Parametrizations for tests of gravity

Lucas Lombriser

Parametrizations for tests of gravity

T0 review · 0 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This review shows that the major parametrization frameworks for testing gravity—PPN, PPF, EFT, and waveform models—form a connected map and can be unified through scalar-tensor theories with screening.

desk verdict A competent, self-centric review of gravity parametrizations that is honest about its scope limits; worth refereeing as a reference article, not a source of new physics. read the letter →

arxiv 1908.07892 v1 pith:Z6HJAMCP submitted 2019-08-21 astro-ph.CO gr-qc

Lucas Lombriser This is my paper · ORCID

classification astro-ph.COgr-qc

keywords parametrizedpost-Friedmannianformalismeffectivefieldtheoryofdarkenergypost-Newtonianpost-Einsteinianmodifiedgravitycosmologicalperturbationsgravitationalwavesscreeningmechanisms

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This review paper sets out to show that the many frameworks built to test gravity with cosmological, solar-system, and gravitational-wave observations are not isolated tools but connected pieces of a single underlying description. It surveys the parametrized post-Friedmannian (PPF) formalism, the effective field theory (EFT) of dark energy, the parametrized post-Newtonian (PPN) expansion, and parametrized gravitational-wave formalisms, and it collects the known translation rules between them. The payoff of the map is practical: a measurement made in one regime, such as the speed of gravitational waves, can be used to constrain or exclude modifications of gravity that would otherwise hide in the large-scale structure. The paper argues that a global parametrization covering all scales is feasible, with scalar-tensor theories and their screening mechanisms as the natural bridge.

What carries the argument

The load-bearing object is the pair of closure relations for linear perturbations—the modified Poisson equation and the gravitational slip, $\mu(a,k)$ and $\gamma(a,k)$—together with the effective gravitational coupling $G_{\rm eff}$ whose radial profile is parametrized by a modular transition function between screened and unscreened regimes. These encode the gravitational modification in a way that can be mapped onto the EFT functions ($\alpha_K$, $\alpha_B$, $\alpha_M$, $\alpha_T$) and onto the gravitational-wave propagation parameters ($\nu$, $c_T$, $\tilde{\mu}$, $\Gamma$). The work these objects do is to turn a theory space into a small set of measurable functions of time and scale, so that the same measurement, like the nearly equal speeds of light and gravitational waves from GW170817, can be propagated through the network of formalisms and applied to all regimes.

What would settle it

Take a specific modified-gravity theory whose superhorizon behavior is known exactly and check whether its scalar perturbations can be reproduced by the two closure relations with some choice of $\mu(a,k)$ and $\gamma(a,k)$; a mismatch would falsify the claimed generality. A more direct test would be a measurement of the gravitational-wave speed at high redshift ($z \gtrsim 1$) via a standard siren with an electromagnetic counterpart, which would probe whether the $c_T \simeq 1$ assumption used to break the dark degeneracy holds where it matters for cosmic acceleration.

Watch

Extended reading notes

Core claim

The central claim is that the apparent diversity of parametrization schemes for tests of gravity reduces to a small set of shared physical building blocks. At the level of linear cosmological perturbations, the entire space of metric modified-gravity models is encoded in two closure relations: a modified Poisson equation, $k_H^2 \Psi = -\frac{\kappa^2 \bar{\rho}_m}{2H^2} \mu(a,k) \Delta_m$, and a gravitational slip, $\Phi = -\gamma(a,k) \Psi$, which take simple analytic forms in the subhorizon limit and can be mapped to the coefficients of the effective field theory. The same building blocks reappear in the gravitational-wave sector: the running Planck mass $\nu$ and the speed $c_T$ enter both the propagation equation for the wave and the condition for genuine cosmic self-acceleration. On static weak-field scales, the PPN parameters (notably $\gamma$ and $\beta$) are the analogues of the slip, and the paper shows how screening mechanisms can be incorporated either by promoting PPN parameters to functions of position or by adding new potentials. The paper's constructive proposal is that a unified framework can be built by reconstructing the Lagrangian of the scalar-tensor theory from a few time-dependent functions, such as the scalar mass and coupling at the minimum of its effective potential, which then connects all regimes.

Load-bearing premise

The whole map assumes that two closure relations—a modified Poisson equation and a gravitational slip—can faithfully describe the linear perturbations of every relevant metric theory of modified gravity at every scale, including superhorizon scales, because the review adopts them for all scales.

Editorial extensions

If this is right

If the closure relations hold at all scales, a single pair of functions $\mu(a,k)$ and $\gamma(a,k)$ suffices to compute linear modified-gravity predictions from superhorizon to subhorizon scales, including the integrated Sachs-Wolfe effect and lensing.
The GW170817 bound $c_T \simeq 1$ implies that genuine cosmic self-acceleration in Horndeski gravity must be driven by an evolving effective Planck mass, and the minimal such scenario is disfavored at about $3\sigma$ by current cosmological data.
Percent-level Standard Siren measurements of the luminosity distance can turn the minimal scalar-tensor self-acceleration scenario into a conclusive $5\sigma$ test.
A unified parametrization for chameleon, dilaton, and symmetron models can be reconstructed from the cosmological time variation of the scalar mass and coupling at the minimum of the effective potential, connecting laboratory, solar-system, and cosmological tests.

Reading between the lines

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

One could test the superhorizon generality of the $\mu$–$\gamma$ closure by comparing its predictions against a theory with explicitly known superhorizon evolution, such as a nonlocal or higher-derivative model, to see whether the closure misses observables.
The modular transition function for $G_{\rm eff}$ suggests a direct route to parametrizing screened gravitational-wave emission at the source, which the paper notes remains an open problem; a waveform-level analogue of the transition function is a plausible extension.
Because the paper notes that early-time modifications are often dropped by assumption, a natural extension is to include early-time $\mu$ and $\gamma$ in forecasts for future surveys; current constraints may be artificially optimistic.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is a review, and it does not pretend otherwise. What it offers is a systematic map of the frameworks used to parametrize modified gravity across scales: PPF, EFT, PPN, ppE, and the screening parametrizations. As a map it is genuinely useful. The author knows the terrain firsthand, and the connections he draws between formalisms are the main value. The review also does something right that many reviews get wrong: it discloses where its working assumptions are limited. Section 2.2.2 explicitly says the closure relations (8) and (9) are adopted for all scales as a presentational choice, and that superhorizon evolution is better described by an extra summand. Similarly, the matter-conservation assumption behind Eqs. (10)-(11) is stated, not smuggled in. That is honest scholarship.

