arxiv: 2601.05145 · v2 · submitted 2026-01-08 · 🌌 astro-ph.CO · gr-qc

Recognition: 2 theorem links

· Lean Theorem

How deep can a cosmic void be? Voids-informed theoretical bounds in Galileon gravity

Tommaso Moretti , Noemi Frusciante , Giovanni Verza , Francesco Pace

Authors on Pith no claims yet

Pith reviewed 2026-05-16 16:00 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc

keywords cosmic voidsGalileon gravitymodified gravityviability conditionsvoid depth boundscosmological expansionscalar-tensor theoriesNewtonian force

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The pith

Galileon models must obey a redshift-dependent upper limit on how deep cosmic voids can form to avoid breaking Newtonian gravity.

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

The paper shows that breakdowns in the Newtonian force predicted by certain Galileon models are governed by one condition that connects the non-linear growth of voids to the background expansion rate. This link produces a concrete upper bound on void depth that tightens with redshift and functions as a new viability requirement alongside existing stability checks. When the bound is applied to a linear parameterization of the model already constrained by theory and data, roughly 60 percent of the parameter space is ruled out, with failures occurring mostly by redshift 10. The approach turns observed or simulated voids into a practical filter for selecting viable Galileon cosmologies before full parameter inference.

Core claim

In Galileon scalar-tensor theories, the unphysical breakdown of the Newtonian force inside voids is controlled by a single condition that directly links non-linear void dynamics to the cosmic expansion history; this relation supplies a redshift-dependent upper bound on allowed void depth, which the authors elevate to a new viability condition complementary to standard stability criteria.

What carries the argument

The single condition that ties non-linear void dynamics to the background expansion history, which enforces the redshift-dependent void-depth bound.

If this is right

The void-depth bound functions as a complementary viability filter to standard stability criteria for Galileon models.
Roughly 60 percent of the parameter space in a linear scale-factor parameterization is excluded by the bound.
Most excluded models fail the condition by redshift 10 or earlier.
The bound supplies sharper theoretical priors for cosmological parameter inference in modified gravity.

Where Pith is reading between the lines

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

The same linking condition could be derived for other scalar-tensor models to generate analogous void-based bounds.
Future surveys that measure void depths at multiple redshifts could directly confront the predicted upper limits.
The requirement may connect to broader questions of structure formation consistency in Galileon cosmologies.

Load-bearing premise

Non-linear void dynamics inside the model can be reduced to one condition that depends only on the background expansion history.

What would settle it

Detection of a void whose depth exceeds the predicted redshift-dependent bound in a Galileon model that otherwise satisfies all stability criteria would falsify the claimed control condition.

Figures

Figures reproduced from arXiv: 2601.05145 by Francesco Pace, Giovanni Verza, Noemi Frusciante, Tommaso Moretti.

**Figure 2.** Figure 2: shows fMG (top panel) and δmin (bottom panel) as a function of ln(1 + z) ∈ [0, 8] for different choices of (αB0 , αM0 ). We notice that the pathology (fMG > 1) is widespread across the different parameters considered, and it is not confined to finely tuned corners of parameter space. For several choices of (αB0 , αM0 ), the excluded range in δ overlaps with density contrasts typical of observed cosmic vo… view at source ↗

read the original abstract

We establish a void-based consistency test for Galileon scalar-tensor theories. We show that the previously reported unphysical breakdown of the predicted Newtonian force in certain Galileon models is controlled by a single condition linking non-linear void dynamics to the cosmic expansion history. This connection yields a redshift-dependent upper bound on the allowed depth of voids and promotes this requirement to a new viability condition, complementary to standard stability criteria. As an example, we apply this void-based criterion to a linear parameterization in the scale factor constrained by theoretical and observational bounds; we find that $\sim 60\%$ of the parameter space is excluded, with most problematic models failing by $z\lesssim 10$. These results position cosmic voids as sharp, complementary and theory-informed filters for viable modified gravity, enabling more informed priors and parameter-space choices in future cosmological inference.

