposed redshift differences onto the dilaton coupling strengths to substantiate the excluded regions.
minor comments (2)
  1. Clarify the precise functional form of the environmentally dependent dilaton potential and the definition of the coupling strengths early in the text to aid readability for readers outside the immediate subfield.
  2. Consider adding a summary table of projected frequency shifts for each environment (vacuum, water, osmium) under both continuous and discrete modeling assumptions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have identified areas where additional clarity and detail will strengthen the presentation. We address each major comment below and describe the revisions we will make.

read point-by-point responses

  1. Referee: [Modeling section] Modeling section: the discrete particle representation of low-density mass distributions is presented as the key advance that yields a quantitatively different scalar profile than the continuous approximation, yet no explicit side-by-side comparison of the resulting scalar-field solutions or propagated frequency shifts is provided. Without this, it remains unclear whether the difference exceeds the projected clock precision (∼10^{-18}–10^{-19}) or is masked by environmental systematics on atomic transitions.

    Authors: We agree that an explicit side-by-side comparison is needed to demonstrate the quantitative impact of the discrete representation. In the revised manuscript we will add a new figure and accompanying text that directly compares the scalar-field profiles and the induced frequency shifts obtained from the continuous approximation versus the discrete particle representation for the low-density environments (ultrahigh vacuum and water). The comparison will show that the difference reaches the level of a few parts in 10^{-19} in the regimes of interest, which lies within the target precision of next-generation atomic clocks. We will also expand the discussion of environmental systematics on atomic transitions and outline mitigation strategies based on differential measurements. revision: yes

  2. Referee: [Parameter-space analysis] Parameter-space analysis: the central claim that accessible regions are primarily sensitive to relatively weak couplings and complementary to existing constraints relies on forward projections, but the manuscript lacks detailed quantitative scans, error budgets, or explicit mapping of the proposed redshift differences onto the dilaton coupling strengths to substantiate the excluded regions.

    Authors: We acknowledge that the current parameter-space discussion would be strengthened by more detailed quantitative support. In the revision we will include additional figures presenting scans over the dilaton coupling and mass parameters, together with an explicit error budget that incorporates the projected clock precision, environmental uncertainties, and statistical considerations. These scans will map the expected redshift differences directly onto the coupling strengths, thereby providing a clearer quantitative basis for the claimed complementarity with existing bounds and the accessibility of the weak-coupling regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward-looking proposal relies on external benchmarks

full rationale

The paper proposes future atomic clock experiments to constrain the environmentally dependent dilaton model via gravitational redshift differences in varying mass densities. It introduces discrete mass modeling for low-density environments as an extension beyond continuous approximations but does not fit any parameters to data within the paper, nor does any prediction reduce by construction to inputs or self-citations. The central claim about accessible parameter space and complementarity with existing tests draws from standard scalar-tensor gravity and general relativity as independent external frameworks. No load-bearing self-citation chains or self-definitional reductions are present in the derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the environmentally dependent dilaton model as a conformal scalar-tensor theory and on the assumption that gravitational redshift measurements can isolate scalar field effects in different densities. No new entities are postulated; the work constrains parameters of a pre-existing model.

free parameters (1)
  • dilaton coupling strengths
    The model parameters that determine the strength of the scalar field interaction with matter, which the proposed experiment aims to constrain rather than fit internally.
axioms (2)
  • domain assumption The environmentally dependent dilaton model correctly describes possible deviations from general relativity in scalar-tensor gravity.
    Invoked as the theoretical framework throughout the abstract for identifying constrained parameter regions.
  • domain assumption Atomic clock frequency shifts in different mass density environments can be compared to isolate scalar field contributions to gravitational redshift.
    Central to the proposed experimental scheme.

pith-pipeline@v0.9.0 · 5705 in / 1506 out tokens · 55980 ms · 2026-05-18T13:04:50.070764+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Constraining interacting dark energy models with black hole superradiance

    astro-ph.CO 2025-11 unverdicted novelty 7.0

    Black hole superradiance constrains the coupling strength in interacting dark energy-dark matter models through modifications to the effective mass of ultralight bosons in two scenarios.

