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Horndeski in motion

T0 review · 2 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that a shift-symmetric scalar with a linear spatial gradient creates homogeneous, axisymmetric cosmologies whose momentum density evolves universally, and that this provides a field-theoretic realization of moving dark…

desk verdict The universal momentum-density relation (2.16) is a genuinely new and rigorously derived result; the moving-dark-energy application is honestly presented but rests on an unverified stability of the anisotropic background, so treat the CMB predictions as conditional. read the letter →

arxiv 2412.12018 v2 pith:ZB7BEZKJ submitted 2024-12-16 astro-ph.CO gr-qc

J. Bayron Orjuela-Quintana , Jose Beltrán Jiménez This is my paper · ORCID
classification astro-ph.COgr-qc PACS 95.36.+x98.80.-k
keywords shift-symmetricHorndeskimovingdarkenergyBianchiIcosmologyKineticGravityBraidingCMBdipolequadrupolebulkflowsconservedcurrent
topics Dark Energy
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

The paper aims to establish that dark energy can be 'moving' in a fundamental field theory, not only in a phenomenological fluid parametrization. It considers shift-symmetric Horndeski theories, the most general scalar-tensor theories with second-order field equations, and allows the scalar to carry a constant spatial gradient while preserving homogeneity through a combined translation-and-shift symmetry. The central result is a universal law: the momentum density of these configurations is $\sqrt{-g} T^{0i} = -Q\lambda^i$, with $Q$ a conserved charge and $\lambda^i$ the gradient direction, independent of the coupling functions. If true, this gives a concrete gravitational theory behind the moving dark energy explanation of CMB dipole, bulk flows, and a preferred direction, while explaining why vector-field attempts fail. The paper then shows that a moving Kinetic Gravity Braiding field can generate the observed dipole without violating quadrupole bounds.

What carries the argument

The load-bearing object is the shift-symmetric conserved current $J^\mu$ together with the inhomogeneous scalar profile $\langle\phi\rangle=\phi(t)+\lambda_i x^i$, which realizes homogeneity as a diagonal combination of translations and internal shifts. The identity that carries the argument is $\sqrt{-g} T^{0i}=-J^0\lambda^i$, derived from the off-shell Bianchi identities for a generic diffeomorphism-invariant action with a vector field $A_\mu$ that, when identified with $\nabla_\mu\phi$, turns the field equation into the conserved current. This reduces the momentum density to the universal law $\sqrt{-g} T^{0i}=-Q\lambda^i$, with $Q$ the conserved Noether charge. For the phenomenological part, the equivalent-fluid formulation and the cosmic-center-of-mass frame convert this law into a constraint that determines the radiation velocity and the CMB dipole.

What would settle it

Compute the linear perturbation spectrum around the axisymmetric Bianchi I background with the scalar profile $\phi(t)+\vec\lambda\cdot\vec x$ in a shift-symmetric KGB theory, with parameters saturating the dipole bound $\lambda\bar{Q}\simeq1.5\times10^{-7}$; if a ghost or gradient instability appears, the universal law still holds off-shell but the moving-dark-energy dipole and quadrupole predictions do not survive.

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Extended reading notes

Core claim

The paper's central discovery is that homogeneous but anisotropic cosmologies can be supported by an inhomogeneous scalar profile $\phi(t)+\vec\lambda\cdot\vec x$ in any shift-symmetric Horndeski theory. Because the theory is invariant under $\phi\to\phi+c$, the spatial dependence can be absorbed into a diagonal symmetry combining translations with internal shifts, so all observables stay homogeneous while a preferred axis persists. The momentum density is then exactly $T^{0i}=-J^0\lambda^i$, and since the shift symmetry gives the conservation law $\sqrt{-g}J^0=Q$, the momentum density evolves as $\sqrt{-g} T^{0i}=-Q\lambda^i$ for every coupling function in the class. The paper proves this identity from the off-shell Bianchi identities for a generic shift-symmetric scalar-tensor action, and contrasts it with vector-field theories where the analogous identity has the field equation in place of the conserved current, forcing $T^{0i}$ to vanish on-shell. Applied to Kinetic Gravity Braiding, this yields a moving dark energy realization whose CMB dipole is fixed by the product $\lambda\bar{Q}$, whose quadrupole is model-dependent but estimated below observational bounds, and which naturally produces large-scale bulk flows.

Load-bearing premise

The assumption that carries the dark-energy application is that the drifting scalar-field configuration is stable under small ripples; the paper does not run that stability check and leaves it for future work.

Editorial extensions

If this is right

  • The CMB dipole from a moving KGB dark energy component is determined by the single parameter combination $\lambda\bar{Q}$, with current CMB data bounding $\lambda\bar{Q}\lesssim1.5\times10^{-7}$.
  • A moving KGB sector before decoupling makes radiation keep a constant velocity relative to the cosmic center of mass while matter velocities decay as $1/a$, producing a late-time matter-radiation relative motion and large-scale bulk flows.
  • The quadrupole contribution is second order in velocities and depends on the specific KGB model; for the imperfect dark energy example it is $\sim1.6\times10^{-6}$, below the conservative CMB quadrupole bound.
  • Vector-field constructions of moving dark energy are blocked by an on-shell identity, whereas shift-symmetric scalars evade it through the conserved current, so the scalar route is the viable field-theoretic one.
  • The moving configurations are physically nontrivial only when at least one additional cosmic component exists; otherwise the momentum constraint forces $\lambda^i=0$ or $Q=0$ and the scenario degenerates to the isotropic case.

Reading between the lines

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

  • Beyond the paper: if stability under perturbations is confirmed, the same mechanism could be pushed into the early universe, where a moving KGB-like component would imprint relative baryon-photon velocities before decoupling and could be constrained by future 21-cm or CMB-spectral measurements.
  • Beyond the paper: the off-shell Bianchi derivation suggests the universal law extends to shift-symmetric beyond-Horndeski and DHOST theories, so any homogeneous moving scalar of that type would obey the same $Q\lambda^i$ evolution without extra conditions.
  • Beyond the paper: since the CMB quadrupole receives an additive stochastic inflationary component, a dedicated search could compare the dipole direction inferred from the moving component with the axis of the quadrupole pattern; a stable correlation would be a distinctive signature not present in standard $\Lambda$CDM.
  • Beyond the paper: the preferred direction $\lambda^i$ breaks isotropy at all epochs; if it existed during inflation, it would generate a scale-dependent anisotropic power spectrum, offering a testable extension linking moving dark energy to inflationary anomalies.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. This paper considers shift-symmetric Horndeski theories on homogeneous, anisotropic backgrounds sourced by the scalar profile ϕ = ϕ(t) + λ·x. The central result is Eq. (2.16): for the whole shift-symmetric Horndeski class, the momentum density satisfies √-g T^0i = -Q λ^i, with Q the conserved Noether charge, so the evolution of T^0i is independent of the coupling functions. The relation is verified by direct computation, by off-shell diffeomorphism (Bianchi) identities in Sec. 2.2, by a mini-superspace reduction in Sec. 2.4, and by a 2-form dual in Sec. 2.5. The framework is then applied to moving dark energy: specializing to Kinetic Gravity Braiding, the authors derive a model-independent CMB dipole constraint λQ̄ ≲ 1.476×10^-7, estimate the induced quadrupole, and give an explicit imperfect-dark-energy example whose parameters saturate the dipole bound and produce a quadrupole of order 10^-6.