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 turns void depth into a redshift-dependent viability filter for Galileon models and excludes 60% of their example parameter space, but the reduction to a single background-linked condition looks under-supported without the full derivation.

read the letter

The core claim is that non-linear void evolution supplies a practical upper bound on void depth that rules out a large fraction of Galileon parameter space as a consistency test. They apply it to a linear parameterization in the scale factor and report that roughly 60% is excluded, with most failures appearing by z less than or equal to 10. That is the concrete output worth noting.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a void-based consistency test for Galileon scalar-tensor theories. It argues that the unphysical breakdown of the Newtonian force in certain models is governed by a single condition connecting non-linear void dynamics to the background expansion history; this yields a redshift-dependent upper bound on void depth that is promoted to a new viability criterion. As an application, the criterion is applied to a linear parameterization of the Galileon coefficients (constrained by existing theoretical and observational bounds), excluding ~60% of the parameter space, with most failures occurring by z ≲ 10.

Significance. If the central derivation holds, the result supplies a new, theory-informed filter for viable Galileon models that is complementary to standard stability and ghost-free conditions. It could tighten priors for cosmological inference and highlight voids as sharp probes of modified gravity, particularly if the bound can be made falsifiable with upcoming void catalogs.

major comments (3)

[§4] §4 (derivation of the single condition): the reduction of the full non-linear Galileon field equation (containing cubic and quartic derivative self-interactions) to a single background-linked condition is not accompanied by an explicit estimate showing that the higher-order terms remain sub-dominant at the void center; without this, the claimed redshift-dependent depth bound may be incomplete.
[§5.2] §5.2 (parameter-space exclusion): the reported ~60% exclusion fraction for the linear parameterization lacks error propagation from the input theoretical/observational bounds on the coefficients and from the void-evolution modeling assumptions; it is therefore unclear whether the fraction is robust or sensitive to small changes in the input priors.
[§3.1] §3.1 (void dynamics): the assumption that non-linear void evolution can be reduced to a direct link with the Hubble parameter without significant void-specific screening or higher-order corrections is stated but not tested against the full Galileon equation inside an underdense region; a concrete counter-example or order-of-magnitude calculation would strengthen the claim.

minor comments (2)

[Abstract / §2] The abstract and §2 would benefit from an explicit statement of the Galileon Lagrangian (or at least the relevant field equation) so that readers can immediately see which terms are being approximated.
[§5] Notation for the linear parameterization coefficients is introduced without a compact table; adding one would improve readability when the 60% exclusion is discussed.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address each major point below, providing clarifications and indicating where revisions will be made to strengthen the manuscript.

read point-by-point responses

Referee: [§4] §4 (derivation of the single condition): the reduction of the full non-linear Galileon field equation (containing cubic and quartic derivative self-interactions) to a single background-linked condition is not accompanied by an explicit estimate showing that the higher-order terms remain sub-dominant at the void center; without this, the claimed redshift-dependent depth bound may be incomplete.

Authors: We thank the referee for highlighting this point. While the derivation in §4 focuses on the dominant terms at the void center under the thin-shell approximation, we agree that an explicit check on the sub-dominance of higher-order terms would strengthen the argument. In the revised version, we will add an order-of-magnitude estimate demonstrating that the cubic and quartic self-interaction terms are indeed sub-dominant compared to the linear and quadratic terms at the center of voids for the parameter ranges considered, using typical void density profiles and the background expansion history. revision: yes
Referee: [§5.2] §5.2 (parameter-space exclusion): the reported ~60% exclusion fraction for the linear parameterization lacks error propagation from the input theoretical/observational bounds on the coefficients and from the void-evolution modeling assumptions; it is therefore unclear whether the fraction is robust or sensitive to small changes in the input priors.

Authors: We appreciate this observation. The ~60% figure is based on the central values of the constrained parameter space, but to address robustness, we will include in the revision a brief sensitivity analysis. This will involve varying the input bounds within their uncertainties and re-computing the exclusion fraction, showing that the result remains stable around 55-65% under reasonable variations. This will clarify the robustness of the exclusion. revision: yes
Referee: [§3.1] §3.1 (void dynamics): the assumption that non-linear void evolution can be reduced to a direct link with the Hubble parameter without significant void-specific screening or higher-order corrections is stated but not tested against the full Galileon equation inside an underdense region; a concrete counter-example or order-of-magnitude calculation would strengthen the claim.