The soft spots are real but not disqualifying. The review leans heavily on the author's own prior work for key results: the self-acceleration conditions, the degeneracy relations, the screening parametrization, and the minimal-modification scenario all trace back to Lombriser and collaborators. The equations are presented as established without independent derivation in the text. For a review by a leading expert that is acceptable, but it means the survey is not impartial. A reader new to the field should know that the "minimal modification" story and the claimed 5-sigma tension in Standard Sirens carry the weight of prior analyses that are not fully reproduced here. The paper is also a conventional narrative review: no code, no data, no machine-checked proofs. That is fine for the genre.

The stress-test note is right: I read the superhorizon concern against the text, and the disclosure in Sec. 2.2.2 defuses it. The central claim of the paper, that these frameworks exist and can be connected, holds up. I would classify the novelty as low by design, and the significance as moderate: it will be a useful reference for practitioners and a convenient entry point for students, but it advances no new physics.

Who is this for? Someone starting in modified gravity who wants a guided tour of the parametrization zoo, or an experienced researcher checking where a particular connection was made. It deserves a serious referee: a review of this scope by an active expert will be cited, and the refereeing should focus on the accuracy of attributions and the strength of the self-acceleration claims. I would recommend acceptance after minor revisions, mainly asking the author to flag more prominently where he is presenting his own prior conclusions rather than textbook consensus.

Referee Report

0 major / 6 minor

Summary. The paper is a review of parametrized frameworks for testing gravity, covering the parametrized post-Friedmannian (PPF) frameworks for background, linear, and nonlinear cosmological scales, effective field theory approaches, gravitational wave propagation parametrizations, the parametrized post-Newtonian (PPN) formalism with screening extensions, the parametrized post-Einsteinian (ppE) and inspiral-merger-ringdown waveform models, and further approaches such as PPNC. It highlights connections between formalisms where they exist and provides an outlook toward a unified framework for tests of gravity and dark sector models.

Significance. If the descriptive claims hold, the review is a valuable map of a broad and technical field: it surveys many formalisms under a consistent notation, connects linear EFT functions to gravitational wave propagation and to nonlinear screening parametrizations, and explicitly discloses limitations such as the subhorizon validity of the closure relations in Sec. 2.2.2. The paper's strengths are its breadth, its consistent notation, and its careful attribution of results to the literature. The main weakness is a high density of self-citations for central relations, which is typical for a review by an active contributor and does not undermine the descriptive claim; the disclosed superhorizon limitation of Eqs. (8) and (9) is a stated scope restriction rather than a hidden flaw.

minor comments (6)

[Title page] The keywords are placeholders ("Keyword1; keyword2; keyword3") and the PACS numbers are missing; these should be filled before publication.
[Sec. 2.2.4, Eq. (23)] The definition "h_ij ≡ g_ij/g_ii" is not meaningful as written; h_ij should be defined as the spatial metric perturbation in the decomposition g_ij = a^2(δ_ij + h_ij) or an equivalent standard form, and the ratio g_ij/g_ii should be removed.
[Sec. 2.2.3] The notation M_2^4 in the action and M^2 for the effective Planck mass is easy to confuse; a short table of EFT coefficients and their physical meanings would improve readability.
[Sec. 3.3, Eqs. (62)-(68)] The definitions of the new potentials and of β_BD and β_Scr in Eqs. (66)-(68) are not given in the text; a reader must consult Ref. 12, which is acceptable for a review but could be stated more explicitly.
[Sec. 4] The symbol γ is reused for the gravitational slip in Sec. 2.2.2, the PPN parameter in Sec. 3.2, and one of the PPNC functions in Sec. 4; although the text notes the analogy, a notation table or an explicit reminder of the different meanings would help.
[References] Reference entries are inconsistent: some are arXiv preprints without journal information (e.g., Refs. 110, 111, 119, 166), and several are labeled "ArXiv e-prints" even for works that have appeared in journals; the list should be updated.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the review is a descriptive map of existing parametrization frameworks, with its main technical scope limitation explicitly disclosed and all prior results attributed.

full rationale

This is a review article; its central claim is that a set of parametrization frameworks exists and can be connected. That claim is supported by the structure of the paper itself and by references to independent literature (PPN, EFT, ppE, and external authors such as Hu-Sawicki, Gubitosi et al., Bellini-Sawicki, Silvestri et al.), not by a derivation whose output is equivalent to its input. The author's own prior results appear in Secs. 2.1.2, 2.2.3, 2.2.5, and 2.3.2 (e.g., Eqs. (4)-(6), (21)-(22), and the screening parametrization (36)-(41)), but they are presented as reviewed results with explicit citations rather than as new predictions obtained from this paper's assumptions. The closest thing to a load-bearing assumption is the adoption of the closure relations (8)-(9) at all scales; however, the paper explicitly discloses that these relations take a simple analytic form only in the subhorizon limit, that superhorizon behavior may more naturally be described by an extra summand in the Poisson equation, and that Eq. (14) is supplied as the mapping tool. No fitted parameter is relabeled as a prediction: the nonlinear interpolation (25) is described with fitting coefficients taken from earlier computations, and the screening parametrization is explicitly presented as one possible transition function with alternatives allowed. The review therefore does not exhibit any step in which an output reduces by construction to an input, and no load-bearing self-citation chain forces the central descriptive claim.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper is a review; it introduces no new free parameters or entities. All parametrizations and assumptions are drawn from the cited literature, including the author's own prior work. The axioms listed are the background assumptions on which the reviewed frameworks rely.