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages · cited by 1 Pith paper · 17 internal anchors

  1. [1]

    Testing screened scalar-tensor theories of gravity with atomic clocks,

    Hugo L´ evy and Jean-Philippe Uzan, “Testing screened scalar-tensor theories of gravity with atomic clocks,” Phys. Rev. D111, 064012 (2025), arXiv:2410.17292 [gr- qc]

    work page arXiv 2025

  2. [2]

    Extended Theories of Gravity

    Salvatore Capozziello and Mariafelicia De Laurentis, “Extended Theories of Gravity,” Phys. Rept.509, 167– 321 (2011), arXiv:1108.6266 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  3. [3]

    Late-time cosmology in (phantom) scalar-tensor theory: dark energy and the cosmic speed-up

    Emilio Elizalde, Shin’ichi Nojiri, and Sergei D. Odintsov, “Late-time cosmology in (phantom) scalar-tensor theory: Dark energy and the cosmic speed-up,” Phys. Rev. D70, 043539 (2004), arXiv:hep-th/0405034

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  4. [4]

    Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

    Elcio Abdalla et al., “Cosmology intertwined: A re- view of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anoma- lies,” JHEAp34, 49–211 (2022), arXiv:2203.06142 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  5. [5]

    Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale

    D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gund- lach, Blayne R. Heckel, C. D. Hoyle, and H. E. Swanson, “Tests of the gravitational inverse-square law below the dark-energy length scale,” Phys. Rev. Lett.98, 021101 (2007), arXiv:hep-ph/0611184

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  6. [6]

    Casimir tests of scalar-tensor theories,

    Philippe Brax, Anne-Christine Davis, and Benjamin El- der, “Casimir tests of scalar-tensor theories,” Phys. Rev. D107, 084025 (2023), arXiv:2211.07840 [gr-qc]

    work page arXiv 2023

  7. [7]

    Astrophysical Tests of Modified Gravity

    Jeremy Sakstein, Astrophysical Tests of Modified Gravity, Ph.D. thesis, Cambridge U., DAMTP (2014), arXiv:1502.04503 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  8. [8]

    Chameleon cos- mology,

    Justin Khoury and Amanda Weltman, “Chameleon cos- mology,” Phys. Rev. D69, 044026 (2004), arXiv:astro- ph/0309411

    work page arXiv 2004

  9. [9]

    Symmetron Fields: Screening Long-Range Forces Through Local Symmetry Restoration

    Kurt Hinterbichler and Justin Khoury, “Symmetron Fields: Screening Long-Range Forces Through Local Symmetry Restoration,” Phys. Rev. Lett.104, 231301 (2010), arXiv:1001.4525 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  10. [10]

    The String Dilaton and a Least Coupling Principle

    T. Damour and Alexander M. Polyakov, “The String dilaton and a least coupling principle,” Nucl. Phys. B 423, 532–558 (1994), arXiv:hep-th/9401069

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  11. [11]

    To the problem of nonvanishing grav- itation mass,

    A. I. Vainshtein, “To the problem of nonvanishing grav- itation mass,” Phys. Lett. B39, 393–394 (1972)

    work page 1972

  12. [12]

    Khoury, M.-X

    Justin Khoury, Meng-Xiang Lin, and Mark Trodden, “Apparentw <−1 and a LowerS 8 from Dark Axion and Dark Baryons Interactions,” (2025), arXiv:2503.16415 [astro-ph.CO]

    work page arXiv 2025

  13. [13]

    Symmetron dark energy in laboratory experiments

    Amol Upadhye, “Symmetron dark energy in labora- tory experiments,” Phys. Rev. Lett.110, 031301 (2013), arXiv:1210.7804 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  14. [14]

