pith. sign in

arxiv: 2606.18491 · v1 · pith:KDDZ2S6Xnew · submitted 2026-06-16 · 🌌 astro-ph.CO · astro-ph.IM· hep-ph· stat.ME

The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories

Raul Jimenez , Carlos Pe\~na Garay , Fergus Simpson , Licia Verde This is my paper

Pith reviewed 2026-06-26 22:46 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IMhep-phstat.ME
keywords Coherence PrincipleBayesian model selectiontheoretical grammarcosmologyparticle physicsmodel priorssymmetriesconservation laws
0
0 comments X

The pith

The Coherence Principle assigns Bayesian model priors according to compatibility with a theory's validated grammar of symmetries and conservation laws.

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

The paper proposes the Coherence Principle as a method for setting prior probabilities on competing models in Bayesian inference. It does this by assigning lower weights to models that make unmotivated violations of the established structural rules of physics, such as symmetries, conservation laws, locality, and Lorentz invariance. This approach makes the influence of theoretical knowledge explicit and testable rather than hidden in arbitrary prior choices. A sympathetic reader would care because it addresses the common problem where model selection depends heavily on unacknowledged prior assumptions, allowing data to play a clearer role when they are strong enough.

Core claim

The Coherence Principle is a reproducible prescription for assigning model priors according to compatibility with the validated structure of an existing theory. This structure, or grammar, includes symmetries, conservation laws, locality, Lorentz invariance, and universality patterns. Unmotivated violations of these rules incur a coherence cost, converted into a prior weight through a maximum-entropy exponential form controlled by one calibratable parameter α. The resulting prior is distinct from both the Bayesian Occam factor and naturalness: it penalizes not parameter volume or fine tuning, but departures from validated theoretical grammar.

What carries the argument

The Coherence Principle, which converts unmotivated violations of a theory's grammar into a coherence cost that determines prior weights via a maximum-entropy exponential form controlled by one calibratable parameter α.

If this is right

  • It favors the historically successful choices in reconstructed cases such as general relativity, Pauli's neutrino, parity violation, and special relativity.
  • In cosmology and particle physics it can be applied to neutrino mass mechanisms, dark energy and modified gravity, inflation, and beyond-Standard-Model sectors.
  • The principle leaves empirical likelihoods free to dominate when data are sufficiently constraining.
  • It turns trust in validated structural rules into a transparent, testable, and overrulable component of Bayesian inference.

Where Pith is reading between the lines

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

  • The same approach could be tested by checking whether the assigned priors correctly anticipate which models survive when new data become available in ongoing cosmological surveys.
  • If the grammar can be specified consistently, the principle might be extended to rank models in other domains that possess clear structural rules, such as certain areas of chemistry or materials science.
  • One could examine whether different choices of the single parameter α lead to stable rankings across multiple independent model-selection problems.

Load-bearing premise

The grammar of a theory can be defined objectively in the correct domain and historical time, and unmotivated violations can be identified consistently enough to assign a reproducible coherence cost.

What would settle it

A case where, with the grammar defined in the correct domain and time, the principle assigns a low prior to the model that later evidence confirms as correct, or a high prior to one that is ruled out.