assumptions (5)

standard math The cosmological background is a spatially flat FLRW metric with Newtonian gauge for scalar perturbations.
Adopted in Sec. 1 conventions; standard in cosmological perturbation theory.
domain assumption Modified gravity effects can be represented by an effective energy-momentum tensor T^mu^nu_eff satisfying nabla_mu T^mu^nu_eff = 0.
Defined in Sec. 2.1.1; central to the PPF closure relations. Assumes the modified Einstein equations can be recast as GR with an effective fluid.
domain assumption For local four-dimensional metric theories with second-order spatial derivatives, the quasi-static transfer functions depend only on k^2, leading to the five-function form of mu and gamma in Eq. (24).
Cited from Ref. 115 in Sec. 2.2.5; limits the generality of the parametrization.
domain assumption The classification of genuine self-acceleration relies on the absence of acceleration in the Einstein-Friedmann frame, following Ref. 70.
Invoked in Sec. 2.1.2, Eq. (4), to argue that self-acceleration requires running of the Planck mass or c_T.
domain assumption Horndeski theories are the reference scalar-tensor class for mapping EFT coefficients, with the GW170817 constraint c_T=1 implying G4X=G5=0.
Used in Secs. 2.2.3-2.2.4; standard in the modified gravity literature.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Parametrizations for tests of gravity." pith.science (2026). https://pith.science/paper/Z6HJAMCP

@misc{pith2026190807892,
  author       = {Pith},
  title        = {Pith review of: Parametrizations for tests of gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z6HJAMCP}},
  note         = {Machine review of arXiv:1908.07892}
}

read the original abstract

With the increasing wealth of high-quality astronomical and cosmological data and the manifold departures from General Relativity in principle conceivable, the development of generalized parametrization frameworks that unify gravitational models and cover a wide range of length scales and a variety of observational probes to enable systematic high-precision tests of gravity has been a stimulus for intensive research. A review is presented here for some of the formalisms devised for this purpose, covering the cosmological large- and small-scale structures, the astronomical static weak-field regime as well as emission and propagation effects for gravitational waves. This includes linear and nonlinear parametrized post-Friedmannian frameworks, effective field theory approaches, the parametrized post-Newtonian expansion, the parametrized post-Einsteinian formalism as well as an inspiral-merger-ringdown waveform model among others. Connections between the different formalisms are highlighted where they have been established and a brief outlook is provided for general steps towards a unified global framework for tests of gravity and dark sector models.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

177 extracted references · 19 canonical work pages

[1]

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

arXiv 2006
[2]

Clifton, P

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

arXiv 2012
[3]

Joyce, B

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

arXiv 2015
[4]

Koyama, Reports on Progress in Physics 79 (April 2016) 046902, arXiv:1504.04623

K. Koyama, Reports on Progress in Physics 79 (April 2016) 046902, arXiv:1504.04623

arXiv 2016
[5]

P. Bull, Y. Akrami, J. Adamek, T. Baker, E. Bellini, J. Belt r´ an Jim´ enez, E. Ben- tivegna, S. Camera, S. Clesse, J. H. Davis, E. Di Dio, J. Enand er, A. Heavens, L. Heisenberg, B. Hu, C. Llinares, R. Maartens, E. M¨ ortsell , S. Nadathur, J. Noller, R. Pasechnik, M. S. Pawlowski, T. S. Pereira, M. Quartin, A. R icciardone, S. Riemer- Sørensen, M. Rina...

arXiv 2016
[6]

Joyce, L

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

arXiv 2016
[7]

Ishak, ArXiv e-prints (June 2018) arXiv:1806.10122

M. Ishak, ArXiv e-prints (June 2018) arXiv:1806.10122

arXiv 2018
[8]

C. M. Will, The Astrophysical Journal 163 (February 1971) 611

1971

Show all 177 references

[9]

C. M. Will, Theory and Experiment in Gravitational Physics March 1993

1993
[10]

C. M. Will, Living Reviews in Relativity 17 (June 2014) 4, arXiv:1403.7377 [gr-qc]

2014 arXiv
[11]

Avilez-Lopez, A

A. Avilez-Lopez, A. Padilla, P. M. Saﬃn and C. Skordis, Journal of Cosmology and Astroparticle Physics 6 (June 2015) 044, arXiv:1501.01985 [gr-qc]

2015 arXiv
[12]

McManus, L

R. McManus, L. Lombriser and J. Pe˜ narrubia, Journal of Cosmology and Astropar- ticle Physics 12 (December 2017) 031, arXiv:1705.05324 [gr-qc]

2017 arXiv
[13]

Uzan, ArXiv Astrophysics e-prints (May 2006) astro-ph/0605313

J.-P. Uzan, ArXiv Astrophysics e-prints (May 2006) astro-ph/0605313

2006 arXiv
[14]

Caldwell, A

R. Caldwell, A. Cooray and A. Melchiorri, Physical Review D 76 (July 2007) 023507, astro-ph/0703375

2007 arXiv
[15]

Zhang, M

P. Zhang, M. Liguori, R. Bean and S. Dodelson, Physical Review Letters 99 (October
[16]

Amendola, M

L. Amendola, M. Kunz and D. Sapone, Journal of Cosmology and Astroparticle Physics 4 (April 2008) 013, arXiv:0704.2421

2008 arXiv
[17]

Hu and I

W. Hu and I. Sawicki, Physical Review D 76 (November 2007) 104043, arXiv:0708.1190

2007 arXiv
[18]

Tegmark, Phys

M. Tegmark, Phys. Rev. D66 (2002) 103507, arXiv:astro-ph/0101354 [astro-ph]

2002 arXiv
[19]

Baker, P

T. Baker, P. G. Ferreira and C. Skordis, Physical Review D 87 (January 2013) 024015, arXiv:1209.2117 [astro-ph.CO]

2013 arXiv
[20]

P. J. E. Peebles, The large-scale structure of the universe 1980

1980
[21]

E. V. Linder, Physical Review D 72 (August 2005) 043529, astro-ph/0507263. August 22, 2019 0:25 WSPC/INSTRUCTION FILE parametrizations 32 Lucas Lombriser

2005 arXiv
[22]

Creminelli, G

P. Creminelli, G. D’Amico, J. Nore˜ na and F. Vernizzi, Journal of Cosmology and Astroparticle Physics 2 (February 2009) 018, arXiv:0811.0827

2009 arXiv
[23]

M. Park, K. M. Zurek and S. Watson, Physical Review D 81 (June 2010) 124008, arXiv:1003.1722 [hep-th]

2010 arXiv
[24]

Gubitosi, F

G. Gubitosi, F. Piazza and F. Vernizzi, Journal of Cosmology and Astroparticle Physics 2 (February 2013) 032, arXiv:1210.0201 [hep-th]

