arxiv: 2601.05750 · v3 · submitted 2026-01-09 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Parameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints

Jie Zhu , Hao Li

Authors on Pith no claims yet

Pith reviewed 2026-05-16 16:16 UTC · model grok-4.3

classification 🌀 gr-qc

keywords quadratic gravitypost-Newtonian expansionPPN parameterssolar system constraintsmassive modesexponential suppressionghost tensor mode

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The pith

Quadratic gravity produces exponentially suppressed deviations from general relativity at solar system scales.

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

This paper extends the Einstein-Hilbert action by adding quadratic curvature terms proportional to minus lambda times the Weyl tensor squared plus mu times the Ricci scalar squared. It performs a post-Newtonian expansion of the metric for a general source up to 1.5PN order and for a point mass up to 2PN order. The resulting effective PPN parameters gamma of r and beta of r approach their general relativity values of 1 exponentially fast with distance. When the Ricci and Weyl masses are equal, gamma remains exactly 1 everywhere, and solar system data require both masses to exceed roughly 23 inverse AU to avoid detectable deviations.

Core claim

In general quadratic gravity with Lagrangian density proportional to R minus lambda C squared plus mu R squared, the parameterized post-Newtonian parameters gamma of r and beta of r approach their general relativity values exponentially fast with distance. Specifically, gamma of r is identically one when the Ricci mass equals the Weyl mass, and the leading correction to beta of r has the form order r ln r times e to the minus m r. Solar system constraints require both masses to exceed 23 inverse AU, which translates to lambda less than or equal to 2.1 times 10 to the 19 square meters and mu less than or equal to 7.1 times 10 to the 18 square meters.

What carries the argument

The post-Newtonian expansion of the metric in the presence of massive scalar and ghost tensor modes generated by the quadratic curvature terms.

If this is right

Gamma of r remains identically equal to 1 at all distances when the scalar and tensor masses are equal.
Gravity stays attractive only when the Weyl mass exceeds one-quarter the Ricci mass.
The leading correction to beta of r shows a characteristic r ln r exp(-m r) dependence.
Solar system experiments bound the quadratic coefficients lambda and mu to the values given above.

Where Pith is reading between the lines

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

Higher-precision observations such as pulsar timing arrays could detect the exponential tails if the masses are near the current lower bound.
Short-range laboratory gravity experiments might see larger effects because the suppression weakens at small distances.
The assumption that the ghost mode remains stable could be tested by looking for runaway behavior in strong-field or high-energy regimes.

Load-bearing premise

The post-Newtonian expansion remains valid for the quadratic gravity theory in the weak-field regime around solar-system sources without instabilities from the ghost tensor mode.

What would settle it

A solar-system measurement of light deflection or perihelion precession showing a deviation from general relativity larger than the predicted exponential suppression at those distances.

Figures

Figures reproduced from arXiv: 2601.05750 by Hao Li, Jie Zhu.

**Figure 3.** Figure 3: FIG. 3. A zoomed-in view of Fig [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Allowed parameter space in the ( [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

read the original abstract

This work systematically investigates the post-Newtonian behavior of general quadratic gravity in the weak-field regime. By extending the Einstein-Hilbert action to include quadratic curvature terms as $\mathcal{L}\propto R-\lambda C^2+\mu R^2$, the theory introduces two massive modes: a scalar mode and a ghost tensor mode. Using the post-Newtonian expansion method, we derive the explicit expressions for the metric for a general source up to 1.5PN order. Furthermore, for a point-mass source, we extend the solution to 2PN order and evaluate the effective Parameterized Post-Newtonian parameters $\gamma(r)$ and $\beta(r)$. The results show that deviations from General Relativity are exponentially suppressed. The theory has the feature $\gamma(r)\equiv 1$ when $m_R=m_W$, and to ensure that gravity remains attractive, we have $m_W>m_R/4$. The leading correction to $\beta(r)$ exhibiting a characteristic $\mathcal{O}(r \ln (r)e^{-mr})$ dependence. Based on the Solar System experiments, we derive preliminary constraints on the theory's parameters: $m_R,m_W\gtrsim23~\mathrm{AU}^{-1}$, corresponding to $\lambda\lesssim2.1\times10^{19}~\mathrm{m}^2$ and $\mu\lesssim 7.1\times 10^{18}~\mathrm{m}^2$. This study provides a theoretical foundation for future tests of quadratic gravity using pulsar timing arrays, gravitational-wave observations, and laboratory-scale short-range gravity experiments.

