Pith. sign in

REVIEW 2 major objections 4 minor 1 cited by

A `singular' bounce in the theory of gravity with non-minimal derivative coupling

T0 review · 2 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read This paper argues that a bounce in a closed universe with non-minimal derivative coupling is geometrically regular but dynamically singular: the scalar field's time derivative diverges at the moment the scale factor reaches its minimum.

desk verdict The singular-bounce claim is correct for q≠0, but the paper never flags that the q=0 sector has no bounce at all, so the conclusion is broader than the equations actually support. read the letter →

arxiv 2502.05786 v1 pith:CX42TQZC submitted 2025-02-09 gr-qc

S. V. Sushkov , R. G. Galeev This is my paper · ORCID
classification gr-qc MSC 83F0583D0583C15 PACS 98.80.-k04.50.Kd
keywords cosmologicalbouncenon-minimalderivativecouplingscalarfieldsingularitycloseduniversemodifiedFriedmannequationspatialcurvaturecharge
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 studies homogeneous, isotropic cosmologies in a scalar-tensor theory where the scalar field's kinetic term is coupled to the Einstein tensor through a term proportional to $\zeta G_{\mu\nu} \nabla^{\mu}\varphi\nabla^{\nu}\varphi$. It claims that in a closed (positive-curvature) universe this theory admits a bounce at a minimal scale factor $a_{\min} = (3\zeta\Omega_2)^{1/2}$, and that this value depends only on the coupling $\zeta$ and the curvature density $\Omega_2$, not on the cosmological constant or ordinary matter. Near that bounce the scale factor, Hubble parameter, curvature invariants, and matter energy densities all remain finite and regular. The paper's central discovery is that the scalar field does not follow suit: its time derivative behaves as $\varphi' \propto 1/\Delta\tau^2$ and diverges as the bounce is approached, even though the metric is smooth. Because the scalar field is part of the gravitational sector in this theory, the authors conclude that the complete dynamical system is singular, a scenario they name a 'singular' bounce.

What carries the argument

The load-bearing object is the first integral of the scalar-field equation, $\varphi'(1 - 3\zeta(h^2 + \Omega_2/a^2)) = q/a^3$, where $q$ (the dimensionless scalar charge) is a constant of integration. The same algebraic condition that selects the bounce, $1 - 3\zeta\Omega_2/a^2 = 0$ at $a = a_{\min} = (3\zeta\Omega_2)^{1/2}$, makes the parenthesis in this first integral vanish, since $h=0$ there. With $q \neq 0$ the equation then has no finite solution for $\varphi'$ at the bounce; leading-order balance gives $\varphi' \approx 27\zeta q/(2 a_{\min}^3 \Delta\tau^2)$. Thus one and the same factor produces both the geometric turnaround and the scalar-field pole.

What would settle it

Locate a trajectory of the full system (12)-(13) with $\zeta>0$, $\Omega_2>0$, $\Omega_6>0$, and $q\neq0$ that passes through the bounce with finite $\varphi'$; the leading-order balance $\varphi' \propto q/\Delta\tau^2$ makes such a trajectory impossible unless an omitted term cancels the pole, so demonstrating that cancellation would falsify the paper's conclusion.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the bounce solution in this theory comes in two layers. The metric and matter sector are regular: near $\tau_*$ the scale factor behaves as $a(\tau) \approx a_{\min}(1 + \Delta\tau^2/18\zeta)$, the Hubble parameter as $h(\tau) \approx \Delta\tau/9\zeta$, the Ricci scalar tends to $R_* = 6(1/a_{\min}^2 + 1/9\eta)$, and the matter densities $\rho_m \sim a^{-3}$, $\rho_r \sim a^{-4}$ stay finite. The scalar field, however, obeys the first integral $\varphi'(1 - 3\zeta(h^2 + \Omega_2/a^2)) = q/a^3$; because the factor in parentheses vanishes exactly at the bounce ($h=0$ and $a^2 = 3\zeta\Omega_2$), a nonzero scalar charge $q$ forces $\varphi' \approx 27\zeta q/(2 a_{\min}^3 \Delta\tau^2)$, which diverges as $\Delta\tau \to 0$. The paper concludes from this that the complete dynamical system (12)-(14) is singular near the bounce, even though the geometry is perfectly smooth, and calls this a 'singular' bounce.

Load-bearing premise

The divergence claim assumes the scalar charge $q$ in the first integral (12) is nonzero (equivalently $\Omega_6 > 0$); if $q = 0$, the right-hand side of that equation vanishes and the pole in $\varphi'$ disappears, a degenerate case the paper does not analyze.