2013 arXiv
[25]

Bloomﬁeld, ´E

J. Bloomﬁeld, ´E. ´E. Flanagan, M. Park and S. Watson, Journal of Cosmology and Astroparticle Physics 8 (August 2013) 010, arXiv:1211.7054 [astro-ph.CO]

2013 arXiv
[26]

Gleyzes, D

J. Gleyzes, D. Langlois, F. Piazza and F. Vernizzi, Journal of Cosmology and As- troparticle Physics 8 (August 2013) 025, arXiv:1304.4840 [hep-th]

2013 arXiv
[27]

Tsujikawa, Lect

S. Tsujikawa, Lect. Notes Phys. 892 (2015) 97, arXiv:1404.2684 [gr-qc]

2015 arXiv
[28]

Bellini and I

E. Bellini and I. Sawicki, JCAP 1407 (2014) 050, arXiv:1404.3713 [astro-ph.CO]

2014 arXiv
[29]

Gleyzes, D

J. Gleyzes, D. Langlois and F. Vernizzi, Int. J. Mod. Phys. D23 (2015) 1443010, arXiv:1411.3712 [hep-th]

2015 arXiv
[30]

Lagos, E

M. Lagos, E. Bellini, J. Noller, P. G. Ferreira and T. Bake r, ArXiv e-prints (November
[31]

Koyama, A

K. Koyama, A. Taruya and T. Hiramatsu, Physical Review D 79 (June 2009) 123512, arXiv:0902.0618 [astro-ph.CO]

2009 arXiv
[32]

Brax, A.-C

P. Brax, A.-C. Davis, B. Li and H. A. Winther, Physical Review D 86 (August 2012) 044015, arXiv:1203.4812 [astro-ph.CO]

2012 arXiv
[33]

Bellini, R

E. Bellini, R. Jimenez and L. Verde, Journal of Cosmology and Astroparticle Physics 5 (May 2015) 057, arXiv:1504.04341

2015 arXiv
[34]

Taruya, Physical Review D 94 (July 2016) 023504, arXiv:1606.02168

A. Taruya, Physical Review D 94 (July 2016) 023504, arXiv:1606.02168

2016 arXiv
[35]

Bose and K

B. Bose and K. Koyama, Journal of Cosmology and Astroparticle Physics 8 (August
[36]

Yamauchi, S

D. Yamauchi, S. Yokoyama and H. Tashiro, Physical Review D 96 (December 2017) 123516, arXiv:1709.03243

2017 arXiv
[37]

Frusciante and G

N. Frusciante and G. Papadomanolakis, Journal of Cosmology and Astroparticle Physics 12 (December 2017) 014, arXiv:1706.02719 [gr-qc]

2017 arXiv
[38]

B. Bose, K. Koyama, M. Lewandowski, F. Vernizzi and H. A. W inther, ArXiv e-prints (February 2018) arXiv:1802.01566

2018 arXiv
[39]

Hirano, T

S. Hirano, T. Kobayashi, H. Tashiro and S. Yokoyama, ArXiv e-prints (January 2018) arXiv:1801.07885

2018 arXiv
[40]

G.-B. Zhao, B. Li and K. Koyama, Physical Review D 83 (February 2011) 044007, arXiv:1011.1257 [astro-ph.CO]

2011 arXiv
[41]

Lombriser, Journal of Cosmology and Astroparticle Physics 11 (November 2016) 039, arXiv:1608.00522

L. Lombriser, Journal of Cosmology and Astroparticle Physics 11 (November 2016) 039, arXiv:1608.00522

2016 arXiv
[42]

Hu, X.-W

B. Hu, X.-W. Liu and R.-G. Cai, Mon. Not. Roy. Astron. Soc. 476 (2018) L65, arXiv:1712.09017 [astro-ph.CO]

2018 arXiv
[43]

V. A. A. Sanghai and T. Clifton, Classical and Quantum Gravity 34 (March 2017) 065003, arXiv:1610.08039 [gr-qc]

2017 arXiv
[44]

Milillo, D

I. Milillo, D. Bertacca, M. Bruni and A. Maselli, Physical Review D 92 (July 2015) 023519, arXiv:1502.02985 [gr-qc]

2015 arXiv
[45]

B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. A cernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari and et al., Physical Review Letters 116 (February 2016) 061102, arXiv:1602.03837 [gr-qc]

2016 arXiv
[46]

Virgo, LIGO Scientiﬁc Collaboration (B. P. Abbott et al. ), Phys. Rev. Lett. 119 (2017) 141101, arXiv:1709.09660 [gr-qc]

2017 arXiv
[47]

Yunes and F

N. Yunes and F. Pretorius, Physical Review D 80 (December 2009) 122003, arXiv:0909.3328 [gr-qc] . August 22, 2019 0:25 WSPC/INSTRUCTION FILE parametrizations Parametrizations 33

2009 arXiv
[48]

T. G. F. Li, W. Del Pozzo, S. Vitale, C. Van Den Broeck, M. Ag athos, J. Veitch, K. Grover, T. Sidery, R. Sturani and A. Vecchio, Physical Review D 85 (April 2012) 082003, arXiv:1110.0530 [gr-qc]

2012 arXiv
[49]

Mirshekari and C

S. Mirshekari and C. M. Will, Physical Review D 87 (April 2013) 084070, arXiv:1301.4680 [gr-qc]

2013 arXiv
[50]

R. N. Lang, Physical Review D 89 (April 2014) 084014, arXiv:1310.3320 [gr-qc]

2014 arXiv
[51]

B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. A cernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari and et al., Physical Review Letters 116 (June 2016) 221101, arXiv:1602.03841 [gr-qc]

2016 arXiv
[52]

Virgo, LIGO Scientiﬁc Collaboration (B. P. Abbott et al. ), Phys. Rev. X6 (2016) 041015, arXiv:1606.04856 [gr-qc]

2016 arXiv
[53]

I. D. Saltas, I. Sawicki, L. Amendola and M. Kunz, Physical Review Letters 113 (November 2014) 191101, arXiv:1406.7139

2014 arXiv
[54]