Significance. The universal relation (2.16) is a clean, non-trivial result. It is supported by several independent derivations, and it explains why vector-field constructions fail (on-shell δS/δA_0 = 0 makes T^0i vanish) while shift-symmetric scalars evade the obstruction. It also provides a field-theoretic underpinning to the previously phenomenological moving-dark-energy framework, with a partially model-independent dipole prediction. The paper is honest about its main limitation: the stability of the moving background is not analyzed. The strengths of the paper are the parameter-free character of the momentum-density evolution and the explicit cross-checks (Bianchi identity, mini-superspace, 2-form dual).

major comments (2)
  1. [Secs. 3.1–3.4 and Conclusions] The quantitative dark-energy results — the dipole bound in Eq. (3.21), the quadrupole estimate in Eq. (3.64), and the parameter values in Eq. (3.67) — assume that the moving-KGB configuration, i.e., the profile (2.9) on the Bianchi I metric (3.4), is a stable cosmological background from before decoupling until today. The paper does not compute the quadratic action for scalar and tensor perturbations around this background; the only stability-related statements are the reference to Ref. [101] for non-linear gravitational-wave instabilities in KGB and the Conclusions' explicit deferral of a perturbation analysis to future work. Because the dipole-saturating case uses v_r = 1.23×10^-3, a ghost or a negative sound speed along λ would invalidate the CMB predictions. I ask the authors either to provide a stability analysis for the background used in Sec. 3 or to clearly mark the phenomenological section as conditional on such an analysis.
  2. [Sec. 3.4, Eqs. (3.49) and (3.67)] The numerical values quoted at the end of Sec. 3.4, λ ≈ 5.77×10^-4 m_P H_0 and Q ≈ 7.63×10^-4 m_P H_0, are said to agree with the analytical estimates, but the latter value violates the bound Q ≤ 2.3×10^-4 m_P H_0 derived in Eq. (3.49). Repeating the algebra from Eqs. (3.46)–(3.48) for a_eq ≈ 3×10^-4 suggests that the correct bound is about an order of magnitude weaker, so the numerical value may be consistent with the intended ρ_eq < 0.1 ρ_r,eq constraint while Eq. (3.49) as displayed is not. The relation between λQ̄, Q, and ρ_crit needs to be stated unambiguously and the bound corrected; as written, the parameter-space claims in Sec. 3.4 are internally inconsistent.
minor comments (6)
  1. [Sec. 2, Eqs. (2.15)–(2.16); Sec. 3.1, Eq. (3.5)] The symbol T^{0i} is sometimes used for the mixed component T^0{}_i and sometimes for the contravariant component; the index conventions should be fixed once at the start of Sec. 2.
  2. [Sec. 4, Conclusions] The word 'analised' should be 'analysed'.
  3. [Sec. 3.4, Eq. (3.65)] The approximation |J^z/J^0|_max ≈ (5/6)√u_max should state the definition of u_max and the origin of the factor 5/6.
  4. [Sec. 3.4, Eqs. (3.49)–(3.67)] The relation between Q, Q̄, and ρ_crit is not stated in the main text; adding this relation would resolve ambiguities in the parameter values quoted later.
  5. [Fig. 3 caption] The caption says 'the shear decays over time', but the right panel shows σ asymptoting to a constant; clarify that Σ decays while σ approaches a constant that can be absorbed by a coordinate redefinition.
  6. [References] Reference [14] lists a DOI (10.1016/j.dark.2024.101653) that does not match the cited article; please correct it.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the universal relation (2.16) is derived from the action by direct computation and off-shell Bianchi identities, and the phenomenological constraints use observed CMB quantities as inputs rather than as fitted predictions.

full rationale

The central result, Eq. (2.16), T^{0i} = -Q λ^i / sqrt(-g), is established by explicit evaluation of T^{0i} and the conserved current in Sec. 2.2, and independently from the off-shell Bianchi identity in Eq. (2.38); neither step defines the relation into existence, and the 2-form dual analysis in Sec. 2.5 reproduces the same law for G2(Y) without importing it. The moving-dark-energy application in Sec. 3.2 rederives the dipole from the Sachs-Wolfe effect and then uses the measured CMB dipole only to set the inequality λ Qbar ≲ 1.476×10^{-7} (Eq. (3.21)); the numerical example in Sec. 3.4 deliberately saturates that bound rather than fitting the quadrupole, so the resulting quadrupole estimate (δT/T0) ≲ 1.6×10^{-6} is a derived consequence, not a fitted input renamed as a prediction. Although the authors cite their own earlier moving-dark-energy papers (e.g., Refs. [28-30]) for background and motivation, the load-bearing identities and the dipole and quadrupole computations are carried out in the present paper and do not reduce to those citations. The profile (2.9) is an explicit ansatz of the model, not smuggled in through a citation, and the universal relation follows from that stated assumption rather than being assumed as the conclusion. The main caveat is physical, not circular: the Conclusions state that 'the motion of the KGB field will also affect the stability conditions of these models' and 'We leave these issues for future work', and Sec. 3.1 notes that GWs impose severe stability constraints on KGB models at nonlinear order. Stability of the anisotropic background (2.9) is therefore an unverified assumption for the dark-energy predictions, but that is a correctness and viability risk, not a circularity of the derivation.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

The construction introduces a new scalar profile (2.9) as an ansatz and relies on several physical assumptions (perfect fluid components, GW170817 restriction, small velocities, assumed stability) that are not derived from first principles. The conserved charge Q, gradient vector lambda, and mass scale Lambda are free parameters constrained by observations.