read the original abstract

Bayesian model selection in cosmology and particle physics is often performed where posterior odds inherit a strong, often unacknowledged dependence on the prior assigned to competing models. Standard responses -- reference priors, hierarchical priors, or appeals to naturalness -- ignore relevant theoretical knowledge or rely on criteria hard to define operationally. We propose the \emph{Coherence Principle}: a reproducible prescription for assigning model priors according to compatibility with the validated structure of an existing theory. This structure, or \emph{grammar}, includes symmetries, conservation laws, locality, Lorentz invariance, and universality patterns. Unmotivated violations of these rules incur a coherence cost, converted into a prior weight through a maximum-entropy exponential form controlled by one calibratable parameter $\alpha$. The resulting prior is distinct from both the Bayesian Occam factor and naturalness: it penalizes not parameter volume or fine tuning, but departures from validated theoretical grammar. We illustrate the principle with examples from cosmology and fundamental physics: neutrino mass mechanisms, dark energy and modified gravity, inflation, beyond-Standard-Model sectors, and hierarchical astrophysical inference. We test it also on four historical cases -- general relativity, Pauli's neutrino, parity violation, and special relativity -- where evidential and theoretical contexts can be reconstructed. These examples show that it favors the historically successful choice when the proper grammar is defined in the correct domain and time. The Coherence Principle makes explicit a common but usually tacit part of physical reasoning: trust in validated structural rules. It turns this judgment into a transparent, testable, and overrulable component of Bayesian inference, leaving empirical likelihoods free to dominate when data are sufficiently constraining.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 0 minor

Summary. The manuscript proposes the Coherence Principle as a method for assigning priors in Bayesian model selection. Models incur a coherence cost, implemented via a maximum-entropy exponential prior controlled by a single parameter α, for unmotivated violations of the grammar of an established theory (symmetries, conservation laws, locality, Lorentz invariance, universality patterns). The principle is illustrated with examples from neutrino mass mechanisms, dark energy/modified gravity, inflation, BSM sectors, and hierarchical astrophysical inference, and tested on four historical cases (general relativity, Pauli's neutrino, parity violation, special relativity) where it favors the successful theory when the proper grammar is defined in the correct domain and time.

Significance. If the grammar and its violations can be defined objectively and reproducibly, the principle would convert tacit theoretical judgment into an explicit, testable, and overrulable component of Bayesian inference, distinct from both the Occam factor and naturalness arguments. This could be valuable in cosmology and particle physics where posterior odds are prior-sensitive and data are not yet decisive. The historical tests provide a form of empirical check, but the overall utility depends on whether the approach avoids the subjectivity it aims to replace.

major comments (2)
  1. [Abstract] Abstract: the claim that the principle 'favors the historically successful choice when the proper grammar is defined in the correct domain and time' makes success conditional on a retrospective choice of grammar. Without independent, pre-specified operational criteria for identifying the 'proper' grammar and 'unmotivated' violations, the prior assignment risks the same hindsight bias the method seeks to avoid, rendering the reproducibility claim unsupported by the presented evidence.
  2. [Abstract] Abstract: the prior depends on a single calibratable parameter α whose value must be chosen or fitted. The manuscript provides no procedure for calibrating α that is independent of the same historical cases used to validate the principle, which introduces a potential circularity between the prior construction and the validation data.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We respond point-by-point to the two major comments and outline revisions that address the concerns while preserving the manuscript's core claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the principle 'favors the historically successful choice when the proper grammar is defined in the correct domain and time' makes success conditional on a retrospective choice of grammar. Without independent, pre-specified operational criteria for identifying the 'proper' grammar and 'unmotivated' violations, the prior assignment risks the same hindsight bias the method seeks to avoid, rendering the reproducibility claim unsupported by the presented evidence.

    Authors: We agree that the abstract phrasing risks implying hindsight bias and that the reproducibility claim requires stronger support. The grammar is intended to be the structure of an established theory as accepted at the relevant time on independent grounds, and 'unmotivated' refers to violations introduced without separate theoretical justification. To address this directly, we will revise the abstract to qualify the historical-test statement and add an explicit subsection providing operational criteria for grammar specification and for distinguishing motivated from unmotivated violations (e.g., presence of independent symmetry or unification arguments versus purely data-driven extensions). The historical cases will be reframed strictly as consistency checks. These changes will be made in the revised manuscript. revision: partial

  2. Referee: [Abstract] Abstract: the prior depends on a single calibratable parameter α whose value must be chosen or fitted. The manuscript provides no procedure for calibrating α that is independent of the same historical cases used to validate the principle, which introduces a potential circularity between the prior construction and the validation data.