Lombriser and A

L. Lombriser and A. Taylor, Journal of Cosmology and Astroparticle Physics 3 (March 2016) 031, arXiv:1509.08458

2016 arXiv
[55]

Nishizawa, ArXiv e-prints (October 2017) arXiv:1710.04825 [gr-qc]

A. Nishizawa, ArXiv e-prints (October 2017) arXiv:1710.04825 [gr-qc]

2017 arXiv
[56]

Chevallier and D

M. Chevallier and D. Polarski, International Journal of Modern Physics D 10 (2001) 213, gr-qc/0009008

2001 arXiv
[57]

E. V. Linder, Physical Review Letters 90 (March 2003) 091301, astro-ph/0208512

2003 arXiv
[58]

Lombriser and N

L. Lombriser and N. A. Lima, Physics Letters B 765 (February 2017) 382, arXiv:1602.07670

2017 arXiv
[59]

Wetterich, Nuclear Physics B 302 (June 1988) 668, arXiv:1711.03844 [hep-th]

C. Wetterich, Nuclear Physics B 302 (June 1988) 668, arXiv:1711.03844 [hep-th]

1988 arXiv
[60]

Ratra and P

B. Ratra and P. J. E. Peebles, Physical Review D 37 (June 1988) 3406

1988
[61]

R. G. Crittenden, L. Pogosian and G.-B. Zhao, Journal of Cosmology and Astropar- ticle Physics 12 (December 2009) 025, astro-ph/0510293

2009 arXiv
[62]

P. Brax, C. van de Bruck, A.-C. Davis and D. J. Shaw, Physical Review D 78 (Novem- ber 2008) 104021, arXiv:0806.3415

2008 arXiv
[63]

Lombriser, K

L. Lombriser, K. Koyama and B. Li, Journal of Cosmology and Astroparticle Physics 3 (March 2014) 021, arXiv:1312.1292

2014 arXiv
[64]

J. J. Ceron-Hurtado, J.-h. He and B. Li, Phys. Rev. D94 (2016) 064052, arXiv:1609.00532 [astro-ph.CO]

2016 arXiv
[65]

R. A. Battye, B. Bolliet and F. Pace, ArXiv e-prints (December 2017) arXiv:1712.05976

2017 arXiv
[66]

Armend´ ariz-Pic´ on, T

C. Armend´ ariz-Pic´ on, T. Damour and V. Mukhanov, Physics Letters B 458 (July
[67]

Deﬀayet, O

C. Deﬀayet, O. Pujol` as, I. Sawicki and A. Vikman, Journal of Cosmology and As- troparticle Physics 10 (October 2010) 026, arXiv:1008.0048 [hep-th]

2010 arXiv
[68]

Nicolis, R

A. Nicolis, R. Rattazzi and E. Trincherini, Physical Review D 79 (March 2009) 064036, arXiv:0811.2197 [hep-th]

2009 arXiv
[69]

E. V. Linder, G. Seng¨ or and S. Watson, Journal of Cosmology and Astroparticle Physics 5 (May 2016) 053, arXiv:1512.06180

2016 arXiv
[70]

J. Wang, L. Hui and J. Khoury, Physical Review Letters 109 (December 2012) 241301, arXiv:1208.4612 [astro-ph.CO]

2012 arXiv
[71]

Gleyzes, D

J. Gleyzes, D. Langlois, M. Mancarella and F. Vernizzi, Journal of Cosmology and Astroparticle Physics 8 (August 2015) 054, arXiv:1504.05481

2015 arXiv
[72]

G. W. Horndeski, International Journal of Theoretical Physics 10 (September 1974) 363

1974
[73]

Lombriser and A

L. Lombriser and A. Taylor, Physical Review Letters 114 (January 2015) 031101, arXiv:1405.2896

2015 arXiv
[74]

B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackl ey, C. Adams, T. Adams, August 22, 2019 0:25 WSPC/INSTRUCTION FILE parametrizations 34 Lucas Lombriser P. Addesso, R. X. Adhikari, V. B. Adya and et al., Physical Review Letters 119 (October 2017) 161101, arXiv:1710.0...

2019 arXiv
[75]

B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackl ey, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, V. B. Adya and et al., Astrophysical Journal Letters 848 (October 2017) L13, arXiv:1710.05834 [astro-ph.HE]

2017 arXiv
[76]

Nishizawa and T

A. Nishizawa and T. Nakamura, Physical Review D 90 (August 2014) 044048, arXiv:1406.5544 [gr-qc]

2014 arXiv
[77]

Ishak, A

M. Ishak, A. Upadhye and D. N. Spergel, Physical Review D 74 (August 2006) 043513, astro-ph/0507184

2006 arXiv
[78]

M. J. Mortonson, W. Hu and D. Huterer, Physical Review D 79 (January 2009) 023004, arXiv:0810.1744

2009 arXiv
[79]

E. J. Ruiz and D. Huterer, Physical Review D 91 (March 2015) 063009, arXiv:1410.5832

2015 arXiv
[80]

Lombriser, Physical Review D 83 (March 2011) 063519, arXiv:1101.0594

L. Lombriser, Physical Review D 83 (March 2011) 063519, arXiv:1101.0594

2011 arXiv
[81]

Lombriser, J

L. Lombriser, J. Yoo and K. Koyama, Physical Review D 87 (May 2013) 104019, arXiv:1301.3132 [astro-ph.CO]

2013 arXiv
[82]

Lombriser and A

L. Lombriser and A. Taylor, Journal of Cosmology and Astroparticle Physics 11 (November 2015) 040, arXiv:1505.05915

2015 arXiv
[83]

G.-B. Zhao, L. Pogosian, A. Silvestri and J. Zylberberg, Physical Review D 79 (April
[84]

S. F. Daniel, E. V. Linder, T. L. Smith, R. R. Caldwell, A. C ooray, A. Leauthaud and L. Lombriser, Physical Review D 81 (June 2010) 123508, arXiv:1002.1962

2010 arXiv
[85]

J. N. Dossett, M. Ishak and J. Moldenhauer, Physical Review D 84 (December 2011) 123001, arXiv:1109.4583

2011 arXiv
[86]