free parameters (4)
  • lambda (magnitude of spatial gradient vector) = Constrained by CMB dipole bound lambda * Qbar <= 1.476e-7; numerical example uses lambda ~ 5.77e-4 m_P H0
    Constant vector in the scalar field profile (2.9); its magnitude is a free parameter of the construction, constrained by observations rather than derived.
  • Q (conserved charge of shift symmetry) = Constrained by Q/(H0 m_P) <= 2.3e-4 from early dark energy bound; numerical example uses Q ~ 7.63e-4 m_P H0
    Integration constant of the current conservation; sets the amplitude of the momentum density and the radiation velocity.
  • Lambda (mass scale of the imperfect DE Lagrangian) = Numerical example gives Lambda^3 ~ 6.12 m_P H0^2; analytic estimate Lambda^3 ~ 3 sqrt(6) m_P H0^2
    Mass scale in the KGB Lagrangian (3.39), fixed by requiring the scalar field to drive the current accelerated expansion.
  • Initial conditions for the dynamical system = x1,i = -1.2e-13, x3,i = 3e-3, ui ~ 0.26, Omega_r,i = 0.975, Omega_b,i = 0.004, Sigma_i = 0 at z = 1.3e5
    Chosen to reproduce the observed cosmic energy budget today and to saturate the CMB dipole bound (lambda * Qbar = 1.476e-7). They are not derived from first principles.
assumptions (8)
  • ad hoc to paper Scalar field profile (2.9): phi = phi(t) + lambda * x preserves homogeneity via shift symmetry
    This profile is the central construction; it is postulated, with the shift symmetry justifying homogeneity despite the spatial gradient.
  • domain assumption Axisymmetric Bianchi I metric (2.10) is the appropriate spacetime for the profile
    The profile breaks isotropy but preserves axisymmetry, so the metric ansatz is a choice adapted to the symmetry.
  • domain assumption Shift-symmetric Horndeski theories with Gi = Gi(X)
    The analysis is restricted to shift-symmetric theories; explicit phi dependence is integrated away via the arguments in the text.
  • domain assumption GW170817 constraint c_T = 1 restricts to the KGB subclass
    Given current observational constraints on gravitational wave speed, the paper focuses on cubic Horndeski (KGB) for the dark energy application.
  • domain assumption Additional components (radiation, matter) are required for non-trivial moving effects
    The paper shows that with only one component the shift can be trivially eliminated; the physical application assumes the presence of radiation and matter.
  • domain assumption Small lambda / small velocity approximation
    Many expressions are expanded to first order in lambda or velocities; the paper checks consistency a posteriori (e.g., lambda << phi_dot).
  • domain assumption Absence of intrinsic anisotropic stress for radiation and matter
    Only the scalar field and relative motions source shear; the standard perfect fluid assumption is used for radiation and matter.
  • domain assumption Stability of the moving KGB background is assumed but not analyzed
    Perturbations and stability are left for future work; the phenomenological claims rely on the background being stable.

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Pith. "Pith review of Horndeski in motion." pith.science (2026). https://pith.science/paper/ZB7BEZKJ

@misc{pith2026241212018,
  author       = {Pith},
  title        = {Pith review of: Horndeski in motion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZB7BEZKJ}},
  note         = {Machine review of arXiv:2412.12018}
}
read the original abstract

We study a class of homogeneous but anisotropic cosmologies within the family of shift-symmetric Horndeski theories, where the scalar field features an inhomogeneous profile but it preserves a translational symmetry that is realised as a combination of spatial translations and internal shifts. The spatial gradient of the scalar field introduces a preferred direction, so the resulting cosmologies are of the axisymmetric Bianchi I type. The momentum density of these configurations exhibits a universal evolution and an additional component with non-vanishing momentum density is required to have non-trivial effects. We show the relation of these scenarios with cosmologies of non-comoving components and, in particular, we explain how they provide a specific realisation of moving dark energy models. Among the class of shift-symmetric Horndeski theories, we analyse in more detail the case of Kinetic Gravity Braiding with emphasis on its application to moving dark energy models and its effects on large scale dark flows as well as the CMB dipole and quadrupole.

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Forward citations

Cited by 1 Pith paper

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

  1. Isotropic universes with a preferred direction

    astro-ph.CO 2026-08 conditional novelty 7.0 of 10

    A tuned vector-field EFT can have an exactly isotropic FLRW background while hiding a preferred direction that reappears in perturbations as direction-dependent propagation and scalar–tensor mixing.

Reference graph

Works this paper leans on

122 extracted references · 22 canonical work pages · cited by 1 Pith paper

  1. [101]

    Creminelli, G

    P. Creminelli, G. Tambalo, F. Vernizzi, and V. Yingcharoenrat, Dark-Energy Instabilities induced by Gravitational Waves , JCAP 05 (2020) 002, [ arXiv:1910.14035], [doi:10.1088/1475-7516/2020/05/002]

    arXiv 2020

  2. [1]

    Weinberg, The Cosmological Constant Problem , Rev

    S. Weinberg, The Cosmological Constant Problem , Rev. Mod. Phys.61 (1989) 1–23, [doi:10.1103/RevModPhys.61.1]

    doi:10.1103/revmodphys.61.1 1989

  3. [2]

    J. Martin, Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask) , Comptes Rendus Physique13 (2012) 566–665, [arXiv:1205.3365], [doi:10.1016/j.crhy.2012.04.008]

    arXiv 2012

  4. [3]

    Clifton, P

    T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, Modified Gravity and Cosmology , Phys. Rept. 513 (2012) 1–189, [ arXiv:1106.2476], [doi:10.1016/j.physrep.2012.01.001]

    arXiv 2012

  5. [4]

    Joyce, B

    A. Joyce, B. Jain, J. Khoury, and M. Trodden, Beyond the Cosmological Standard Model , Phys. Rept.568 (2015) 1–98, [ arXiv:1407.0059], [doi:10.1016/j.physrep.2014.12.002]

    arXiv 2015

  6. [5]

    G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space , Int. J. Theor. Phys.10 (1974) 363–384, [ doi:10.1007/BF01807638]

    doi:10.1007/bf01807638 1974

  7. [6]

    Deffayet, X

    C. Deffayet, X. Gao, D. A. Steer, and G. Zahariade, From k-essence to generalised Galileons, Phys. Rev. D84 (2011) 064039, [ arXiv:1103.3260], [doi:10.1103/PhysRevD.84.064039]

    arXiv 2011

  8. [7]

    Zumalac´ arregui and J

    M. Zumalac´ arregui and J. Garc ´ ıa-Bellido,Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian , Phys. Rev. D 89 (2014) 064046, [ arXiv:1308.4685], [doi:10.1103/PhysRevD.89.064046]

    arXiv 2014

Show all 122 references
  1. [8]

    Gleyzes, D

    J. Gleyzes, D. Langlois, F. Piazza, and F. Vernizzi, Healthy theories beyond Horndeski , Phys. Rev. Lett. 114 (2015), no. 21 211101, [ arXiv:1404.6495], [doi:10.1103/PhysRevLett.114.211101]

    2015 arXiv

  2. [9]

    Langlois and K

    D. Langlois and K. Noui, Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability, JCAP 02 (2016) 034, [ arXiv:1510.06930], [doi:10.1088/1475-7516/2016/02/034]

    2016 arXiv

  3. [10]

    Armendariz-Picon, T

    C. Armendariz-Picon, T. Damour, and V. F. Mukhanov, k - inflation , Phys. Lett. B458 (1999) 209–218, [ arXiv:hep-th/9904075], [doi:10.1016/S0370-2693(99)00603-6]

    1999 arXiv

  4. [11]

    Arkani-Hamed, P

    N. Arkani-Hamed, P. Creminelli, S. Mukohyama, and M. Zaldarriaga, Ghost inflation , JCAP 04 (2004) 001, [ arXiv:hep-th/0312100], [doi:10.1088/1475-7516/2004/04/001]

    2004 arXiv

  5. [12]

    Alishahiha, E

    M. Alishahiha, E. Silverstein, and D. Tong, DBI in the sky , Phys. Rev. D70 (2004) 123505, [arXiv:hep-th/0404084], [doi:10.1103/PhysRevD.70.123505]. – 39 –

    2004 arXiv

  6. [13]