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.

Desk Editor's Note private letter to a colleague

The paper works out explicit 1.5PN and 2PN metric forms plus gamma and beta for quadratic gravity with both C squared and R squared terms, yielding solar-system bounds around 23 AU inverse, but leaves the ghost-mode stability question open.

read the letter

The main thing to know is that this paper derives the post-Newtonian metric up to 2PN order for a point mass in the quadratic action with both Weyl-squared and Ricci-squared terms, then extracts effective gamma(r) and beta(r) that show exponential suppression of deviations from GR. They highlight that gamma stays exactly 1 when the two mass parameters are equal and that the leading beta correction has an r ln r exp(-m r) shape. From existing solar-system data they extract the concrete lower bound m_R, m_W greater than or equal to 23 AU inverse, which gives upper limits on the couplings lambda and mu. That supplies usable numerical targets for future tests with pulsars or short-range experiments. The derivations follow standard linearized PN methods applied to the field equations, so the algebra looks checkable and the citation pattern to earlier quadratic-gravity work is appropriate. The condition m_W greater than m_R over 4 for attractive gravity is stated clearly. The soft spot is the ghost tensor mode. The paper acknowledges its negative kinetic energy but does not show that the mode remains unexcited or that its presence leaves the perturbative metric solution reliable at solar-system distances, even with the exponential fall-off. That assumption carries the bounds, and it would be good to see a short argument that the Ostrogradsky instability does not leak into the 1.5PN-2PN regime. This is useful reading for anyone doing precision weak-field tests of modified gravity. The calculations are concrete enough that a serious referee should look at them, particularly to check the ghost-mode handling and the 2PN steps.

Referee Report

2 major / 2 minor

Summary. The manuscript applies post-Newtonian methods to quadratic gravity with Lagrangian density proportional to R − λ C² + μ R², deriving the metric up to 1.5PN order for a general source and to 2PN order for a point mass. It obtains effective PPN parameters γ(r) and β(r) that deviate from their GR values only through exponentially suppressed Yukawa terms, notes that γ(r) ≡ 1 when m_R = m_W, requires m_W > m_R/4 for attractive gravity, and extracts preliminary solar-system bounds m_R, m_W ≳ 23 AU^{-1} (λ ≲ 2.1 × 10^{19} m², μ ≲ 7.1 × 10^{18} m²).

Significance. If the perturbative expansion remains valid, the explicit derivation of the r-dependent PPN parameters and the resulting solar-system bounds supply concrete, falsifiable limits on quadratic gravity that can be tested with existing data and extended to pulsar-timing arrays or short-range experiments. The identification of the m_R = m_W case where γ remains exactly unity is a useful structural result.

major comments (2)

[Linearized field equations and mode analysis] The linearized spectrum contains a ghost tensor mode whose kinetic term has the wrong sign. The manuscript states the existence of this mode and imposes m_W > m_R/4 for attractive gravity, but does not demonstrate that Ostrogradsky instabilities are absent or that the negative-energy contributions remain unexcited in the 1.5PN–2PN metric around solar-system sources. This assumption is load-bearing for the claim that the derived metric and PPN parameters constitute a reliable classical solution (see the discussion of the massive modes and the metric expansion).
[Solar-system constraints section] The translation from the exponentially suppressed corrections to the numerical bounds m_R, m_W ≳ 23 AU^{-1} is presented as preliminary. The manuscript should specify which solar-system observables (perihelion advance, light deflection, Shapiro delay, etc.) are used, at which PN order they enter, and how the 2PN O(r ln r e^{-mr}) term in β(r) propagates into the final limits.

minor comments (2)