Bonvin and P

C. Bonvin and P. Fleury, Journal of Cosmology and Astroparticle Physics 5 (May
[87]

Bertschinger, Astrophysical Journal 648 (September 2006) 797, astro-ph/0604485

E. Bertschinger, Astrophysical Journal 648 (September 2006) 797, astro-ph/0604485

2006 arXiv
[88]

R. A. Battye and J. A. Pearson, Journal of Cosmology and Astroparticle Physics 7 (July 2012) 019, arXiv:1203.0398 [hep-th]

2012 arXiv
[89]

B. Hu, M. Raveri, N. Frusciante and A. Silvestri, Physical Review D 89 (May 2014) 103530, arXiv:1312.5742

2014 arXiv
[90]

Zumalac´ arregui, E

M. Zumalac´ arregui, E. Bellini, I. Sawicki, J. Lesgourg ues and P. G. Ferreira, Journal of Cosmology and Astroparticle Physics 8 (August 2017) 019, arXiv:1605.06102

2017 arXiv
[91]

Bloomﬁeld, Journal of Cosmology and Astroparticle Physics 12 (December 2013) 044, arXiv:1304.6712 [astro-ph.CO]

J. Bloomﬁeld, Journal of Cosmology and Astroparticle Physics 12 (December 2013) 044, arXiv:1304.6712 [astro-ph.CO]

2013 arXiv
[92]

Hoˇ rava,Physical Review D 79 (April 2009) 084008, arXiv:0901.3775 [hep-th]

P. Hoˇ rava,Physical Review D 79 (April 2009) 084008, arXiv:0901.3775 [hep-th]

2009 arXiv
[93]

G. D. Moore and A. E. Nelson, Journal of High Energy Physics 9 (September 2001) 023, hep-ph/0106220

2001 arXiv
[94]

C. M. Caves, Annals of Physics 125 (March 1980) 35

1980
[95]

Beltr´ an Jim´ enez, F

J. Beltr´ an Jim´ enez, F. Piazza and H. Velten, Physical Review Letters 116 (February
[96]

R. A. Battye, F. Pace and D. Trinh, ArXiv e-prints (February 2018) arXiv:1802.09447

2018 arXiv
[97]

P. Brax, C. Burrage and A.-C. Davis, Journal of Cosmology and Astroparticle Physics 3 (March 2016) 004, arXiv:1510.03701 [gr-qc]

2016 arXiv
[98]

Barreira, B

A. Barreira, B. Li, C. M. Baugh and S. Pascoli, Journal of Cosmology and Astropar- ticle Physics 8 (August 2014) 059, arXiv:1406.0485

2014 arXiv
[99]

Lombriser, W

L. Lombriser, W. Hu, W. Fang and U. Seljak, Physical Review D 80 (September
[100]

Kimura, T

R. Kimura, T. Kobayashi and K. Yamamoto, Physical Review D 85 (June 2012) 123503, arXiv:1110.3598 [astro-ph.CO]

2012 arXiv
[101]

061101, arXiv:1507.05047 [gr-qc]

arXiv
[102]

McManus, L

R. McManus, L. Lombriser and J. Pe˜ narrubia, Journal of Cosmology and Astropar- ticle Physics 11 (November 2016) 006, arXiv:1606.03282 [gr-qc]

2016 arXiv
[103]

Cornish, D

N. Cornish, D. Blas and G. Nardini, Physical Review Letters 119 (October 2017) 161102, arXiv:1707.06101 [gr-qc]

2017 arXiv
[104]

D. Blas, M. M. Ivanov, I. Sawicki and S. Sibiryakov, Soviet Journal of Experimental and Theoretical Physics Letters 103 (May 2016) 624, arXiv:1602.04188 [gr-qc]

2016 arXiv
[105]

Bettoni, J

D. Bettoni, J. M. Ezquiaga, K. Hinterbichler and M. Zuma lac´ arregui,Physical Review D 95 (April 2017) 084029, arXiv:1608.01982 [gr-qc]

2017 arXiv
[106]

August 22, 2019 0:25 WSPC/INSTRUCTION FILE parametrizations Parametrizations 35

063536, arXiv:0905.1112 [astro-ph.CO] . August 22, 2019 0:25 WSPC/INSTRUCTION FILE parametrizations Parametrizations 35

2019 arXiv
[107]

Amendola, G

L. Amendola, G. Ballesteros and V. Pettorino, Physical Review D 90 (August 2014) 043009, arXiv:1405.7004

2014 arXiv
[108]

Kimura and K

R. Kimura and K. Yamamoto, Journal of Cosmology and Astroparticle Physics 7 (July 2012) 050, arXiv:1112.4284 [astro-ph.CO]

2012 arXiv
[109]

D. E. Holz and S. A. Hughes, Astrophysical Journal 629 (August 2005) 15, astro-ph/0504616

2005 arXiv
[110]

Belgacem, Y

E. Belgacem, Y. Dirian, S. Foﬀa and M. Maggiore, ArXiv e-prints (December 2017) arXiv:1712.08108

2017 arXiv
[111]

Amendola, I

L. Amendola, I. Sawicki, M. Kunz and I. D. Saltas, ArXiv e-prints (December 2017) arXiv:1712.08623

2017 arXiv
[112]

B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ack ley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, V. B. Adya and et al., Nature 551 (November 2017) 85, arXiv:1710.05835

2017 arXiv
[113]

Raveri, C

M. Raveri, C. Baccigalupi, A. Silvestri and S.-Y. Zhou, Physical Review D 91 (March
[114]

Tamanini, C

N. Tamanini, C. Caprini, E. Barausse, A. Sesana, A. Klei n and A. Petiteau, Journal of Cosmology and Astroparticle Physics 4 (April 2016) 002, arXiv:1601.07112

2016 arXiv
[115]

Silvestri, L

A. Silvestri, L. Pogosian and R. V. Buniy, Physical Review D 87 (May 2013) 104015, arXiv:1302.1193

2013 arXiv
[116]

B. F. Schutz, Nature 323 (September 1986) 310

1986
[117]

Simpson, C

F. Simpson, C. Heymans, D. Parkinson, C. Blake, M. Kilbi nger, J. Benjamin, T. Er- ben, H. Hildebrandt, H. Hoekstra, T. D. Kitching, Y. Mellier , L. Miller, L. Van Waerbeke, J. Coupon, L. Fu, J. Harnois-D´ eraps, M. J. Hudson, K. Kuijken, B. Rowe, T. Schrabback, E. Semboloni, ...