Editorial extensions

If this is right

  • In this theory, bouncing universes require positive spatial curvature; models with $k\le 0$ have no turning points at all.
  • The bounce scale $a_{\min}$ depends only on $\zeta$ and $\Omega_2$, so near the bounce the cosmological constant and ordinary matter are screened and do not set the bounce size.
  • The regularity of $a(\tau)$, $h(\tau)$, the curvature invariants, and $\rho_m \sim a^{-3}$, $\rho_r \sim a^{-4}$ near the bounce is not enough to make the model singularity-free; the scalar-field kinetic term diverges as $(\tau-\tau_*)^{-2}$.
  • Since the scalar field is part of the gravitational dynamics, the 'singular' bounce means this theory does not provide a fully regular alternative to the initial singularity, at least in the closed isotropic sector with $\Omega_6>0$.

Reading between the lines

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

  • An implication the authors leave implicit is that bounce criteria should inspect all fields, not only the metric and energy densities; a geometrically regular bounce can still be dynamically singular.
  • A testable extension is to compute scalar-field invariants such as $(\nabla\varphi)^2$ near the bounce; the pole $\varphi' \sim \Delta\tau^{-2}$ would make them diverge even though curvature invariants do not, sharpening what 'singular' means for the matter sector.
  • The degenerate case $\Omega_6=0$ (zero scalar charge) is left open; if a completely regular bounce solution exists there, the singular bounce would be a codimension-one phenomenon rather than the generic fate of closed bouncing models in this theory.
  • Because $a_{\min}$ depends only on $\zeta$ and $\Omega_2$, a future measurement of the bounce scale and the spatial-curvature density would translate directly into a constraint on the coupling $\zeta$; the authors do not discuss that observational consequence.
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.

Referee Report

2 major / 4 minor

Summary. The paper studies homogeneous and isotropic FLRW cosmologies with arbitrary spatial curvature in the theory of gravity with non-minimal derivative coupling of a scalar field to the Einstein tensor. It finds that turning points and bounces exist only for positive spatial curvature, with the bounce occurring at a_min = (3ζΩ2)^{1/2}, a value independent of Ω0, Ω3, and Ω4. Near the bounce the scale factor and Hubble parameter are regular, but the scalar field derivative diverges as φ' ∝ 1/Δτ², so the authors conclude that the complete dynamical system is singular at the bounce even though the spacetime geometry and matter energy densities remain regular. The main derivation is analytic and self-contained, but the central claim is stated without the necessary condition that the scalar charge q be nonzero.

Significance. If the result holds, it provides an explicit example in a Horndeski-type theory where the geometry is regular at a bounce while the scalar field sector becomes singular, which is an interesting and non-obvious feature. The calculation is transparent and reproducible: the divergence coefficient in Eq. (28) is obtained directly from the paper's own field equations rather than from a fitted or imported result, and the algebraic derivation of the turning-point conditions is internally consistent. The main limitation is that the singular-bounce phenomenon requires a nonzero scalar charge q (equivalently Ω6 > 0), a condition that is never stated in the paper. With that caveat addressed, the result would be a worthwhile contribution to the bouncing-cosmology literature, although its scope is confined to a specific subclass of Horndeski models.