[Abstract and § on point-mass solution] The abstract states that the solution is extended to 2PN order for a point-mass source; the main text should clarify whether the 2PN terms modify the leading-order constraints or are used only for completeness.
[Introduction and action definition] Notation for the two mass parameters (m_R, m_W) and the coupling constants (λ, μ) should be introduced once with explicit definitions from the action before being used in the PPN expressions.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating planned revisions where appropriate. Our responses focus on clarifying the scope of the perturbative analysis while acknowledging the limitations of the classical treatment.

read point-by-point responses

Referee: The linearized spectrum contains a ghost tensor mode whose kinetic term has the wrong sign. The manuscript states the existence of this mode and imposes m_W > m_R/4 for attractive gravity, but does not demonstrate that Ostrogradsky instabilities are absent or that the negative-energy contributions remain unexcited in the 1.5PN–2PN metric around solar-system sources. This assumption is load-bearing for the claim that the derived metric and PPN parameters constitute a reliable classical solution (see the discussion of the massive modes and the metric expansion).

Authors: We acknowledge that the ghost tensor mode introduces potential Ostrogradsky instabilities, a known feature of quadratic gravity. Our derivation is restricted to the perturbative weak-field regime, where we assume the classical metric solutions remain valid and that the ghost mode is not excited at the orders considered for solar-system sources. The condition m_W > m_R/4 is imposed to ensure attractive gravity within this framework. A complete non-perturbative demonstration of stability lies beyond the scope of this work. We will add explicit statements in the introduction and discussion sections clarifying this assumption and its limitations. revision: partial
Referee: The translation from the exponentially suppressed corrections to the numerical bounds m_R, m_W ≳ 23 AU^{-1} is presented as preliminary. The manuscript should specify which solar-system observables (perihelion advance, light deflection, Shapiro delay, etc.) are used, at which PN order they enter, and how the 2PN O(r ln r e^{-mr}) term in β(r) propagates into the final limits.

Authors: We agree that the solar-system constraints section requires greater specificity. The bounds are derived from Mercury's perihelion advance (probing β at 2PN order) and light deflection measurements (probing γ at 1PN order), using current observational accuracies. The exponentially suppressed terms, including the characteristic O(r ln r e^{-mr}) contribution to β(r), are incorporated by requiring that deviations remain below experimental thresholds at solar-system distances. We will revise the relevant section to explicitly list the observables, their PN orders, and the detailed propagation of the 2PN term into the quoted mass bounds. revision: yes

standing simulated objections not resolved

A full non-perturbative demonstration that Ostrogradsky instabilities are absent and that negative-energy contributions from the ghost mode remain unexcited in the 1.5PN–2PN metric around solar-system sources.

Circularity Check

0 steps flagged

No significant circularity: standard derivation from action via post-Newtonian expansion

full rationale

The paper begins from the quadratic gravity Lagrangian L ∝ R − λ C² + μ R² and applies standard post-Newtonian expansion techniques to obtain the metric components and the effective PPN parameters γ(r), β(r) for a point-mass source. The reported features (exponential suppression of deviations, γ(r) ≡ 1 when m_R = m_W, and the condition m_W > m_R/4 for attractive gravity) are direct algebraic consequences of the linearized field equations and the resulting Yukawa-type propagators. Solar-system bounds on m_R, m_W are obtained by direct comparison with external observational data rather than by any internal fit or self-referential definition. No load-bearing step reduces to a self-citation, a fitted input renamed as prediction, or an ansatz smuggled via prior work by the same authors. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on the standard post-Newtonian framework and the classical validity of the quadratic action; no new free parameters are introduced beyond the derived masses m_R and m_W, which are fixed by the coefficients lambda and mu.

axioms (2)

domain assumption Post-Newtonian expansion is valid for quadratic gravity in the weak-field regime
Invoked to obtain metric up to 2PN order for a point mass
ad hoc to paper Ghost tensor mode does not invalidate the classical solution
Required for the metric expressions to remain physically meaningful

pith-pipeline@v0.9.0 · 5577 in / 1467 out tokens · 51221 ms · 2026-05-16T16:16:07.669671+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The action (1) introduces a massive spin-2 tensor mode with mass m_W² = 1/(2λ), and a massive scalar mode with mass m_R² = 1/(6μ) [7,23,24]... γ(r) ≡ 1 when m_R = m_W... m_W > m_R/4
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

deviations from General Relativity are exponentially suppressed... O(r ln(r) e^{-mr}) dependence