    Kobayashi, M

    T. Kobayashi, M. Yamaguchi, and J. Yokoyama, Generalized G-inflation: Inflation with the most general second-order field equations , Prog. Theor. Phys.126 (2011) 511–529, [arXiv:1105.5723], [doi:10.1143/PTP.126.511]

    2011 arXiv

  7. [14]

    Martin, C

    J. Martin, C. Ringeval, and V. Vennin, Encyclopædia Inflationaris: Opiparous Edition , Phys. Dark Univ. 5-6 (2014) 75–235, [ arXiv:1303.3787], [doi:10.1016/j.dark.2024.101653]

    2014 arXiv

  8. [15]

    Cheung, P

    C. Cheung, P. Creminelli, A. L. Fitzpatrick, J. Kaplan, and L. Senatore, The Effective Field Theory of Inflation , JHEP 03 (2008) 014, [ arXiv:0709.0293], [doi:10.1088/1126-6708/2008/03/014]

    2008 arXiv

  9. [16]

    Gubitosi, F

    G. Gubitosi, F. Piazza, and F. Vernizzi, The Effective Field Theory of Dark Energy , JCAP 02 (2013) 032, [ arXiv:1210.0201], [doi:10.1088/1475-7516/2013/02/032]

    2013 arXiv

  10. [17]

    Finelli, G

    B. Finelli, G. Goon, E. Pajer, and L. Santoni, The Effective Theory of Shift-Symmetric Cosmologies, JCAP 05 (2018) 060, [ arXiv:1802.01580], [doi:10.1088/1475-7516/2018/05/060]

    2018 arXiv

  11. [18]

    R. J. Scherrer, Purely kinetic k-essence as unified dark matter , Phys. Rev. Lett.93 (2004) 011301, [arXiv:astro-ph/0402316], [doi:10.1103/PhysRevLett.93.011301]

    2004 arXiv

  12. [19]

    Deffayet, O

    C. Deffayet, O. Pujolas, I. Sawicki, and A. Vikman, Imperfect Dark Energy from Kinetic Gravity Braiding, JCAP 10 (2010) 026, [ arXiv:1008.0048], [doi:10.1088/1475-7516/2010/10/026]

    2010 arXiv

  13. [20]

    De Felice and S

    A. De Felice and S. Tsujikawa, Cosmology of a covariant Galileon field , Phys. Rev. Lett.105 (2010) 111301, [ arXiv:1007.2700], [doi:10.1103/PhysRevLett.105.111301]

    2010 arXiv

  14. [21]

    Germani, L

    C. Germani, L. Martucci, and P. Moyassari, Introducing the Slotheon: a slow Galileon scalar field in curved space-time , Phys. Rev. D85 (2012) 103501, [ arXiv:1108.1406], [doi:10.1103/PhysRevD.85.103501]

    2012 arXiv

  15. [22]

    Barreira, B

    A. Barreira, B. Li, A. Sanchez, C. M. Baugh, and S. Pascoli, Parameter space in Galileon gravity models, Phys. Rev. D87 (2013) 103511, [ arXiv:1302.6241], [doi:10.1103/PhysRevD.87.103511]

    2013 arXiv

  16. [23]

    Martin-Moruno and N

    P. Martin-Moruno and N. J. Nunes, Attracted to de Sitter II: cosmology of the shift-symmetric Horndeski models, JCAP 09 (2015) 056, [ arXiv:1506.02497], [doi:10.1088/1475-7516/2015/09/056]

    2015 arXiv

  17. [24]

    Germani and P

    C. Germani and P. Martin-Moruno, Tracking our Universe to de Sitter by a Horndeski scalar , Phys. Dark Univ.18 (2017) 1–5, [ arXiv:1707.03741], [doi:10.1016/j.dark.2017.09.002]

    2017 arXiv

  18. [25]

    Borislavov Vasilev, M

    T. Borislavov Vasilev, M. Bouhmadi-L´ opez, and P. Mart ´ ın-Moruno,Dark energy with a shift-symmetric scalar field: Obstacles, loophole hunting and dead ends , Phys. Dark Univ.46 (2024) 101679, [ arXiv:2406.12576], [doi:10.1016/j.dark.2024.101679]

    2024 arXiv

  19. [26]

    A. A. Starobinsky, S. V. Sushkov, and M. S. Volkov, Anisotropy screening in Horndeski cosmologies, Phys. Rev. D101 (2020), no. 6 064039, [ arXiv:1912.12320], [doi:10.1103/PhysRevD.101.064039]

    2020 arXiv

  20. [27]

    Galeev, R

    R. Galeev, R. Muharlyamov, A. A. Starobinsky, S. V. Sushkov, and M. S. Volkov, Anisotropic cosmological models in Horndeski gravity , Phys. Rev. D103 (2021), no. 10 104015, [arXiv:2102.10981], [doi:10.1103/PhysRevD.103.104015]

    2021 arXiv

  21. [28]

    A. L. Maroto, Moving dark energy and the cmb dipole , JCAP 05 (2006) 015, [arXiv:astro-ph/0512464], [doi:10.1088/1475-7516/2006/05/015]

    2006 arXiv

  22. [29]

    Beltran Jimenez and A

    J. Beltran Jimenez and A. L. Maroto, Cosmology with moving dark energy and the CMB quadrupole, Phys. Rev. D76 (2007) 023003, [ arXiv:astro-ph/0703483], [doi:10.1103/PhysRevD.76.023003]

    2007 arXiv

  23. [30]

    Beltr´ an Jim´ enez and A

    J. Beltr´ an Jim´ enez and A. L. Maroto,Large-scale cosmic flows and moving dark energy , JCAP 03 (2009) 015, [ arXiv:0811.3606], [doi:10.1088/1475-7516/2009/03/015]. – 40 –

    2009 arXiv

  24. [31]

    Harko and F

    T. Harko and F. S. N. Lobo, Cosmological anisotropy from non-comoving dark matter and dark energy, JCAP 07 (2013) 036, [ arXiv:1304.0757], [doi:10.1088/1475-7516/2013/07/036]

    2013 arXiv

  25. [32]

    J. A. R. Cembranos, A. L. Maroto, and H. Villarrubia-Rojo, Non-comoving Cosmology, JCAP 06 (2019) 041, [ arXiv:1903.11009], [doi:10.1088/1475-7516/2019/06/041]

    2019 arXiv

  26. [33]

    J. A. R. Cembranos, A. L. Maroto, and H. Villarrubia-Rojo, Magnetic fields from cosmological bulk flows , Mon. Not. Roy. Astron. Soc.497 (2020), no. 3 3537–3541, [ arXiv:1911.04988], [doi:10.1093/mnras/staa2189]

    2020 arXiv

  27. [34]

    Villarrubia Rojo, Cosmological and astrophysical signatures of alternative dark sector models

    H. Villarrubia Rojo, Cosmological and astrophysical signatures of alternative dark sector models. PhD thesis, UCM, Madrid, Dept. Phys., Madrid U., 2020

    2020

  28. [35]