    Authors: The manuscript does not currently supply an independent calibration procedure for α, so the potential circularity is a valid observation. In revision we will add a concrete calibration protocol that uses a separate collection of contemporary, well-established model-comparison problems (distinct from the four historical cases) in which the grammar is fixed by current theory and data sensitivity can be assessed. We will also note the option of marginalizing over α as a hyperparameter. The historical examples will remain validation illustrations only and will not be used for α calibration. The abstract and relevant sections will be updated accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the Coherence Principle proposal

full rationale

The paper introduces the Coherence Principle as an explicit prior construction using a maximum-entropy exponential form on coherence costs derived from an independently stated grammar of validated theoretical structures. No equations or derivations reduce by construction to their own inputs, no parameter fitting is presented as a prediction, and no self-citation chain is invoked to justify uniqueness or load-bearing premises. Historical illustrations are conditional on grammar definition but do not constitute fitted inputs renamed as predictions or self-definitional loops. The method remains self-contained against external benchmarks with the central claim independent of the examples.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on one free parameter alpha and on the domain assumption that a theory possesses an identifiable grammar of structural rules whose violations can be quantified independently of the data being modeled.

free parameters (1)
  • α
    Single calibratable parameter that sets the strength of the exponential penalty converting coherence cost into prior weight.
axioms (1)
  • domain assumption The validated structure of an existing theory includes symmetries, conservation laws, locality, Lorentz invariance, and universality patterns that can be used to define a grammar.
    This grammar is the reference against which new models are scored for coherence.

pith-pipeline@v0.9.1-grok · 5849 in / 1500 out tokens · 42736 ms · 2026-06-26T22:46:24.369348+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

92 extracted references · 2 canonical work pages

  1. [1]

    Trotta,Bayes in the sky: Bayesian inference and model selection in cosmology, Contemporary Physics49(2008) 71 [0803.4089]

    R. Trotta,Bayes in the sky: Bayesian inference and model selection in cosmology, Contemporary Physics49(2008) 71 [0803.4089]

    Pith/arXiv arXiv 2008

  2. [2]

    Vardanyan, R

    M. Vardanyan, R. Trotta and J. Silk,Applications of Bayesian model averaging to the curvature and size of the Universe,Monthly Notices of the Royal Astronomical Society413 (2011) L91 [1101.5476]

    Pith/arXiv arXiv 2011

  3. [3]

    Efstathiou,Limitations of Bayesian evidence applied to cosmology,Monthly Notices of the Royal Astronomical Society388(2008) 1314 [0802.3185]

    G. Efstathiou,Limitations of Bayesian evidence applied to cosmology,Monthly Notices of the Royal Astronomical Society388(2008) 1314 [0802.3185]

    Pith/arXiv arXiv 2008

  4. [4]

    Liddle,Information criteria for astrophysical model selection,Monthly Notices of the Royal Astronomical Society: Letters377(2007) L74 [astro-ph/0701113]

    A.R. Liddle,Information criteria for astrophysical model selection,Monthly Notices of the Royal Astronomical Society: Letters377(2007) L74 [astro-ph/0701113]

    Pith/arXiv arXiv 2007

  5. [5]

    Simpson, R

    F. Simpson, R. Jimenez, C. Pe˜ na-Garay and L. Verde,Strong evidence for the normal neutrino hierarchy,JCAP06(2017) 029 [1703.03425]

    Pith/arXiv arXiv 2017

  6. [6]

    Strong Evidence for the Normal Neutrino Hierarchy

    T. Schwetz, K. Freese, M. Gerbino, E. Giusarma, S. Hannestad, M. Lattanzi et al.,Comment on “Strong Evidence for the Normal Neutrino Hierarchy”,1703.04585

    Pith/arXiv arXiv

  7. [7]

    Heavens and E

    A.F. Heavens and E. Sellentin,Objective Bayesian analysis of neutrino masses and hierarchy, JCAP04(2018) 047 [1802.09450]

    Pith/arXiv arXiv 2018

  8. [8]