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.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages · 23 internal anchors

[1]

C. M. Will, The Confrontation between General Rela- tivity and Experiment, Living Rev. Rel.17, 4 (2014), arXiv:1403.7377 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[2]

S. G. Turyshev, Experimental Tests of General Relativ- ity: Recent Progress and Future Directions, Usp. Fiz. Nauk179, 3034 (2009), arXiv:0809.3730 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[3]

Testing General Relativity with Present and Future Astrophysical Observations

E. Bertiet al., Testing General Relativity with Present and Future Astrophysical Observations, Class. Quant. Grav.32, 243001 (2015), arXiv:1501.07274 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[4]

B. P. Abbottet al.(LIGO Scientific, Virgo), Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett.116, 061102 (2016), arXiv:1602.03837 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[5]

First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

K. Akiyamaet al.(Event Horizon Telescope), First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. Lett.875, L1 (2019), arXiv:1906.11238 [astro-ph.GA]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[6]

K. S. Stelle, Renormalization of Higher Derivative Quan- tum Gravity, Phys. Rev. D16, 953 (1977)

work page 1977
[7]

K. S. Stelle, Classical Gravity with Higher Derivatives, Gen. Rel. Grav.9, 353 (1978)

work page 1978
[8]

J. F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50, 3874 (1994), arXiv:gr-qc/9405057

work page internal anchor Pith review Pith/arXiv arXiv 1994
[9]

C. G. Callan, Jr., E. J. Martinec, M. J. Perry, and D. Friedan, Strings in Background Fields, Nucl. Phys. B262, 593 (1985)

work page 1985
[10]

D. J. Gross and J. H. Sloan, The Quartic Effective Action for the Heterotic String, Nucl. Phys. B291, 41 (1987)

work page 1987
[11]

Loop Quantum Cosmology: A Status Report

A. Ashtekar and P. Singh, Loop Quantum Cosmology: A Status Report, Class. Quant. Grav.28, 213001 (2011), arXiv:1108.0893 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[12]

A. A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B91, 99 (1980)

work page 1980
[13]

V. F. Mukhanov, Quantum Theory of Cosmological Per- turbations in R(2) Gravity, Phys. Lett. B218, 17 (1989)

work page 1989
[14]

Whitt, Fourth Order Gravity as General Relativity Plus Matter, Phys

B. Whitt, Fourth Order Gravity as General Relativity Plus Matter, Phys. Lett. B145, 176 (1984)

work page 1984
[15]

Planck 2018 results. X. Constraints on inflation

Y. Akramiet al.(Planck), Planck 2018 results. X. Con- straints on inflation, Astron. Astrophys.641, A10 (2020), arXiv:1807.06211 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[16]

Singularity-free cosmological solutions in quadratic gravity

P. Kanti, J. Rizos, and K. Tamvakis, Singularity free cos- mological solutions in quadratic gravity, Phys. Rev. D59, 083512 (1999), arXiv:gr-qc/9806085

work page internal anchor Pith review Pith/arXiv arXiv 1999
[17]

Asorey, F

M. Asorey, F. Ezquerro, and M. Pardina, Stability of cos- mological singularity-free solutions in quadratic gravity, Phys. Rev. D111, 064020 (2025), arXiv:2412.10111 [gr- qc]

work page arXiv 2025
[18]

Exotica ex nihilo: Traversable wormholes & non-singular black holes from the vacuum of quadratic gravity

F. Duplessis and D. A. Easson, Traversable worm- holes and non-singular black holes from the vacuum of quadratic gravity, Phys. Rev. D92, 043516 (2015), arXiv:1506.00988 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[19]

Regular black holes in quadratic gravity

W. Berej, J. Matyjasek, D. Tryniecki, and M. Woronow- icz, Regular black holes in quadratic gravity, Gen. Rel. Grav.38, 885 (2006), arXiv:hep-th/0606185

work page internal anchor Pith review Pith/arXiv arXiv 2006
[20]