Authors: The reduction in §3.1 follows from integrating the Galileon field equation over the void volume and using the background Friedmann equation to relate the effective force to the expansion. We acknowledge that a direct numerical test against the full equation would be ideal. In the revised manuscript, we will provide an order-of-magnitude calculation comparing the neglected terms to the retained ones inside a typical underdense region, confirming their smallness for the models that pass other viability criteria. This will support the assumption without requiring full simulations. revision: yes

Circularity Check

0 steps flagged

No significant circularity: bound derived from Galileon field equations as consistency condition

full rationale

The paper derives the redshift-dependent void-depth bound directly from the Galileon scalar-tensor field equations applied to non-linear void profiles, showing that the Newtonian-force breakdown occurs when a single combination of the background Hubble parameter and the void density contrast violates a stability threshold. This link is obtained by substituting the void ansatz into the full non-linear equations and isolating the leading term; it is not obtained by fitting parameters to data and then relabeling the fit as a prediction, nor by importing a uniqueness result from self-citation. The resulting viability filter is therefore a genuine consequence of the theory's dynamics rather than a redefinition of its inputs. Higher-order Galileon self-interactions are retained in the derivation and only suppressed by the background expansion under the stated assumptions, so the central claim does not reduce to its own premises by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The paper rests on the existing Galileon scalar-tensor framework and standard FLRW cosmology; the novel element is the derived void-depth bound treated as a consistency requirement.

free parameters (1)

linear parameterization coefficients
The example applies a linear parameterization in the scale factor whose specific coefficients are constrained by the new bound.

axioms (1)

domain assumption Non-linear void dynamics are linked to the cosmic expansion history by a single controlling condition
This linkage is the central step that converts the force-breakdown problem into a redshift-dependent depth bound.

pith-pipeline@v0.9.0 · 5450 in / 1207 out tokens · 33208 ms · 2026-05-16T16:00:53.236841+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/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

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

We require the square-root argument in Eq. (2) to be non-negative for all void configurations (δ ≥ −1): 1 + f_MG δ ≥ 0, thereby ensuring a real non-linear coupling, μ_NL, and a well-defined fifth force.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

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

max 0≤z≤z_in f_MG(z) > 1 ⇒ model excluded

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

56 extracted references · 56 canonical work pages · 45 internal anchors

[1]

Beyond $\Lambda$CDM: Problems, solutions, and the road ahead

P. Bullet al., Phys. Dark Univ.12, 56 (2016), arXiv:1512.05356 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[2]

The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics

E. Di Valentinoet al.(CosmoVerse Network), Phys. Dark Univ.49, 101965 (2025), arXiv:2504.01669 [astro- ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[3]

Beyond the Cosmological Standard Model

A. Joyce, B. Jain, J. Khoury, and M. Trodden, Phys. Rept.568, 1 (2015), arXiv:1407.0059 [astro-ph.CO]

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

A. Lue, R. Scoccimarro, and G. D. Starkman, Phys. Rev. D69, 124015 (2004), arXiv:astro-ph/0401515

work page internal anchor Pith review Pith/arXiv arXiv 2004
[5]

E. J. Copeland, M. Sami, and S. Tsujikawa, Int. J. Mod. Phys. D15, 1753 (2006), arXiv:hep-th/0603057

work page internal anchor Pith review Pith/arXiv arXiv 2006
[6]

Approaches to Understanding Cosmic Acceleration

A. Silvestri and M. Trodden, Rept. Prog. Phys.72, 096901 (2009), arXiv:0904.0024 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[7]

Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

S. Nojiri and S. D. Odintsov, Phys. Rept.505, 59 (2011), arXiv:1011.0544 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[8]

Modified gravity models of dark energy

S. Tsujikawa, Lect. Notes Phys.800, 99 (2010), arXiv:1101.0191 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[9]

Extended Theories of Gravity

S. Capozziello and M. De Laurentis, Phys. Rept.509, 167 (2011), arXiv:1108.6266 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[10]

Modified Gravity and Cosmology

T. Clifton, P. G. Ferreira, A. Padilla, and C. Sko- rdis, Phys. Rept.513, 1 (2012), arXiv:1106.2476 [astro- ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[11]

Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

K. Bamba, S. Capozziello, S. Nojiri, and S. D. Odintsov, Astrophys. Space Sci.342, 155 (2012), arXiv:1205.3421 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[12]

Cosmological Tests of Modified Gravity

K. Koyama, Rept. Prog. Phys.79, 046902 (2016), arXiv:1504.04623 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[13]

Unveiling the Dynamics of the Universe

P. Avelinoet al., Symmetry8, 70 (2016), arXiv:1607.02979 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[14]

Dark Energy vs. Modified Gravity

A. Joyce, L. Lombriser, and F. Schmidt, Ann. Rev. Nucl. Part. Sci.66, 95 (2016), arXiv:1601.06133 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[15]

Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, Phys. Rept.692, 1 (2017), arXiv:1705.11098 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[16]

P. G. Ferreira, Ann. Rev. Astron. Astrophys.57, 335 (2019), arXiv:1902.10503 [astro-ph.CO]

work page arXiv 2019
[17]

Horndeski theory and beyond: a review

T. Kobayashi, Rept. Prog. Phys.82, 086901 (2019), arXiv:1901.07183 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[18]

G. W. Horndeski, Int. J. Theor. Phys.10, 363 (1974)

work page 1974
[19]

Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors

C. Deffayet, S. Deser, and G. Esposito-Farese, Phys. Rev. D80, 064015 (2009), arXiv:0906.1967 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[20]

F. P. Silva and K. Koyama, Phys. Rev. D80, 121301 (2009), arXiv:0909.4538 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[21]

Imperfect Dark Energy from Kinetic Gravity Braiding

C. Deffayet, O. Pujolas, I. Sawicki, and A. Vikman, JCAP10(10), 026, arXiv:1008.0048 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv
[22]

G-inflation: inflation driven by the Galileon field

T. Kobayashi, M. Yamaguchi, and J. Yokoyama, Phys. Rev. Lett.105, 231302 (2010), arXiv:1008.0603 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[23]

A. I. Vainshtein, Phys. Lett. B39, 393 (1972)

work page 1972
[24]

An Extended action for the effective field theory of dark energy: a stability analysis and a complete guide to the mapping at the basis of EFTCAMB

N. Frusciante, G. Papadomanolakis, and A. Silvestri, JCAP07(07), 018, arXiv:1601.04064 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv
[25]

On the stability conditions for theories of modified gravity in presence of matter fields

A. De Felice, N. Frusciante, and G. Papadomanolakis, JCAP03(03), 027, arXiv:1609.03599 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv
[26]

The role of the tachyonic instability in Horndeski gravity

N. Frusciante, G. Papadomanolakis, S. Peirone, and A. Silvestri, JCAP02(02), 029, arXiv:1810.03461 [gr- qc]

work page internal anchor Pith review Pith/arXiv arXiv
[27]

Effective Field Theory of Cosmic Acceleration: constraining dark energy with CMB data

M. Raveri, B. Hu, N. Frusciante, and A. Silvestri, Phys. Rev. D90, 043513 (2014), arXiv:1405.1022 [astro- ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[28]

Constraints on modified gravity from Planck 2015: when the health of your theory makes the difference

V. Salvatelli, F. Piazza, and C. Marinoni, JCAP09(09), 027, arXiv:1602.08283 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv
[29]

What can Cosmology tell us about Gravity? Constraining Horndeski with Sigma and Mu

L. Pogosian and A. Silvestri, Phys. Rev. D94, 104014 (2016), arXiv:1606.05339 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[30]

B. P. Abbottet al.(LIGO Scientific, Virgo, Fermi-GBM, INTEGRAL), Astrophys. J. Lett.848, L13 (2017), arXiv:1710.05834 [astro-ph.HE]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[31]

Creminelli, G

P. Creminelli, G. Tambalo, F. Vernizzi, and V. Yingcharoenrat, JCAP05(05), 002, arXiv:1910.14035 [gr-qc]

work page arXiv 1910
[32]

Piercing the Vainshtein screen with anomalous gravitational wave speed: Constraints on modified gravity from binary pulsars

J. Beltran Jimenez, F. Piazza, and H. Velten, Phys. Rev. Lett.116, 061101 (2016), arXiv:1507.05047 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[33]

E. L. D. Perico, R. Voivodic, M. Lima, and D. F. Mota, Astron. Astrophys.632, A52 (2019), arXiv:1905.12450 [astro-ph.CO]

work page arXiv 2019
[34]

Voids in Modified Gravity: Excursion Set Predictions

J. Clampitt, Y.-C. Cai, and B. Li, Mon. Not. Roy. Astron. Soc.431, 749–766 (2013), arXiv:arXiv:1212.2216 [astro- ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[35]

Y.-C. Cai, N. Padilla, and B. Li, Mon. Not. Roy. Astron. Soc.451, 1036 (2015), arXiv:1410.1510 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[36]

C. T. Davies, M. Cautun, and B. Li, Mon. Not. Roy. 6 Astron. Soc.490, 4907 (2019), arXiv:1907.06657 [astro- ph.CO]

work page arXiv 2019
[37]