major comments (2)
  1. [§III, Eqs. (20)-(21); §IV, Eq. (28)] The central claim of a singular bounce requires q ≠ 0, but the paper only imposes Ω6 ≥ 0. In the q = 0 sector, Eq. (12) gives φ' = 0 wherever the kinetic bracket is nonzero, and Eq. (13) reduces to the standard Friedmann equation. In that case the root a² = 3ζΩ2 found from Eq. (21) is a spurious factor of c0(a), not a genuine turning point of h², unless the additional standard turning-point condition Ω0 − Ω2/a² + Ω3/a³ + Ω4/a⁴ = 0 also holds at that radius. Consequently, the statement in §IV that "the complete dynamical system represented by equations (12), (13), (14) is singular near the bounce" is not valid for Ω6 = 0. The authors should explicitly state and justify the assumption Ω6 > 0 (equivalently q ≠ 0), or qualify all conclusions accordingly and discuss the q = 0 sector separately.
  2. [Appendix, Eqs. (30)-(31)] The asymptotic series (30) for y = h² near the bounce is treated as determining the bounce branch, but no convergence or remainder estimate is provided, and the coefficients \tilde y_n are not uniformly small in the stated parameter range: for example, \tilde y_2 is proportional to a_*²/Ω6 and diverges as Ω6 → 0. The numerical estimates for the single Planck-like parameter set do not establish that the truncated series is valid for all allowed Ω6 > 0. Since Eq. (28) is obtained by substituting the asymptotic forms (24)-(25) into Eq. (12), the paper should either supply a rigorous existence argument for the bounce branch (for instance, a balancing or implicit-function argument applied to Eq. (29)) or explicitly present the result as a leading-order asymptotic statement whose subleading corrections are assumed small.
minor comments (4)
  1. [Abstract and §IV] There are several language issues: "the bounce is happened" should be "the bounce occurs", and "On our knowledge" should be "To our knowledge".
  2. [Eq. (16), §III] The text says Eq. (16) is fulfilled when P(a,y) = 0 and the denominator 1 − 3ζ(y + Ω2/a²) ≠ 0, but at the bounce the denominator actually vanishes; the subsequent limiting argument is only implicit and should be explained in the main text rather than deferred to the appendix.
  3. [§II, Eqs. (9)-(15)] The paper should state explicitly that Ω6 = 0 corresponds to q = 0 and that the scalar charge q is a free integration constant; this connection is central to the interpretation of the results but is never made explicit.
  4. [Eq. (14) and constraint] The abstract mentions six dimensionless parameters while §IV says five are independent; this counting is understandable because of the constraint (14), but it would help the reader to see the distinction stated in one place.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the bounce asymptotics and scalar-field divergence follow from the paper's own field equations; the q≠0 requirement is an unstated parameter restriction, not a circular reduction.

full rationale

The derivation chain is self-contained. The bounce scale a_min=(3ζΩ2)^{1/2} is obtained from the vanishing of c0(a) in Eq. (18) via Eq. (21), which follows algebraically from the modified Friedmann equation (13) rewritten as Eq. (16). The regular asymptotics a(τ)≈a_min(1+Δτ²/18ζ) and h(τ)≈Δτ/9ζ are derived in the appendix by a series solution of Eq. (29), not imported from a fitted or external result. The claimed scalar-field divergence φ'≈27ζq/(2a_min³Δτ²) is then obtained by substituting these asymptotics into the first integral (12). This is a direct consequence of the paper's own equations; no parameter is fitted to data and no 'prediction' is equivalent to an input by construction. The self-citations to Refs. [36] and [39] supply the screening terminology and prior context, but the central calculation does not rely on their conclusions. A genuine caveat is that Ω6≥0 permits q=0, in which case Eq. (28) gives φ'=0 and no singular bounce occurs; the paper does not flag that its 'singular' bounce requires q≠0. This is an overstatement of the parameter domain, not a circular step, because it does not reduce the derivation to its own input.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper introduces a scenario name, 'singular bounce', but no new particles, forces, or conserved quantities beyond the existing scalar charge q and coupling ζ. The only hidden input is the nonzero scalar charge needed for the singularity.

free parameters (3)
  • ζ (dimensionless non-minimal derivative coupling) = chosen by hand; illustrative value 10^-5 used in estimates
    The bounce scale amin = (3ζΩ2)^{1/2} and the singularity amplitude are proportional to powers of ζ, so the central result is parameter-dependent. No observational constraint on ζ is imposed in the paper.
  • Ω2 (spatial curvature density) = 0.044 in the illustrative Planck-based estimate
    The bounce exists only for Ω2 > 0, and amin depends on Ω2. The value is taken from Planck data for the numerical check of correction terms, not fitted to the target result.
  • q (scalar charge) or Ω6 = nonzero; Ω6 ≈ 0.0442 in the illustrative estimate
    The scalar-field divergence is proportional to q; if q = 0 the singular behavior disappears. The paper assumes Ω6 ≥ 0 without flagging that q ≠ 0 is required.
assumptions (6)
  • domain assumption The action (1) with non-minimal derivative coupling is the effective theory.
    All results are derived within this Horndeski subclass; no independent evidence for the action is provided.
  • domain assumption FLRW metric with k = 0, ±1 and homogeneous scalar field.
    The analysis is restricted to homogeneous and isotropic cosmologies; anisotropic perturbations or backgrounds could alter the conclusion.
  • domain assumption Parameter restrictions ζ ≥ 0, Ω0 ≥ 0, Ω3 ≥ 0, Ω4 ≥ 0, Ω6 ≥ 0, and Ω2 > 0 for bounces.
    The absence of bounces for k ≤ 0 and the existence of amin rely on these sign choices; negative ζ or Λ would require re-analysis.
  • domain assumption Matter is a mixture of dust and radiation with ρ = ρm a^{-3} + ρr a^{-4}.
    The turning-point conditions (20)-(21) use this specific matter model from Eq. (8).
  • ad hoc to paper The series expansion (30) converges and the omitted ỹn terms are negligible.
    The asymptotics (24)-(25) are obtained by truncating this series; smallness is checked only for one illustrative parameter set, not proven in general.
  • ad hoc to paper The scalar charge q is nonzero (Ω6 > 0).
    The claimed divergence φ' ∝ 1/Δτ² requires q ≠ 0; the paper only states Ω6 ≥ 0.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A `singular' bounce in the theory of gravity with non-minimal derivative coupling." pith.science (2026). https://pith.science/paper/CX42TQZC