    Constraint on $f(R)$ Gravity through the Redshift Space Distortion

    Lixin Xu, “Constraint onf(R) Gravity through the Red- shift Space Distortion,” Phys. Rev. D91, 063008 (2015), arXiv:1411.4353 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  15. [15]

    Experiment to detect dark energy forces using atom interferometry,

    Dylan O. Sabulsky, Indranil Dutta, E. A. Hinds, Ben- jamin Elder, Clare Burrage, and Edmund J. Copeland, “Experiment to detect dark energy forces using atom interferometry,” Phys. Rev. Lett.123, 061102 (2019), arXiv:1812.08244 [physics.atom-ph]

    work page arXiv 2019

  16. [16]

    Atomic Precision Tests and Light Scalar Couplings

    Philippe Brax and Clare Burrage, “Atomic Precision Tests and Light Scalar Couplings,” Phys. Rev. D83, 035020 (2011), arXiv:1010.5108 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  17. [17]

    Gravity Resonance Spectroscopy Constrains Dark Energy and Dark Matter Scenarios

    T. Jenke et al., “Gravity Resonance Spectroscopy Con- strains Dark Energy and Dark Matter Scenarios,” Phys. Rev. Lett.112, 151105 (2014), arXiv:1404.4099 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  18. [18]

    (mis)interpreting supernovae observations in a lumpy universe,

    Chris Clarkson, George F. R. Ellis, Andreas Fal- tenbacher, Roy Maartens, Obinna Umeh, and Jean-Philippe Uzan, “(mis)interpreting supernovae observations in a lumpy universe,” Monthly Notices of the Royal Astronomical Society426, 1121–1136 (2012), https://academic.oup.com/mnras/article- pdf/426/2/1121/2961523/426-2-1121.pdf

    work page 2012

  19. [19]

    Cosmic backreaction and Gauss's law

    Pierre Fleury, “Cosmic backreaction and Gauss’s law,” Phys. Rev. D95, 124009 (2017), arXiv:1609.03724 [gr- qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  20. [20]

    Cosmic convergence and shear with extended sources

    Pierre Fleury, Julien Larena, and Jean-Philippe Uzan, “Cosmic convergence and shear with extended sources,” Phys. Rev. D99, 023525 (2019), arXiv:1809.03919 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  21. [21]

    Observables in a lattice Universe

    Jean-Philippe Bruneton and Julien Larena, “Observables in a lattice Universe,” Class. Quant. Grav.30, 025002 (2013), arXiv:1208.1411 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  22. [22]

    The Dilaton and Modified Gravity

    Philippe Brax, Carsten van de Bruck, Anne-Christine Davis, and Douglas Shaw, “The Dilaton and Mod- ified Gravity,” Phys. Rev. D82, 063519 (2010), arXiv:1005.3735 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  23. [23]

    Quintessence as a run-away dilaton

    M. Gasperini, F. Piazza, and G. Veneziano, “Quintessence as a runaway dilaton,” Phys. Rev. D65, 023508 (2002), arXiv:gr-qc/0108016

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  24. [24]

    Neutron Stars in Screened Modified Gravity: Chameleon vs Dilaton

    Philippe Brax, Anne-Christine Davis, and Rahul Jha, “Neutron Stars in Screened Modified Gravity: Chameleon vs Dilaton,” Phys. Rev. D95, 083514 (2017), arXiv:1702.02983 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  25. [25]

    Canbin Liang, Bin Zhou, and Weizhen Jia, Differential Geometry and General Relativity, Graduate Texts in Physics (Springer, Singapore, 2023)

    work page 2023

  26. [26]

    Scalar-tensor the- ories at different scales: averaging the scalar sector,

    Jean-Philippe Uzan and Hugo L´ evy, “Scalar-tensor the- ories at different scales: averaging the scalar sector,” (2025), arXiv:2505.03909 [gr-qc]

    work page arXiv 2025