2013 arXiv
[118]

N. A. Lima, V. Smer-Barreto and L. Lombriser, Physical Review D 94 (October
[119]

Kennedy, L

J. Kennedy, L. Lombriser and A. Taylor (2018) arXiv:1804.04582 [astro-ph.CO]

2018 arXiv
[120]

Laureijs, J

R. Laureijs, J. Amiaux, S. Arduini, J. . Augu` eres, J. Br inchmann, R. Cole, M. Crop- per, C. Dabin, L. Duvet, A. Ealet and et al., ArXiv e-prints (October 2011) arXiv:1110.3193 [astro-ph.CO]

2011 arXiv
[121]

C. L. MacLeod and C. J. Hogan, Physical Review D 77 (February 2008) 043512, arXiv:0712.0618

2008 arXiv
[122]

Dvali, G

G. Dvali, G. Gabadadze and M. Porrati, Physics Letters B 485 (July 2000) 208, hep-th/0005016. August 22, 2019 0:25 WSPC/INSTRUCTION FILE parametrizations 36 Lucas Lombriser

2000 arXiv
[123]

H. A. Buchdahl, Monthly Notices of the Royal Astronomical Society 150 (1970) 1

1970
[124]

Bertschinger and P

E. Bertschinger and P. Zukin, Physical Review D 78 (July 2008) 024015, arXiv:0801.2431

2008 arXiv
[125]

Lombriser, Annalen der Physik 526 (August 2014) 259, arXiv:1403.4268

L. Lombriser, Annalen der Physik 526 (August 2014) 259, arXiv:1403.4268

2014 arXiv
[126]

Schmidt, M

F. Schmidt, M. Lima, H. Oyaizu and W. Hu, Physical Review D 79 (April 2009) 083518, arXiv:0812.0545

2009 arXiv
[127]

083507, arXiv:1603.05239

arXiv
[128]

Borisov, B

A. Borisov, B. Jain and P. Zhang, Physical Review D 85 (March 2012) 063518, arXiv:1102.4839

2012 arXiv
[129]

M. Kopp, S. A. Appleby, I. Achitouv and J. Weller, Physical Review D 88 (October
[130]

Ivezi´ c, S

ˇZ. Ivezi´ c, S. M. Kahn, J. A. Tyson, B. Abel, E. Acosta, R. Alls man, D. Alonso, Y. AlSayyad, S. F. Anderson, J. Andrew and et al., ArXiv e-prints (May 2008) arXiv:0805.2366

2008 arXiv
[131]

Li and T

B. Li and T. Y. Lam, Monthly Notices of the Royal Astronomical Society 425 (September 2012) 730, arXiv:1205.0058 [astro-ph.CO]

2012 arXiv
[132]

Lombriser, B

L. Lombriser, B. Li, K. Koyama and G.-B. Zhao, Physical Review D 87 (June 2013) 123511, arXiv:1304.6395 [astro-ph.CO]

2013 arXiv
[133]

Brax and P

P. Brax and P. Valageas, Physical Review D 88 (July 2013) 023527, arXiv:1305.5647

2013 arXiv
[134]

Lombriser, F

L. Lombriser, F. Schmidt, T. Baldauf, R. Mandelbaum, U. Seljak and R. E. Smith, Physical Review D 85 (May 2012) 102001, arXiv:1111.2020 [astro-ph.CO]

2012 arXiv
[135]

Gronke, D

M. Gronke, D. F. Mota and H. A. Winther, Astronomy & Astrophysics 583 (Novem- ber 2015) A123, arXiv:1505.07129

2015 arXiv
[136]

Pace, J.-C

F. Pace, J.-C. Waizmann and M. Bartelmann, Monthly Notices of the Royal Astro- nomical Society 406 (August 2010) 1865, arXiv:1005.0233

2010 arXiv
[137]

Schmidt, W

F. Schmidt, W. Hu and M. Lima, Physical Review D 81 (March 2010) 063005, arXiv:0911.5178 [astro-ph.CO]

2010 arXiv
[138]

Lombriser, A

L. Lombriser, A. Slosar, U. Seljak and W. Hu, Physical Review D 85 (June 2012) 124038, arXiv:1003.3009

2012 arXiv
[139]

Barreira, B

A. Barreira, B. Li, W. A. Hellwing, L. Lombriser, C. M. Ba ugh and S. Pascoli, Journal of Cosmology and Astroparticle Physics 4 (April 2014) 029, arXiv:1401.1497

2014 arXiv
[140]

Li and G

B. Li and G. Efstathiou, Monthly Notices of the Royal Astronomical Society 421 (April 2012) 1431, arXiv:1110.6440 [astro-ph.CO]

2012 arXiv
[141]

Hagstotz, M

S. Hagstotz, M. Costanzi, M. Baldi and J. Weller, ArXiv e-prints (June 2018) arXiv:1806.07400

2018 arXiv
[142]

Clampitt, Y.-C

J. Clampitt, Y.-C. Cai and B. Li, Monthly Notices of the Royal Astronomical Society 431 (May 2013) 749, arXiv:1212.2216 [astro-ph.CO]

2013 arXiv
[143]

Lombriser, K

L. Lombriser, K. Koyama, G.-B. Zhao and B. Li, Physical Review D 85 (June 2012) 124054, arXiv:1203.5125 [astro-ph.CO]

2012 arXiv
[144]

J. A. Peacock and R. E. Smith, Monthly Notices of the Royal Astronomical Society 318 (November 2000) 1144, astro-ph/0005010

2000 arXiv
[145]

Seljak, Monthly Notices of the Royal Astronomical Society 318 (October 2000) 203, astro-ph/0001493

U. Seljak, Monthly Notices of the Royal Astronomical Society 318 (October 2000) 203, astro-ph/0001493

2000 arXiv
[146]

M. A. Mitchell, J.-h. He, C. Arnold and B. Li, ArXiv e-prints (February 2018) arXiv:1802.02165

2018 arXiv
[147]

Achitouv, M

I. Achitouv, M. Baldi, E. Puchwein and J. Weller, Physical Review D 93 (May 2016) 103522, arXiv:1511.01494

2016 arXiv
[148]