    Garc ´ ıa-Garc ´ ıa, A

    C. Garc ´ ıa-Garc ´ ıa, A. L. Maroto, and P. Mart ´ ın-Moruno,Cosmology with moving bimetric fluids, JCAP 12 (2016) 022, [ arXiv:1608.06493], [doi:10.1088/1475-7516/2016/12/022]

    2016 arXiv

  29. [36]

    Beltran Jimenez and A

    J. Beltran Jimenez and A. L. Maroto, Cosmological evolution in vector-tensor theories of gravity, Phys. Rev. D80 (2009) 063512, [ arXiv:0905.1245], [doi:10.1103/PhysRevD.80.063512]

    2009 arXiv

  30. [37]

    Beltran Jimenez and L

    J. Beltran Jimenez and L. Heisenberg, Generalized multi-Proca fields, Phys. Lett. B770 (2017) 16–26, [ arXiv:1610.08960], [doi:10.1016/j.physletb.2017.03.002]

    2017 arXiv

  31. [38]

    Beltr´ an Jim´ enez and L

    J. Beltr´ an Jim´ enez and L. Heisenberg,Non-trivial gravitational waves and structure formation phenomenology from dark energy , JCAP 09 (2018) 035, [ arXiv:1806.01753], [doi:10.1088/1475-7516/2018/09/035]

    2018 arXiv

  32. [39]

    Krishnan, R

    C. Krishnan, R. Mondol, and M. M. Sheikh-Jabbari, Dipole cosmology: the Copernican paradigm beyond FLR W, JCAP 07 (2023) 020, [ arXiv:2209.14918], [doi:10.1088/1475-7516/2023/07/020]

    2023 arXiv

  33. [40]

    Krishnan, R

    C. Krishnan, R. Mondol, and M. M. Sheikh-Jabbari, A tilt instability in the cosmological principle, Eur. Phys. J. C83 (2023), no. 9 874, [ arXiv:2211.08093], [doi:10.1140/epjc/s10052-023-12048-y]

    2023 arXiv

  34. [41]

    Ebrahimian, C

    E. Ebrahimian, C. Krishnan, R. Mondol, and M. M. Sheikh-Jabbari, Towards a realistic dipole cosmology: the dipole ΛCDM model, Class. Quant. Grav.41 (2024), no. 14 145007, [arXiv:2305.16177], [doi:10.1088/1361-6382/ad550d]

    2024 arXiv

  35. [42]

    Allahyari, E

    A. Allahyari, E. Ebrahimian, R. Mondol, and M. M. Sheikh-Jabbari, Big Bang in dipole cosmology, Eur. Phys. J. C85 (2025), no. 2 119, [ arXiv:2307.15791], [doi:10.1140/epjc/s10052-025-13799-6]

    2025 arXiv

  36. [43]

    Krishnan, R

    C. Krishnan, R. Mohayaee, E. O. Colg´ ain, M. M. Sheikh-Jabbari, and L. Yin, Hints of FLR W breakdown from supernovae, Phys. Rev. D105 (2022), no. 6 063514, [ arXiv:2106.02532], [doi:10.1103/PhysRevD.105.063514]

    2022 arXiv

  37. [44]

    Zhai and W

    Z. Zhai and W. J. Percival, Sample variance for supernovae distance measurements and the Hubble tension , Phys. Rev. D106 (2022), no. 10 103527, [ arXiv:2207.02373], [doi:10.1103/PhysRevD.106.103527]

    2022 arXiv

  38. [45]

    Mc Conville and E

    R. Mc Conville and E. O. Colg´ ain,Anisotropic distance ladder in Pantheon+supernovae, Phys. Rev. D 108 (2023), no. 12 123533, [ arXiv:2304.02718], [doi:10.1103/PhysRevD.108.123533]

    2023 arXiv

  39. [46]

    A. Sah, M. Rameez, S. Sarkar, and C. Tsagas, Anisotropy in Pantheon+ supernovae , arXiv:2411.10838

    arXiv

  40. [47]

    P. K. Aluri et al., Is the observable Universe consistent with the cosmological principle? , Class. Quant. Grav.40 (2023), no. 9 094001, [ arXiv:2207.05765], [doi:10.1088/1361-6382/acbefc]

    2023 arXiv

  41. [48]

    Perivolaropoulos and F

    L. Perivolaropoulos and F. Skara, Challenges for ΛCDM: An update , New Astron. Rev.95 (2022) 101659, [ arXiv:2105.05208], [doi:10.1016/j.newar.2022.101659]

    2022 arXiv

  42. [49]

    Koivisto and D

    T. Koivisto and D. F. Mota, Accelerating Cosmologies with an Anisotropic Equation of State , Astrophys. J.679 (2008) 1–5, [ arXiv:0707.0279], [doi:10.1086/587451]. – 41 –

    2008 arXiv

  43. [50]

    Koivisto and D

    T. Koivisto and D. F. Mota, Anisotropic Dark Energy: Dynamics of Background and Perturbations, JCAP 06 (2008) 018, [ arXiv:0801.3676], [doi:10.1088/1475-7516/2008/06/018]

    2008 arXiv

  44. [51]

    T. S. Koivisto, D. F. Mota, M. Quartin, and T. G. Zlosnik, On the Possibility of Anisotropic Curvature in Cosmology , Phys. Rev. D83 (2011) 023509, [ arXiv:1006.3321], [doi:10.1103/PhysRevD.83.023509]

    2011 arXiv

  45. [52]

    Akarsu, E

    O. Akarsu, E. Di Valentino, S. Kumar, M. Ozyigit, and S. Sharma, Testing spatial curvature and anisotropic expansion on top of the ΛCDM model, Phys. Dark Univ.39 (2023) 101162, [arXiv:2112.07807], [doi:10.1016/j.dark.2022.101162]

    2023 arXiv

  46. [53]

    Koivisto and D

    T. Koivisto and D. F. Mota, Vector Field Models of Inflation and Dark Energy , JCAP 08 (2008) 021, [ arXiv:0805.4229], [doi:10.1088/1475-7516/2008/08/021]

    2008 arXiv

  47. [54]

    J. B. Orjuela-Quintana and C. A. Valenzuela-Toledo, Anisotropic k-essence, Phys. Dark Univ. 33 (2021) 100857, [ arXiv:2106.06432], [doi:10.1016/j.dark.2021.100857]

    2021 arXiv

  48. [55]

    Garc ´ ıa-Serna, J

    S. Garc ´ ıa-Serna, J. B. Orjuela-Quintana, C. A. Valenzuela-Toledo, and H. Ocampo-Dur´ an, Reconstructing the parameter space of nonanalytical cosmological fixed points , Int. J. Mod. Phys. D32 (2023), no. 11 2350073, [ arXiv:2302.09181], [doi:10.1142/S0218271823500736]

    2023 arXiv

  49. [56]

    Gallego, J

    D. Gallego, J. B. Orjuela-Quintana, and C. A. Valenzuela-Toledo, Anisotropic dark energy from string compactifications, JHEP 04 (2024) 131, [ arXiv:2402.09570], [doi:10.1007/JHEP04(2024)131]

    2024 arXiv

  50. [57]