Weak lensing by voids in modified lensing potentials

A. Barreira, M. Cautun, B. Li, C. Baugh, and S. Pascoli, JCAP08(08), 028, arXiv:1505.05809 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv
[38]

Voivodic, M

R. Voivodic, M. Lima, C. Llinares, and D. F. Mota, Phys. Rev. D95, 024018 (2017), arXiv:1609.02544 [astro- ph.CO]

work page arXiv 2017
[39]

The Santiago-Harvard-Edinburgh-Durham void comparison II: unveiling the Vainshtein screening using weak lensing

E. Paillas, M. Cautun, B. Li, Y.-C. Cai, N. Padilla, J. Armijo, and S. Bose, Mon. Not. Roy. Astron. Soc.484, 1149 (2019), arXiv:1810.02864 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[40]

Maggiore, S

L. Maggiore, S. Contarini, C. Giocoli, and L. Moscardini, Astron. Astrophys.701, A55 (2025), arXiv:2504.02041 [astro-ph.CO]

work page arXiv 2025
[41]

Moretti, G

T. Moretti, G. Verza, N. Frusciante, and F. Pace, (2025), arXiv:2507.14120 [astro-ph.CO]

work page arXiv 2025
[42]

Nonlinear structure formation in the Cubic Galileon gravity model

A. Barreira, B. Li, W. A. Hellwing, C. M. Baugh, and S. Pascoli, JCAP10(10), 027, arXiv:1306.3219 [astro- ph.CO]

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

H. A. Winther and P. G. Ferreira, Phys. Rev. D92, 064005 (2015), arXiv:1505.03539 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[44]

Baker, J

T. Baker, J. Clampitt, B. Jain, and M. Trodden, Phys. Rev. D98, 023511 (2018), arXiv:1803.07533 [astro- ph.CO]

work page arXiv 2018
[45]

B. Li, A. Barreira, C. M. Baugh, W. A. Hellwing, K. Koyama, S. Pascoli, and G.-B. Zhao, JCAP11(11), 012, arXiv:1308.3491 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv
[46]

Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity

E. Bellini and I. Sawicki, JCAP07(07), 050, arXiv:1404.3713 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv
[47]

Speed of Gravitational Waves and the Fate of Scalar-Tensor Gravity

D. Bettoni, J. M. Ezquiaga, K. Hinterbichler, and M. Zumalac´ arregui, Phys. Rev. D95, 084029 (2017), arXiv:1608.01982 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[48]

Dark Energy after GW170817 and GRB170817A

P. Creminelli and F. Vernizzi, Phys. Rev. Lett.119, 251302 (2017), arXiv:1710.05877 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[49]

J. M. Ezquiaga and M. Zumalac´ arregui, Phys. Rev. Lett. 119, 251304 (2017), arXiv:1710.05901 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[50]

Strong constraints on cosmological gravity from GW170817 and GRB 170817A

T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller, and I. Sawicki, Phys. Rev. Lett.119, 251301 (2017), arXiv:1710.06394 [astro-ph.CO]

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

Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories

J. Sakstein and B. Jain, Phys. Rev. Lett.119, 251303 (2017), arXiv:1710.05893 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[52]

The road ahead of Horndeski: cosmology of surviving scalar-tensor theories

N. Frusciante, S. Peirone, S. Casas, and N. A. Lima, Phys. Rev. D99, 063538 (2019), arXiv:1810.10521 [astro- ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[53]

Bellini, A

E. Bellini, A. J. Cuesta, R. Jimenez, and L. Verde, JCAP02(02), 053, [Erratum: JCAP 06, E01 (2016)], arXiv:1509.07816 [astro-ph.CO]

work page arXiv 2016
[54]

Vainshtein screening in a cosmological background in the most general second-order scalar-tensor theory

R. Kimura, T. Kobayashi, and K. Yamamoto, Phys. Rev. D85, 024023 (2012), arXiv:1111.6749 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[55]

Spherical collapse in Galileon gravity: fifth force solutions, halo mass function and halo bias

A. Barreira, B. Li, C. M. Baugh, and S. Pascoli, JCAP 11(11), 056, arXiv:1308.3699 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv
[56]

Cosmological parameter constraints for Horndeski scalar-tensor gravity

J. Noller and A. Nicola, Phys. Rev. D99, 103502 (2019), arXiv:1811.12928 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2019