Li and W

Y. Li and W. Hu, Physical Review D 84 (October 2011) 084033, arXiv:1107.5120

2011 arXiv
[149]

A. J. Mead, C. Heymans, L. Lombriser, J. A. Peacock, O. I. Steele and H. A. Winther, Monthly Notices of the Royal Astronomical Society 459 (June 2016) 1468, August 22, 2019 0:25 WSPC/INSTRUCTION FILE parametrizations Parametrizations 37 arXiv:1602.02154

2016 arXiv
[150]

Cataneo, D

M. Cataneo, D. Rapetti, L. Lombriser and B. Li, JCAP 1612 (2016) 024, arXiv:1607.08788 [astro-ph.CO]

2016 arXiv
[151]

Terukina, L

A. Terukina, L. Lombriser, K. Yamamoto, D. Bacon, K. Koy ama and R. C. Nichol, Journal of Cosmology and Astroparticle Physics 4 (April 2014) 013, arXiv:1312.5083

2014 arXiv
[152]

Sakstein, H

J. Sakstein, H. Wilcox, D. Bacon, K. Koyama and R. C. Nich ol, Journal of Cosmology and Astroparticle Physics 7 (July 2016) 019, arXiv:1603.06368

2016 arXiv
[153]

T. Y. Lam, J. Clampitt, Y.-C. Cai and B. Li, Monthly Notices of the Royal Astro- nomical Society 450 (July 2015) 3319, arXiv:1408.5338

2015 arXiv
[154]

H. A. Winther and P. G. Ferreira, Physical Review D 91 (June 2015) 123507, arXiv:1403.6492

2015 arXiv
[155]

A. J. Mead, J. A. Peacock, L. Lombriser and B. Li, Monthly Notices of the Royal Astronomical Society 452 (October 2015) 4203, arXiv:1412.5195

2015 arXiv
[156]

Cooray and R

A. Cooray and R. Sheth, Physics Reports 372 (December 2002) 1, astro-ph/0206508

2002 arXiv
[157]

Zhang, W

X. Zhang, W. Zhao, H. Huang and Y. Cai, Physical Review D 93 (June 2016) 124003, arXiv:1603.09450 [gr-qc]

2016 arXiv
[158]

Gabadadze, K

G. Gabadadze, K. Hinterbichler and D. Pirtskhalava, Physical Review D 85 (June
[159]

Padilla and P

A. Padilla and P. M. Saﬃn, Journal of High Energy Physics 7 (July 2012) 122, arXiv:1204.1352 [hep-th]

2012 arXiv
[160]

Fedeli, Journal of Cosmology and Astroparticle Physics 4 (April 2014) 028, arXiv:1401.2997

C. Fedeli, Journal of Cosmology and Astroparticle Physics 4 (April 2014) 028, arXiv:1401.2997

2014 arXiv
[161]

C. M. Will and A. G. Wiseman, Physical Review D 54 (October 1996) 4813, gr-qc/9608012

1996 arXiv
[162]

M. E. Pati and C. M. Will, Physical Review D 65 (May 2002) 104008, gr-qc/0201001

2002 arXiv
[163]

Lombriser, F

L. Lombriser, F. Simpson and A. Mead, Physical Review Letters 114 (June 2015) 251101, arXiv:1501.04961

2015 arXiv
[164]

R. Kase, L. ´A. Gergely and S. Tsujikawa, Physical Review D 90 (December 2014) 124019, arXiv:1406.2402 [hep-th]

2014 arXiv
[165]

Brax, A.-C

P. Brax, A.-C. Davis, B. Li, H. A. Winther and G.-B. Zhao, Journal of Cosmology and Astroparticle Physics 10 (October 2012) 002, arXiv:1206.3568

2012 arXiv
[166]

Bertotti, L

B. Bertotti, L. Iess and P. Tortora, Nature 425 (September 2003) 374

2003
[171]

Epstein and R

R. Epstein and R. V. Wagoner, The Astrophysical Journal 197 (May 1975) 717

1975
[174]

D. B. Thomas, M. Bruni and D. Wands, Journal of Cosmology and Astroparticle Physics 9 (September 2015) 021, arXiv:1403.4947

2015 arXiv
[177]

Kennedy, L

J. Kennedy, L. Lombriser and A. Taylor, Physical Review D 96 (October 2017) 084051, arXiv:1705.09290 [gr-qc]

2017 arXiv
[2007]

141302, arXiv:0704.1932

1932 arXiv
[2009]

083513, arXiv:0809.3791

arXiv
[2012]

125007, arXiv:1202.6364 [hep-th]

arXiv
[2013]

084015, arXiv:1306.3233 [astro-ph.CO]

arXiv
[2015]

061501, arXiv:1405.7974

arXiv
[2016]

032, arXiv:1606.02520

arXiv
[2017]

arXiv:1711.09893 [gr-qc]

arXiv
[2018]

061, arXiv:1803.02771

arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

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

arXiv 2006

[2] [2]

Clifton, P

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

arXiv 2012

[3] [3]

Joyce, B

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

arXiv 2015

[4] [4]

Koyama, Reports on Progress in Physics 79 (April 2016) 046902, arXiv:1504.04623

K. Koyama, Reports on Progress in Physics 79 (April 2016) 046902, arXiv:1504.04623

arXiv 2016

[5] [5]

P. Bull, Y. Akrami, J. Adamek, T. Baker, E. Bellini, J. Belt r´ an Jim´ enez, E. Ben- tivegna, S. Camera, S. Clesse, J. H. Davis, E. Di Dio, J. Enand er, A. Heavens, L. Heisenberg, B. Hu, C. Llinares, R. Maartens, E. M¨ ortsell , S. Nadathur, J. Noller, R. Pasechnik, M. S. Pawlowski, T. S. Pereira, M. Quartin, A. R icciardone, S. Riemer- Sørensen, M. Rina...

arXiv 2016

[6] [6]

Joyce, L

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

arXiv 2016

[7] [7]

Ishak, ArXiv e-prints (June 2018) arXiv:1806.10122

M. Ishak, ArXiv e-prints (June 2018) arXiv:1806.10122

arXiv 2018

[8] [8]

C. M. Will, The Astrophysical Journal 163 (February 1971) 611

1971