    J. P. Beltr´ an Almeida, A. Guarnizo, R. Kase, S. Tsujikawa, and C. A. Valenzuela-Toledo, Anisotropic 2-form dark energy , Phys. Lett. B793 (2019) 396–404, [ arXiv:1902.05846], [doi:10.1016/j.physletb.2019.05.008]

    2019 arXiv

  51. [58]

    J. B. Orjuela-Quintana, J. L. Palacios-C´ ordoba, and C. A. Valenzuela-Toledo, Late-time anisotropy sourced by a 2-form field non-minimally coupled to cold dark matter , Phys. Dark Univ. 46 (2024) 101575, [ arXiv:2202.07546], [doi:10.1016/j.dark.2024.101575]

    2024 arXiv

  52. [59]

    J. B. Orjuela-Quintana, M. Alvarez, C. A. Valenzuela-Toledo, and Y. Rodriguez, Anisotropic Einstein Yang-Mills Higgs Dark Energy , JCAP 10 (2020) 019, [ arXiv:2006.14016], [doi:10.1088/1475-7516/2020/10/019]

    2020 arXiv

  53. [60]

    Guarnizo, J

    A. Guarnizo, J. B. Orjuela-Quintana, and C. A. Valenzuela-Toledo, Dynamical analysis of cosmological models with non-Abelian gauge vector fields , Phys. Rev. D102 (2020), no. 8 083507, [arXiv:2007.12964], [doi:10.1103/PhysRevD.102.083507]

    2020 arXiv

  54. [61]

    L. G. Gomez, Y. Rodriguez, and J. P. Beltran Almeida, Anisotropic scalar field dark energy with a disformally coupled Yang–Mills field , Int. J. Mod. Phys. D31 (2022), no. 08 2250060, [arXiv:2103.11826], [doi:10.1142/S0218271822500602]

    2022 arXiv

  55. [62]

    D. C. Rodrigues, Anisotropic Cosmological Constant and the CMB Quadrupole Anomaly , Phys. Rev. D77 (2008) 023534, [ arXiv:0708.1168], [doi:10.1103/PhysRevD.77.023534]

    2008 arXiv

  56. [63]

    Motoa-Manzano, J

    J. Motoa-Manzano, J. Bayron Orjuela-Quintana, T. S. Pereira, and C. A. Valenzuela-Toledo, Anisotropic solid dark energy , Phys. Dark Univ.32 (2021) 100806, [ arXiv:2012.09946], [doi:10.1016/j.dark.2021.100806]

    2021 arXiv

  57. [64]

    Campanelli, P

    L. Campanelli, P. Cea, and L. Tedesco, Ellipsoidal Universe Can Solve The CMB Quadrupole Problem, Phys. Rev. Lett.97 (2006) 131302, [ arXiv:astro-ph/0606266], [doi:10.1103/PhysRevLett.97.131302]. [Erratum: Phys.Rev.Lett. 97, 209903 (2006)]

    2006 arXiv

  58. [65]

    Campanelli, P

    L. Campanelli, P. Cea, and L. Tedesco, Cosmic Microwave Background Quadrupole and Ellipsoidal Universe , Phys. Rev. D76 (2007) 063007, [ arXiv:0706.3802], [doi:10.1103/PhysRevD.76.063007]

    2007 arXiv

  59. [66]

    Kashlinsky, F

    A. Kashlinsky, F. Atrio-Barandela, D. Kocevski, and H. Ebeling, A measurement of large-scale peculiar velocities of clusters of galaxies: results and cosmological implications , Astrophys. J. Lett.686 (2009) L49–L52, [ arXiv:0809.3734], [doi:10.1086/592947]. – 42 –

    2009 arXiv

  60. [67]

    Watkins, H

    R. Watkins, H. A. Feldman, and M. J. Hudson, Consistently Large Cosmic Flows on Scales of 100 Mpc/h: a Challenge for the Standard LCDM Cosmology , Mon. Not. Roy. Astron. Soc. 392 (2009) 743–756, [ arXiv:0809.4041], [doi:10.1111/j.1365-2966.2008.14089.x]

    2009 arXiv

  61. [68]

    Kashlinsky, F

    A. Kashlinsky, F. Atrio-Barandela, H. Ebeling, A. Edge, and D. Kocevski, A new measurement of the bulk flow of X-ray luminous clusters of galaxies , Astrophys. J. Lett.712 (2010) L81–L85, [ arXiv:0910.4958], [doi:10.1088/2041-8205/712/1/L81]

    2010 arXiv

  62. [69]

    Kashlinsky, F

    A. Kashlinsky, F. Atrio-Barandela, and H. Ebeling, Measuring bulk motion of X-ray clusters via the kinematic Sunyaev-Zeldovich effect: summarizing the ’dark flow’ evidence and its implications, arXiv:1202.0717

    arXiv

  63. [70]

    Atrio-Barandela, A

    F. Atrio-Barandela, A. Kashlinsky, H. Ebeling, D. J. Fixsen, and D. Kocevski, Probing the Dark Flow Signal in Wmap 9 -year and Planck Cosmic Microwave Background Maps , Astrophys. J.810 (2015), no. 2 143, [ arXiv:1411.4180], [doi:10.1088/0004-637X/810/2/143]

    2015 arXiv

  64. [71]

    Watkins, T

    R. Watkins, T. Allen, C. J. Bradford, A. Ramon, A. Walker, H. A. Feldman, R. Cionitti, Y. Al-Shorman, E. Kourkchi, and R. B. Tully, Analysing the large-scale bulk flow using cosmicflows4: increasing tension with the standard cosmological model , Mon. Not. Roy. Astron. Soc. 524...

    2023 arXiv

  65. [72]

    D. T. Son, Low-energy quantum effective action for relativistic superfluids , arXiv:hep-ph/0204199

    arXiv

  66. [73]

    Dubovsky, T

    S. Dubovsky, T. Gregoire, A. Nicolis, and R. Rattazzi, Null energy condition and superluminal propagation, JHEP 03 (2006) 025, [ arXiv:hep-th/0512260], [doi:10.1088/1126-6708/2006/03/025]

    2006 arXiv

  67. [74]

    Nicolis, Low-energy effective field theory for finite-temperature relativistic superfluids , arXiv:1108.2513

    A. Nicolis, Low-energy effective field theory for finite-temperature relativistic superfluids , arXiv:1108.2513

    arXiv

  68. [75]

    Pajer and D

    E. Pajer and D. Stefanyszyn, Symmetric Superfluids, JHEP 06 (2019) 008, [ arXiv:1812.05133], [doi:10.1007/JHEP06(2019)008]

    2019 arXiv

  69. [76]

    Pujolas, I

    O. Pujolas, I. Sawicki, and A. Vikman, The Imperfect Fluid behind Kinetic Gravity Braiding , JHEP 11 (2011) 156, [ arXiv:1103.5360], [doi:10.1007/JHEP11(2011)156]

    2011 arXiv

  70. [77]

    Nicolis, F

    A. Nicolis, F. Piazza, and K. Zeghari, Rotating cosmologies: classical and quantum , JCAP 10 (2022) 059, [ arXiv:2204.04110], [doi:10.1088/1475-7516/2022/10/059]

    2022 arXiv

  71. [78]