    Jimenez, C

    R. Jimenez, C. Pe˜ na-Garay, K. Short, F. Simpson and L. Verde,Neutrino masses and mass hierarchy: evidence for the normal hierarchy,JCAP09(2022) 006 [2203.14247]

    arXiv 2022

  9. [9]

    Kass and A.E

    R.E. Kass and A.E. Raftery,Bayes factors,Journal of the American Statistical Association90 (1995) 773

    1995

  10. [10]

    Jeffreys,An invariant form for the prior probability in estimation problems,Proceedings of the Royal Society of London A186(1946) 453

    H. Jeffreys,An invariant form for the prior probability in estimation problems,Proceedings of the Royal Society of London A186(1946) 453

    1946

  11. [11]

    Bernardo,Reference posterior distributions for Bayesian inference,Journal of the Royal Statistical Society: Series B41(1979) 113

    J.M. Bernardo,Reference posterior distributions for Bayesian inference,Journal of the Royal Statistical Society: Series B41(1979) 113. – 21 –

    1979

  12. [12]

    Berger, J.M

    J.O. Berger, J.M. Bernardo and D. Sun,The formal definition of reference priors,Annals of Statistics37(2009) 905

    2009

  13. [13]

    Jaynes,Probability Theory: The Logic of Science, Cambridge University Press, Cambridge (2003)

    E.T. Jaynes,Probability Theory: The Logic of Science, Cambridge University Press, Cambridge (2003)

    2003

  14. [14]

    Caticha,Lectures on probability, entropy, and statistical physics,0808.0012

    A. Caticha,Lectures on probability, entropy, and statistical physics,0808.0012

    Pith/arXiv arXiv

  15. [15]

    Gelman,Prior distributions for variance parameters in hierarchical models,Bayesian Analysis1(2006) 515

    A. Gelman,Prior distributions for variance parameters in hierarchical models,Bayesian Analysis1(2006) 515

    2006

  16. [16]

    Gelman, J.B

    A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari and D.B. Rubin,Bayesian Data Analysis, CRC Press, Boca Raton, 3 ed. (2013)

    2013

  17. [17]

    ’t Hooft,Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, inRecent Developments in Gauge Theories, G

    G. ’t Hooft,Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, inRecent Developments in Gauge Theories, G. ’t Hooft, C. Itzykson, A. Jaffe, H. Lehmann, P.K. Mitter, I.M. Singer et al., eds., (New York), pp. 135–157, Plenum Press, 1980, DOI

    1980

  18. [18]

    Giudice,Naturally speaking: The naturalness criterion and physics at the LHC, in Perspectives on LHC Physics, G.L

    G.F. Giudice,Naturally speaking: The naturalness criterion and physics at the LHC, in Perspectives on LHC Physics, G.L. Kane and A. Pierce, eds., pp. 155–178, World Scientific (2008), DOI [0801.2562]

    Pith/arXiv arXiv 2008

  19. [19]

    Hossenfelder,Lost in Math: How Beauty Leads Physics Astray, Basic Books, New York (2018)

    S. Hossenfelder,Lost in Math: How Beauty Leads Physics Astray, Basic Books, New York (2018)

    2018

  20. [20]

    Wells,Lectures on Higgs Boson Physics in the Standard Model and Beyond,Proceedings of Theoretical Advanced Study Institute in Elementary Particle Physics(2016) 283 [0909.4541]

    J.D. Wells,Lectures on Higgs Boson Physics in the Standard Model and Beyond,Proceedings of Theoretical Advanced Study Institute in Elementary Particle Physics(2016) 283 [0909.4541]

    Pith/arXiv arXiv 2016

  21. [21]

    Kuhn,The Structure of Scientific Revolutions, University of Chicago Press, Chicago (1962)

    T.S. Kuhn,The Structure of Scientific Revolutions, University of Chicago Press, Chicago (1962)

    1962

  22. [22]