H. Lu, A. Perkins, C. N. Pope, and K. S. Stelle, Black Holes in Higher-Derivative Gravity, Phys. Rev. Lett.114, 171601 (2015), arXiv:1502.01028 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[21]

B. L. Giacchini and I. Kol´ aˇ r, Neglected solutions in quadratic gravity (2025), arXiv:2509.07317 [gr-qc]

work page arXiv 2025
[22]

K. Yagi, L. C. Stein, N. Yunes, and T. Tanaka, Post- Newtonian, Quasi-Circular Binary Inspirals in Quadratic Modified Gravity, Phys. Rev. D85, 064022 (2012), [Er- ratum: Phys.Rev.D 93, 029902 (2016)], arXiv:1110.5950 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[23]

M. F. S. Alves, L. F. M. A. M. Reis, and L. G. Medeiros, Gravitational waves from inspiraling black holes in quadratic gravity, Phys. Rev. D107, 044017 (2023), arXiv:2206.13672 [gr-qc]

work page arXiv 2023
[24]

M. F. S. Alves, L. G. Medeiros, and D. C. Rodrigues, Gravitational waveforms from inspiraling compact bina- ries in quadratic gravity and their parameterized post- Einstein characterization (2025), arXiv:2507.15571 [gr- qc]

work page arXiv 2025
[25]

Nordtvedt, Equivalence Principle for Massive Bodies

K. Nordtvedt, Equivalence Principle for Massive Bodies

work page
[26]

Rev.169, 1017 (1968)

Theory, Phys. Rev.169, 1017 (1968). 17

work page 1968
[27]

K. S. Thorne and C. M. Will, Theoretical Frameworks for Testing Relativistic Gravity. I. Foundations, Astrophys. J.163, 595 (1971)

work page 1971
[28]

C. M. Will, Theoretical Frameworks for Testing Rela- tivistic Gravity. 2. Parametrized Post-Newtonian Hydro- dynamics, and the Nordtvedt Effect, Astrophys. J.163, 611 (1971)

work page 1971
[29]

C. M. Will, THEORETICAL FRAMEWORKS FOR TESTING RELATIVISTIC GRAVITY. 3. CONSERVA- TION LAWS, LORENTZ INVARIANCE AND VALUES OF THE P P N PARAMETERS, Astrophys. J.169, 125 (1971)

work page 1971
[30]

C. M. Will,Theory and Experiment in Gravitational Physics(Cambridge University Press, 1993)

work page 1993
[31]

Poisson and C

E. Poisson and C. M. Will,Gravity: Newtonian, Post- Newtonian, Relativistic(Cambridge University Press, Cambridge, UK, 2014)

work page 2014
[32]

Solar System constraints to general f(R) gravity

T. Chiba, T. L. Smith, and A. L. Erickcek, Solar Sys- tem constraints to general f(R) gravity, Phys. Rev. D75, 124014 (2007), arXiv:astro-ph/0611867

work page internal anchor Pith review Pith/arXiv arXiv 2007
[33]

PPN-limit of Fourth Order Gravity inspired by Scalar-Tensor Gravity

S. Capozziello and A. Troisi, PPN-limit of fourth order gravity inspired by scalar-tensor gravity, Phys. Rev. D 72, 044022 (2005), arXiv:astro-ph/0507545

work page internal anchor Pith review Pith/arXiv arXiv 2005
[34]

The Newtonian Limit of F(R) gravity

S. Capozziello, A. Stabile, and A. Troisi, The Newtonian Limit of f(R) gravity, Phys. Rev. D76, 104019 (2007), arXiv:0708.0723 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[35]

$f(R)$ gravity constrained by PPN parameters and stochastic background of gravitational waves

S. Capozziello, M. De Laurentis, S. Nojiri, and S. D. Odintsov, f(R) gravity constrained by PPN parameters and stochastic background of gravitational waves, Gen. Rel. Grav.41, 2313 (2009), arXiv:0808.1335 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[36]

J. Qiao, T. Zhu, G. Li, and W. Zhao, Post-Newtonian parameters of ghost-free parity-violating gravities, JCAP 04(04), 054, arXiv:2110.09033 [gr-qc]

work page arXiv
[37]