    Beltran Jimenez and T

    J. Beltran Jimenez and T. S. Koivisto, Extended Gauss-Bonnet gravities in Weyl geometry , Class. Quant. Grav.31 (2014) 135002, [ arXiv:1402.1846], [doi:10.1088/0264-9381/31/13/135002]

    2014 arXiv

  72. [79]

    Tasinato, Cosmic Acceleration from Abelian Symmetry Breaking, JHEP 04 (2014) 067, [arXiv:1402.6450], [doi:10.1007/JHEP04(2014)067]

    G. Tasinato, Cosmic Acceleration from Abelian Symmetry Breaking, JHEP 04 (2014) 067, [arXiv:1402.6450], [doi:10.1007/JHEP04(2014)067]

    2014 arXiv

  73. [80]

    Beltran Jimenez and T

    J. Beltran Jimenez and T. S. Koivisto, Spacetimes with vector distortion: Inflation from generalised Weyl geometry, Phys. Lett. B756 (2016) 400–404, [ arXiv:1509.02476], [doi:10.1016/j.physletb.2016.03.047]

    2016 arXiv

  74. [81]

    M. Hull, K. Koyama, and G. Tasinato, Covariantized vector Galileons, Phys. Rev. D93 (2016), no. 6 064012, [ arXiv:1510.07029], [doi:10.1103/PhysRevD.93.064012]

    2016 arXiv

  75. [82]

    Allys, P

    E. Allys, P. Peter, and Y. Rodriguez, Generalized Proca action for an Abelian vector field , JCAP 02 (2016) 004, [ arXiv:1511.03101], [doi:10.1088/1475-7516/2016/02/004]

    2016 arXiv

  76. [83]

    Beltran Jimenez and L

    J. Beltran Jimenez and L. Heisenberg, Derivative self-interactions for a massive vector field , Phys. Lett. B757 (2016) 405–411, [ arXiv:1602.03410], [doi:10.1016/j.physletb.2016.04.017]

    2016 arXiv

  77. [84]

    Beltran Jimenez, L

    J. Beltran Jimenez, L. Heisenberg, and T. S. Koivisto, Cosmology for quadratic gravity in generalized Weyl geometry, JCAP 04 (2016) 046, [ arXiv:1602.07287], [doi:10.1088/1475-7516/2016/04/046]. – 43 –

    2016 arXiv

  78. [85]

    Heisenberg, R

    L. Heisenberg, R. Kase, and S. Tsujikawa, Beyond generalized Proca theories, Phys. Lett. B 760 (2016) 617–626, [ arXiv:1605.05565], [doi:10.1016/j.physletb.2016.07.052]

    2016 arXiv

  79. [86]

    Allys, J

    E. Allys, J. P. Beltran Almeida, P. Peter, and Y. Rodr ´ ıguez,On the 4D generalized Proca action for an Abelian vector field , JCAP 09 (2016) 026, [ arXiv:1605.08355], [doi:10.1088/1475-7516/2016/09/026]

    2016 arXiv

  80. [87]

    Allys, P

    E. Allys, P. Peter, and Y. Rodriguez, Generalized SU(2) Proca Theory, Phys. Rev. D94 (2016), no. 8 084041, [ arXiv:1609.05870], [doi:10.1103/PhysRevD.94.084041]

    2016 arXiv

  81. [88]

    Rodr ´ ıguez and A

    Y. Rodr ´ ıguez and A. A. Navarro,Non-Abelian S-term dark energy and inflation , Phys. Dark Univ. 19 (2018) 129–136, [ arXiv:1711.01935], [doi:10.1016/j.dark.2018.01.003]

    2018 arXiv

  82. [89]

    Errasti D ´ ıez, B

    V. Errasti D ´ ıez, B. Gording, J. A. M´ endez-Zavaleta, and A. Schmidt-May,Complete theory of Maxwell and Proca fields , Phys. Rev. D101 (2020), no. 4 045008, [ arXiv:1905.06967], [doi:10.1103/PhysRevD.101.045008]

    2020 arXiv

  83. [90]

    Errasti D ´ ıez, B

    V. Errasti D ´ ıez, B. Gording, J. A. M´ endez-Zavaleta, and A. Schmidt-May,Maxwell-Proca theory: Definition and construction , Phys. Rev. D101 (2020), no. 4 045009, [arXiv:1905.06968], [doi:10.1103/PhysRevD.101.045009]

    2020 arXiv

  84. [91]

    Gallego Cadavid and Y

    A. Gallego Cadavid and Y. Rodriguez, A systematic procedure to build the beyond generalized Proca field theory, Phys. Lett. B798 (2019) 134958, [ arXiv:1905.10664], [doi:10.1016/j.physletb.2019.134958]

    2019 arXiv

  85. [92]

    K. Aoki, M. A. Gorji, S. Mukohyama, and K. Takahashi, The effective field theory of vector-tensor theories, JCAP 01 (2022), no. 01 059, [ arXiv:2111.08119], [doi:10.1088/1475-7516/2022/01/059]

    2022 arXiv

  86. [93]

    R. S. Palais, The principle of symmetric criticality , Commun. Math. Phys.69 (1979), no. 1 19–30, [doi:10.1007/BF01941322]

    1979 doi

  87. [94]

    M. E. Fels and C. G. Torre, The Principle of symmetric criticality in general relativity , Class. Quant. Grav.19 (2002) 641–676, [ arXiv:gr-qc/0108033], [doi:10.1088/0264-9381/19/4/303]

    2002 arXiv

  88. [95]

    Takahashi and D

    K. Takahashi and D. Yoshida, Ghost-free resummation of gravitational interactions of a two-form gauge field , Phys. Rev. D101 (2020), no. 2 024049, [ arXiv:1910.12508], [doi:10.1103/PhysRevD.101.024049]

    2020 arXiv

  89. [96]

    K. Aoki, J. Beltr´ an Jim´ enez, and D. Figueruelo,Some disquisitions on cosmological 2-form dualities, JCAP 04 (2023) 059, [ arXiv:2212.12427], [doi:10.1088/1475-7516/2023/04/059]

    2023 arXiv

  90. [97]

    B. J. Barros and J. Beltr´ an Jim´ enez,Non-trivial thick brane realisations with 3-forms , JHEP 02 (2024) 002, [ arXiv:2312.12516], [doi:10.1007/JHEP02(2024)002]

    2024 arXiv

  91. [98]

    Yoshida, 2-form gauge theory dual to scalar-tensor theory , Phys

    D. Yoshida, 2-form gauge theory dual to scalar-tensor theory , Phys. Rev. D100 (2019) 084047, [arXiv:1906.02462], [doi:10.1103/PhysRevD.100.084047]

    2019 arXiv

  92. [99]

    Beltran Jimenez, F

    J. Beltran Jimenez, F. Piazza, and H. Velten, Evading the Vainshtein Mechanism with Anomalous Gravitational Wave Speed: Constraints on Modified Gravity from Binary Pulsars , Phys. Rev. Lett.116 (2016), no. 6 061101, [ arXiv:1507.05047], [doi:10.1103/PhysRevLett.116.061101]