    Lakatos,Falsification and the methodology of scientific research programmes, inCriticism and the Growth of Knowledge, I

    I. Lakatos,Falsification and the methodology of scientific research programmes, inCriticism and the Growth of Knowledge, I. Lakatos and A. Musgrave, eds., (Cambridge), pp. 91–196, Cambridge University Press (1970)

    1970

  23. [23]

    Dawid,String Theory and the Scientific Method, Cambridge University Press, Cambridge (2013), 10.1017/CBO9781139342513

    R. Dawid,String Theory and the Scientific Method, Cambridge University Press, Cambridge (2013), 10.1017/CBO9781139342513

    work page doi:10.1017/cbo9781139342513 2013

  24. [24]

    Howson and P

    C. Howson and P. Urbach,Scientific Reasoning: The Bayesian Approach, Open Court, Chicago, 3 ed. (2006)

    2006

  25. [25]

    Wilson and J.B

    K.G. Wilson and J.B. Kogut,The renormalization group and the epsilon expansion,Physics Reports12(1974) 75

    1974

  26. [26]

    Polchinski,Effective field theory and the Fermi surface,Nuclear Physics B396(1993) 667 [hep-th/9210046]

    J. Polchinski,Effective field theory and the Fermi surface,Nuclear Physics B396(1993) 667 [hep-th/9210046]

    Pith/arXiv arXiv 1993

  27. [27]

    Lovelock,The Einstein tensor and its generalizations,Journal of Mathematical Physics12 (1971) 498

    D. Lovelock,The Einstein tensor and its generalizations,Journal of Mathematical Physics12 (1971) 498

    1971

  28. [28]

    Will,The Confrontation between General Relativity and Experiment, Living Reviews in Relativity (2014), 10.12942/lrr-2014-4

    C.M. Will,The Confrontation between General Relativity and Experiment, Living Reviews in Relativity (2014), 10.12942/lrr-2014-4

    work page doi:10.12942/lrr-2014-4 2014

  29. [29]

    Baumann,TASI Lectures on Inflation,Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small(2011) 523 [0907.5424]

    D. Baumann,TASI Lectures on Inflation,Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small(2011) 523 [0907.5424]

    Pith/arXiv arXiv 2011

  30. [30]

    Ach´ ucarro et al.,Inflation: Theory and Observations,2203.08128

    A. Ach´ ucarro et al.,Inflation: Theory and Observations,2203.08128

    arXiv

  31. [31]

    Jaynes,Information theory and statistical mechanics,Physical Review106(1957) 620

    E.T. Jaynes,Information theory and statistical mechanics,Physical Review106(1957) 620

    1957

  32. [32]

    Jeffreys,Theory of Probability, Oxford University Press, Oxford, 3 ed

    H. Jeffreys,Theory of Probability, Oxford University Press, Oxford, 3 ed. (1961)

    1961

  33. [33]

    MacKay,Bayesian interpolation,Neural Computation4(1992) 415

    D.J.C. MacKay,Bayesian interpolation,Neural Computation4(1992) 415

    1992

  34. [34]

    Popper,The Logic of Scientific Discovery, Hutchinson, London (1959)

    K.R. Popper,The Logic of Scientific Discovery, Hutchinson, London (1959). – 22 –

    1959

  35. [35]

    Smolin,The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, Houghton Mifflin, Boston (2006)

    L. Smolin,The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, Houghton Mifflin, Boston (2006)

    2006

  36. [36]

    Clifton, P.G

    T. Clifton, P.G. Ferreira, A. Padilla and C. Skordis,Modified Gravity and Cosmology,Physics Reports513(2012) 1 [1106.2476]

    Pith/arXiv arXiv 2012

  37. [37]

    Minkowski,µ→eγat a rate of one out of10 9 muon decays?,Physics Letters B67(1977) 421

    P. Minkowski,µ→eγat a rate of one out of10 9 muon decays?,Physics Letters B67(1977) 421

    1977

  38. [38]