@misc{pith2026250205786,
  author       = {Pith},
  title        = {Pith review of: A `singular' bounce in the theory of gravity with non-minimal derivative coupling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CX42TQZC}},
  note         = {Machine review of arXiv:2502.05786}
}
abstract

We explore bounce scenarios in the framework of homogeneous and isotropic cosmological models with arbitrary spatial curvature in the theory of gravity with non-minimal derivative coupling. As expected, we find that there are no turning points and/or bounces in cosmological models with negative or zero spatial curvature. At the same time, both a turning point and a bounce can exist in the model with positive spatial curvature. In particular, the bounce is happened at $\tau=\tau_*$ when $a(\tau_*)=a_{min} =(3\zeta\Omega_2)^{1/2}$, where $\tau=H_0 t$ is a dimensionless cosmic time. It is important fact that the value $a_{min}$ depends {\em only} on $\zeta$ and $\Omega_2$, and does {\em not} depend on $\Omega_0$, $\Omega_3$ and $\Omega_4$. We find that near the bounce $a(\tau)\approx a_{min}(1+\Delta\tau^2/18\zeta)$ and $h(\tau)\approx \Delta\tau/9\zeta$, where $\Delta\tau=\tau-\tau_*$. Thus, the scale factor $a(\tau)$, the Hubble parameter $h(\tau)$, and all corresponding geometrical invariants have a regular behavior near the bounce. As well the values characterizing matter energy densities, such as $\rho_m\sim a^{-3}$ and $\rho_r\sim a^{-4}$, are regular near the bounce. Nevertheless, though the spacetime geometry and energy densities remain to be regular near the bounce, the scalar field has a singular behavior there. Namely, $\phi'\propto 1/\Delta\tau^2 \to\infty$ as $\Delta\tau\to 0$. As a result, we conclude that the complete dynamical system describing the cosmological evolution in theory of gravity with non-minimal derivative coupling is singular near the bounce. On our knowledge, such the scenario, when the spacetime geometry and matter energy densities remain to be regular at approaching the universe evolution to the moment of bounce, while the behavior of scalar field becomes singular, was unknown before. For this reason, we term this scenario as a {\em `singular' bounce}.

Discussion (0). Continue with ORCID to comment.

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. Chaos in Horndeski cosmologies

    gr-qc 2025-09 conditional novelty 7.0 of 10

    In Bianchi IX cosmologies, ordinary scalar fields kill mixmaster chaos when their energy is not subleading, but a phantom scalar then produces eternal, chaotic, non-singular bounces.

Reference graph

Works this paper leans on

41 extracted references · 35 canonical work pages · cited by 1 Pith paper

  1. [1]

    Ba- sis”, grant No. 24-1-1-39-1 and partially carried out in accordance with the Strategic Academic Leadership Pro- gram

    Thus, a ‘bounce’ solution y = 0 of Eq. (16) can exist if and only if there exists a∗ such that c0(a∗) = 0. Using Eq. (18), we obtain two separate algebraic conditions for a∗: ( 1 − 3ζΩ 2 a2 ∗ ) ( Ω 0 − Ω 2 a2 ∗ + Ω 3 a3 ∗ + Ω 4 a4 ∗ ) + Ω 6 a6 ∗ = 0, (20) and ( 1 − 3ζΩ 2 a2 ∗ ) = 0. (21) First of all, it is necessary to notice that both algebraic equation...

    work page

  2. [2]

    ¨Uber die Kr¨ ummung des Raumes

    Friedman, A. ¨Uber die Kr¨ ummung des Raumes. Z. Phys. 1922, 10, 377–386

    work page 1922

  3. [3]

    ¨Uber die M¨ oglichkeit einer Welt mit kon- stanter negativer Kr¨ ummung des Raumes

    Friedman, A. ¨Uber die M¨ oglichkeit einer Welt mit kon- stanter negativer Kr¨ ummung des Raumes. Z. Phys. 1924, 21, 326—332

    work page 1924

  4. [4]