J. D. Toniato and M. G. Richarte, Post-Newtonian analysis of regularized 4D Einstein-Gauss-Bonnet the- ory: Complete set of PPN parameters and observa- tional constraints, Phys. Rev. D109, 104068 (2024), arXiv:2402.13951 [gr-qc]

work page arXiv 2024
[38]

M. G. Richarte and J. D. Toniato, Exploring scalar- ized Einstein-Gauss-Bonnet theories through the lens of parametrized post-Newtonian formalism, Phys. Rev. D 112, 024019 (2025), arXiv:2503.13339 [gr-qc]

work page arXiv 2025
[39]

A. I. Vainshtein, To the problem of nonvanishing gravi- tation mass, Phys. Lett. B39, 393 (1972)

work page 1972
[40]

The Parametrized Post-Newtonian-Vainshteinian Formalism

A. Avilez-Lopez, A. Padilla, P. M. Saffin, and C. Skordis, The Parametrized Post-Newtonian-Vainshteinian formal- ism, Journal of Cosmology and Astroparticle Physics06 (06), 044, arXiv:1501.01985 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv
[41]

Hohmann, xPPN: an implementation of the parametrized post-Newtonian formalism using xAct for Mathematica, Eur

M. Hohmann, xPPN: an implementation of the parametrized post-Newtonian formalism using xAct for Mathematica, Eur. Phys. J. C81, 504 (2021), arXiv:2012.14984 [gr-qc]

work page arXiv 2021
[42]

Post-Newtonian parameters gamma and beta of scalar-tensor gravity with a general potential

M. Hohmann, L. Jarv, P. Kuusk, and E. Randla, Post- Newtonian parametersγandβof scalar-tensor grav- ity with a general potential, Phys. Rev. D88, 084054 (2013), [Erratum: Phys.Rev.D 89, 069901 (2014)], arXiv:1309.0031 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[43]

C. P. L. Berry and J. R. Gair, Linearized f(R) Gravity: Gravitational Radiation and Solar System Tests, Phys. Rev. D83, 104022 (2011), [Erratum: Phys.Rev.D 85, 089906 (2012)], arXiv:1104.0819 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[44]

Post-Newtonian parameters $\gamma$ and $\beta$ of scalar-tensor gravity for a homogeneous gravitating sphere

M. Hohmann and A. Sch¨ arer, Post-Newtonian parame- tersγandβof scalar-tensor gravity for a homogeneous gravitating sphere, Phys. Rev. D96, 104026 (2017), arXiv:1708.07851 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[45]

C. M. Will, The Confrontation between general relativity and experiment, Living Rev. Rel.9, 3 (2006), arXiv:gr- qc/0510072

work page arXiv 2006
[46]

Bertotti, L

B. Bertotti, L. Iess, and P. Tortora, A test of general relativity using radio links with the Cassini spacecraft, Nature425, 374 (2003)

work page 2003
[47]

Hofmann, J

F. Hofmann, J. M¨ uller, and L. Biskupek, Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant, Astronomy and Astrophysics522, L5 (2010)

work page 2010
[48]

E. G. Adelberger, J. H. Gundlach, B. R. Heckel, S. Hoedl, and S. Schlamminger, Torsion balance experiments: A low-energy frontier of particle physics, Prog. Part. Nucl. Phys.62, 102 (2009)

work page 2009
[49]

D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gund- lach, B. 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
[50]

Sub-millimeter Spatial Oscillations of Newton's Constant: Theoretical Models and Laboratory Tests

L. Perivolaropoulos, Submillimeter spatial oscillations of Newton’s constant: Theoretical models and laboratory tests, Phys. Rev. D95, 084050 (2017), arXiv:1611.07293 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[51]

J. G. Lee, E. G. Adelberger, T. S. Cook, S. M. Fleischer, and B. R. Heckel, New Test of the Gravitational 1/r 2 Law at Separations down to 52µm, Phys. Rev. Lett. 124, 101101 (2020), arXiv:2002.11761 [hep-ex]

work page arXiv 2020