    Yanagida,Horizontal gauge symmetry and masses of neutrinos, inProceedings of the Workshop on Unified Theory and Baryon Number in the Universe, O

    T. Yanagida,Horizontal gauge symmetry and masses of neutrinos, inProceedings of the Workshop on Unified Theory and Baryon Number in the Universe, O. Sawada and A. Sugamoto, eds., (Tsukuba), pp. 95–99, KEK, 1979

    1979

  39. [39]

    Gell-Mann, P

    M. Gell-Mann, P. Ramond and R. Slansky,Complex spinors and unified theories, in Supergravity, P. van Nieuwenhuizen and D.Z. Freedman, eds., (Amsterdam), pp. 315–321, North-Holland, 1979 [1306.4669]

    Pith/arXiv arXiv 1979

  40. [40]

    Mohapatra and G

    R.N. Mohapatra and G. Senjanovi´ c,Neutrino mass and spontaneous parity nonconservation, Physical Review Letters44(1980) 912

    1980

  41. [41]

    Weinberg,Baryon- and lepton-nonconserving processes,Physical Review Letters43(1979) 1566

    S. Weinberg,Baryon- and lepton-nonconserving processes,Physical Review Letters43(1979) 1566

    1979

  42. [42]

    Forero, M

    D.V. Forero, M. T´ ortola and J.W.F. Valle,Neutrino oscillations refitted,Physical Review D90 (2014) 093006 [1405.7540]

    Pith/arXiv arXiv 2014

  43. [43]

    Gonzalez-Garcia, M

    M.C. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz,Global fit to three neutrino mixing: critical look at present precision,JHEP12(2014) 123 [1409.5439]

    Pith/arXiv arXiv 2014

  44. [44]

    Capozzi, G.L

    F. Capozzi, G.L. Fogli, E. Lisi, A. Marrone, D. Montanino and A. Palazzo,Status of three-neutrino oscillation parameters, circa 2013,Physical Review D89(2014) 093018 [1312.2878]

    Pith/arXiv arXiv 2013

  45. [45]

    Woodard,The theorem of Ostrogradsky,Scholarpedia10(2015) 32243 [1506.02210]

    R.P. Woodard,The theorem of Ostrogradsky,Scholarpedia10(2015) 32243 [1506.02210]

    Pith/arXiv arXiv 2015

  46. [46]

    Ratra and P.J.E

    B. Ratra and P.J.E. Peebles,Cosmological consequences of a rolling homogeneous scalar field, Physical Review D37(1988) 3406

    1988

  47. [47]

    Wetterich,Cosmology and the fate of dilatation symmetry,Nuclear Physics B302(1988) 668

    C. Wetterich,Cosmology and the fate of dilatation symmetry,Nuclear Physics B302(1988) 668

    1988

  48. [48]

    Caldwell, R

    R.R. Caldwell, R. Dave and P.J. Steinhardt,Cosmological imprint of an energy component with general equation of state,Physical Review Letters80(1998) 1582 [astro-ph/9708069]

    Pith/arXiv arXiv 1998

  49. [49]

    Sotiriou and V

    T.P. Sotiriou and V. Faraoni,f(R)theories of gravity,Reviews of Modern Physics82(2010) 451 [0805.1726]

    Pith/arXiv arXiv 2010

  50. [50]

    Horndeski,Second-order scalar-tensor field equations in a four-dimensional space, International Journal of Theoretical Physics10(1974) 363

    G.W. Horndeski,Second-order scalar-tensor field equations in a four-dimensional space, International Journal of Theoretical Physics10(1974) 363

    1974

  51. [51]

    Kobayashi,Horndeski theory and beyond: a review,Reports on Progress in Physics82 (2019) 086901 [1901.07183]

    T. Kobayashi,Horndeski theory and beyond: a review,Reports on Progress in Physics82 (2019) 086901 [1901.07183]

    Pith/arXiv arXiv 2019

  52. [52]