    2016 arXiv

  93. [100]

    LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral , Phys. Rev. Lett.119 (2017), no. 16 161101, [ arXiv:1710.05832], [doi:10.1103/PhysRevLett.119.161101]

    2017 arXiv

  94. [102]

    D. J. Fixsen, The Temperature of the Cosmic Microwave Background , Astrophys. J707 (2009), no. 2 916–920, [ arXiv:0911.1955], [doi:10.1088/0004-637X/707/2/916]. – 44 –

    2009 arXiv

  95. [103]

    Aghanim et al., Planck 2018 results

    Planck Collaboration, N. Aghanim et al., Planck 2018 results. I. Overview and the cosmological legacy of Planck , Astron. Astrophys.641 (2020) A1, [ arXiv:1807.06205], [doi:10.1051/0004-6361/201833880]

    2020 arXiv

  96. [104]

    Akrami et al., Planck 2018 results

    Planck Collaboration, Y. Akrami et al., Planck 2018 results. VII. Isotropy and Statistics of the CMB , Astron. Astrophys.641 (2020) A7, [ arXiv:1906.02552], [doi:10.1051/0004-6361/201935201]

    2020 arXiv

  97. [105]

    Bertone, ed., Particle Dark Matter: Observations, Models and Searches

    G. Bertone, ed., Particle Dark Matter: Observations, Models and Searches . Cambridge Univ. Press, Cambridge, 2010

    2010

  98. [106]

    Navas et al., Review of particle physics , Phys

    Particle Data Group Collaboration, S. Navas et al., Review of particle physics , Phys. Rev. D 110 (2024), no. 3 030001, [ doi:10.1103/PhysRevD.110.030001]

    2024 doi

  99. [107]

    Pontzen and A

    A. Pontzen and A. Challinor, Bianchi Model CMB Polarization and its Implications for CMB Anomalies, Mon. Not. Roy. Astron. Soc.380 (2007) 1387–1398, [ arXiv:0706.2075], [doi:10.1111/j.1365-2966.2007.12221.x]

    2007 arXiv

  100. [108]

    Appleby, R

    S. Appleby, R. Battye, and A. Moss, Constraints on the anisotropy of dark energy , Phys. Rev. D 81 (2010) 081301, [ arXiv:0912.0397], [doi:10.1103/PhysRevD.81.081301]

    2010 arXiv

  101. [109]

    Peirone, G

    S. Peirone, G. Benevento, N. Frusciante, and S. Tsujikawa, Cosmological data favor Galileon ghost condensate over ΛCDM, Phys. Rev. D100 (2019), no. 6 063540, [ arXiv:1905.05166], [doi:10.1103/PhysRevD.100.063540]

    2019 arXiv

  102. [110]

    Campanelli, P

    L. Campanelli, P. Cea, G. L. Fogli, and A. Marrone, Testing the Isotropy of the Universe with Type Ia Supernovae, Phys. Rev. D83 (2011) 103503, [ arXiv:1012.5596], [doi:10.1103/PhysRevD.83.103503]

    2011 arXiv

  103. [111]

    Amirhashchi and S

    H. Amirhashchi and S. Amirhashchi, Constraining Bianchi Type I Universe With Type Ia Supernova and H(z) Data , Phys. Dark Univ.29 (2020) 100557, [ arXiv:1802.04251], [doi:10.1016/j.dark.2020.100557]

    2020 arXiv

  104. [112]

    Lopes, A

    M. Lopes, A. Bernui, C. Franco, and F. Avila, Bulk Flow Motion Detection in the Local Universe with Pantheon+ Type Ia Supernovae , Astrophys. J.967 (2024), no. 1 47, [arXiv:2405.11077], [doi:10.3847/1538-4357/ad3735]

    2024 arXiv

  105. [113]

    Liu et al., Measuring the speed of gravitational waves from the first and second observing run of Advanced LIGO and Advanced Virgo , Phys

    X. Liu et al., Measuring the speed of gravitational waves from the first and second observing run of Advanced LIGO and Advanced Virgo , Phys. Rev. D102 (2020), no. 2 024028, [arXiv:2005.03121], [doi:10.1103/PhysRevD.102.024028]

    2020 arXiv

  106. [114]

    Baker et al., Testing gravitational wave propagation with multiband detections , JCAP 03 (2023) 044, [ arXiv:2209.14398], [doi:10.1088/1475-7516/2023/03/044]

    T. Baker et al., Testing gravitational wave propagation with multiband detections , JCAP 03 (2023) 044, [ arXiv:2209.14398], [doi:10.1088/1475-7516/2023/03/044]

    2023 arXiv

  107. [115]

    J. M. Ezquiaga and M. Zumalac´ arregui, Dark Energy After GW170817: Dead Ends and the Road Ahead, Phys. Rev. Lett.119 (2017), no. 25 251304, [ arXiv:1710.05901], [doi:10.1103/PhysRevLett.119.251304]

    2017 arXiv

  108. [116]

    Creminelli and F

    P. Creminelli and F. Vernizzi, Dark Energy after GW170817 and GRB170817A , Phys. Rev. Lett. 119 (2017), no. 25 251302, [ arXiv:1710.05877], [doi:10.1103/PhysRevLett.119.251302]

    2017 arXiv

  109. [117]

    Baker, E

    T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller, and I. Sawicki, Strong constraints on cosmological gravity from GW170817 and GRB 170817A , Phys. Rev. Lett.119 (2017), no. 25 251301, [arXiv:1710.06394], [doi:10.1103/PhysRevLett.119.251301]

    2017 arXiv

  110. [118]

    C. D. Kreisch and E. Komatsu, Cosmological Constraints on Horndeski Gravity in Light of GW170817, JCAP 12 (2018) 030, [ arXiv:1712.02710], [doi:10.1088/1475-7516/2018/12/030]

    2018 arXiv

  111. [119]

    Cardona, J

    W. Cardona, J. B. Orjuela-Quintana, and C. A. Valenzuela-Toledo, An effective fluid description of scalar-vector-tensor theories under the sub-horizon and quasi-static approximations, JCAP 08 (2022), no. 08 059, [ arXiv:2206.02895], [doi:10.1088/1475-7516/2022/08/059]. – 45 –

    2022 arXiv

  112. [120]

    D. J. C. MacKay, Information theory, inference, and learning algorithms. Cambridge University Press, 2003

    2003

  113. [121]

    Bahamonde, C

    S. Bahamonde, C. G. B¨ ohmer, S. Carloni, E. J. Copeland, W. Fang, and N. Tamanini, Dynamical systems applied to cosmology: dark energy and modified gravity , Phys. Rept. 775-777 (2018) 1–122, [ arXiv:1712.03107], [doi:10.1016/j.physrep.2018.09.001]

    2018 arXiv

  114. [122]

    Kase and S

    R. Kase and S. Tsujikawa, Dark energy scenario consistent with GW170817 in theories beyond Horndeski gravity, Phys. Rev. D97 (2018), no. 10 103501, [ arXiv:1802.02728], [doi:10.1103/PhysRevD.97.103501]. – 46 –

    2018 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.