    Langlois and K

    D. Langlois and K. Noui,Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability,JCAP02(2016) 034 [1510.06930]

    Pith/arXiv arXiv 2016

  53. [53]

    Boulware and S

    D.G. Boulware and S. Deser,Can gravitation have a finite range?,Physical Review D6(1972) 3368

    1972

  54. [54]

    de Rham, G

    C. de Rham, G. Gabadadze and A.J. Tolley,Resummation of Massive Gravity,Physical Review Letters106(2011) 231101 [1011.1232]

    Pith/arXiv arXiv 2011

  55. [55]

    Jacobson and D

    T. Jacobson and D. Mattingly,Einstein-Aether waves,Physical Review D70(2004) 024003 [gr-qc/0402005]. – 23 –

    Pith/arXiv arXiv 2004

  56. [56]

    Hoˇ rava,Quantum Gravity at a Lifshitz Point,Physical Review D79(2009) 084008 [0901.3775]

    P. Hoˇ rava,Quantum Gravity at a Lifshitz Point,Physical Review D79(2009) 084008 [0901.3775]

    Pith/arXiv arXiv 2009

  57. [57]

    Adame et al.,DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations,JCAP02(2025) 021 [2404.03002]

    DESI Collaboration, A.G. Adame et al.,DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations,JCAP02(2025) 021 [2404.03002]

    Pith/arXiv arXiv 2024

  58. [58]

    Joyce, L

    A. Joyce, L. Lombriser and F. Schmidt,Dark Energy Versus Modified Gravity,Annual Review of Nuclear and Particle Science66(2016) 95 [1601.06133]

    Pith/arXiv arXiv 2016

  59. [59]

    Heisenberg,A systematic approach to generalisations of General Relativity and their cosmological implications,Physics Reports796(2019) 1 [1807.01725]

    L. Heisenberg,A systematic approach to generalisations of General Relativity and their cosmological implications,Physics Reports796(2019) 1 [1807.01725]

    Pith/arXiv arXiv 2019

  60. [60]

    Chevallier and D

    M. Chevallier and D. Polarski,Accelerating universes with scaling dark matter,International Journal of Modern Physics D10(2001) 213 [gr-qc/0009008]

    Pith/arXiv arXiv 2001

  61. [61]

    Linder,Exploring the expansion history of the universe,Physical Review Letters90(2003) 091301 [astro-ph/0208512]

    E.V. Linder,Exploring the expansion history of the universe,Physical Review Letters90(2003) 091301 [astro-ph/0208512]

    Pith/arXiv arXiv 2003

  62. [62]

    Caldwell and E.V

    R.R. Caldwell and E.V. Linder,The limits of quintessence,Physical Review Letters95(2005) 141301 [astro-ph/0505494]

    Pith/arXiv arXiv 2005

  63. [63]

    Caldwell,A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state,Physics Letters B545(2002) 23 [astro-ph/9908168]

    R.R. Caldwell,A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state,Physics Letters B545(2002) 23 [astro-ph/9908168]

    Pith/arXiv arXiv 2002

  64. [64]

    Carroll, M

    S.M. Carroll, M. Hoffman and M. Trodden,Can the dark energy equation-of-state parameterw be less than−1?,Physical Review D68(2003) 023509 [astro-ph/0301273]

    Pith/arXiv arXiv 2003

  65. [65]

    Cline, S

    J.M. Cline, S. Jeon and G.D. Moore,The phantom menaced: constraints on low-energy effective ghosts,Physical Review D70(2004) 043543 [hep-ph/0311312]

    Pith/arXiv arXiv 2004

  66. [66]

    Vikman,Can dark energy evolve to the phantom?,Physical Review D71(2005) 023515 [astro-ph/0407107]

    A. Vikman,Can dark energy evolve to the phantom?,Physical Review D71(2005) 023515 [astro-ph/0407107]

    Pith/arXiv arXiv 2005

  67. [67]

    Feng, X.-L

    B. Feng, X.-L. Wang and X. Zhang,Dark energy constraints from the cosmic age and supernova,Physics Letters B607(2005) 35 [astro-ph/0404224]

    Pith/arXiv arXiv 2005

  68. [68]

    Abdul Karim et al.,DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints,2503.14738

    DESI Collaboration, M. Abdul Karim et al.,DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints,2503.14738

    Pith/arXiv arXiv

  69. [69]

    Zhao et al.,Dynamical dark energy in light of the latest observations,Nature Astronomy 1(2017) 627 [1701.08165]

    G.-B. Zhao et al.,Dynamical dark energy in light of the latest observations,Nature Astronomy 1(2017) 627 [1701.08165]

    Pith/arXiv arXiv 2017

  70. [70]

    Mukhanov,Physical Foundations of Cosmology, Cambridge University Press, Cambridge (2005)

    V. Mukhanov,Physical Foundations of Cosmology, Cambridge University Press, Cambridge (2005)

    2005

  71. [71]

    D.N. Spergel et al.,First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters,Astrophysical Journal Supplement Series148(2003) 175 [astro-ph/0302209]

    Pith/arXiv arXiv 2003

  72. [72]

    Aghanim et al.,Planck 2018 results

    Planck Collaboration, N. Aghanim et al.,Planck 2018 results. VI. Cosmological parameters, Astronomy & Astrophysics641(2020) A6 [1807.06209]

    Pith/arXiv arXiv 2018

  73. [73]

    Martin, C

    J. Martin, C. Ringeval and V. Vennin,Encyclopaedia Inflationaris,Physics of the Dark Universe5-6(2014) 75 [1303.3787]

    arXiv 2014

  74. [74]

    Navas et al.,Review of Particle Physics,Physical Review D110 (2024) 030001

    Particle Data Group, S. Navas et al.,Review of Particle Physics,Physical Review D110 (2024) 030001

    2024

  75. [75]

    Aaij et al.,Measurement of lepton universality parameters in B+ →K +ℓ+ℓ− andB 0 →K ∗0ℓ+ℓ− decays,Physical Review Letters131(2023) 051803 [2212.09153]

    LHCb Collaboration, R. Aaij et al.,Measurement of lepton universality parameters in B+ →K +ℓ+ℓ− andB 0 →K ∗0ℓ+ℓ− decays,Physical Review Letters131(2023) 051803 [2212.09153]

    arXiv 2023

  76. [76]

    Buttazzo, A

    D. Buttazzo, A. Greljo, G. Isidori and D. Marzocca,B-physics anomalies: a guide to combined explanations,JHEP11(2017) 044 [1706.07808]. – 24 –

    Pith/arXiv arXiv 2017

  77. [77]

    Desjacques, D

    V. Desjacques, D. Jeong and F. Schmidt,Large-scale galaxy bias,Physics Reports733(2018) 1 [1611.09787]

    Pith/arXiv arXiv 2018

  78. [78]

    Novell-Masot et al.,Full-shape analysis of the power spectrum and bispectrum of DESI DR1 LRG and QSO samples,JCAP06(2025) 005 [2503.09714]

    S. Novell-Masot et al.,Full-shape analysis of the power spectrum and bispectrum of DESI DR1 LRG and QSO samples,JCAP06(2025) 005 [2503.09714]

    arXiv 2025

  79. [79]

    Einstein,Zur Elektrodynamik bewegter K¨ orper,Annalen der Physik322(1905) 891

    A. Einstein,Zur Elektrodynamik bewegter K¨ orper,Annalen der Physik322(1905) 891

    1905

  80. [80]

    E¨ otv¨ os, D

    R.v. E¨ otv¨ os, D. Pek´ ar and E. Fekete,Beitr¨ age zum Gesetze der Proportionalit¨ at von Tr¨ agheit und Gravit¨ at,Annalen der Physik373(1922) 11

    1922

Showing first 80 references.