    R. Penrose. Gravitational collapse and space-time sing u- larities. Phys. Rev. Lett., 14:57–59, 1965

    work page 1965

  5. [5]

    S. W. Hawking. The occurrence of singularities in cos- mology. iii. causality and singularities. Proceedings of t he Royal Society of London. Series A, Mathematical and Physical Sciences, 300(1461):187–201, 1967

    work page 1967

  6. [6]

    S. W. Hawking and R. Penrose. The singularities of grav- itational collapse and cosmology. Proc. Roy. Soc. London Ser. A, 314:529– 548, 1970

    work page 1970

  7. [7]

    J. M. M. Senovilla and D. Garfinkle. The 1965 Pen- rose singularity theorem. Classical Quantum Gravity, 32(12):124008, 45, 2015

    work page 1965

  8. [8]

    The Singularity Theorems of Gen- eral Relativity and Their Low Regularity Extensions

    Steinbauer, R. The Singularity Theorems of Gen- eral Relativity and Their Low Regularity Extensions. Jahresber. Dtsch. Math. Ver. 125, 73–119 (2023). https://doi.org/10.1365/s13291-022-00263-7

    doi:10.1365/s13291-022-00263-7 2023

Show all 41 references
  1. [9]

    Capozziello, M

    S. Capozziello, M. De Laurentis, Extended Theories of Gravity, Phys. Rep. 509, Issues 4–5, pp. 167-321 (2011)

    2011

  2. [10]

    Clifton, P

    T. Clifton, P. G. Ferreira, A. Padilla, and C. Sko- rdis, Modified Gravity and Cosmology, Phys. Rept. 513, 1–189 (2012)

    2012

  3. [11]

    Myrzakulov, L

    R. Myrzakulov, L. Sebastiani, S. Zerbini, Some aspects of generalized modified gravity models, Int. J. Mod. Phys. D 22, no.8, 1330017 (2013)

    2013

  4. [12]

    Berti et al., Testing General Relativity with Presen t and Future Astrophysical Observations, Class

    E. Berti et al., Testing General Relativity with Presen t and Future Astrophysical Observations, Class. Quant. Grav. 32, 243001 (2015)

    2015

  5. [13]

    Nojiri, S

    S. Nojiri, S. D. Odintsov, V. K. Oikonomou, Modified gravity theories on a nutshell: Inflation, bounce and late- time evolution, Phys. Rep. 692, pp. 1-104 (2017)

    2017

  6. [14]

    Langlois, Dark energy and modified gravity in degen- erate higher-order scalar–tensor (DHOST) theories: A review, Int

    D. Langlois, Dark energy and modified gravity in degen- erate higher-order scalar–tensor (DHOST) theories: A review, Int. J. Mod. Phys. D 28, no. 05, 1942006 (2019)

    2019

  7. [15]

    Bouncing Scenario and Cosmic Dynam- ics in Modified Theories of Gravity,

    A. S. Agrawal, “Bouncing Scenario and Cosmic Dynam- ics in Modified Theories of Gravity,” [arXiv:2402.06895 [gr-qc]]

    arXiv

  8. [16]

    G. W. Horndeski, Second-order scalar-tensor field equa - tions in a four-dimensional space, Int. J. Theor. Phys. 10, 363–384 (1974)

    1974

  9. [17]

    Kobayashi, M

    T. Kobayashi, M. Yamaguchi and J. Yokoyama, Prog. Theor. Phys. 126, 511 (2011)

    2011

  10. [18]

    Rinaldi, Black holes with non-minimal derivative co u- pling, Phys

    M. Rinaldi, Black holes with non-minimal derivative co u- pling, Phys. Rev. D 86, 084048 (2012)

    2012

  11. [19]

    Minamitsuji, Solutions in the scalar-tensor theory with nonminimal derivative coupling, Phys

    M. Minamitsuji, Solutions in the scalar-tensor theory with nonminimal derivative coupling, Phys. Rev. D 89, 064017 (2014)

    2014

  12. [20]

    Anabalon, A

    A. Anabalon, A. Cisterna and J. Oliva, Asymptotically locally AdS and flat black holes in Horndeski theory, Phys. Rev. D 89, 084050 (2014)

    2014

  13. [21]

    Babichev, C

    E. Babichev, C. Charmousis, Dressing a black hole with a time-dependent Galileon, JHEP 08, 106 (2014)

    2014

  14. [22]

    Kobayashi and N

    T. Kobayashi and N. Tanahashi, Exact black hole so- lutions in shift symmetric scalar–tensor theories, PTEP 2014, 073E02 (2014)

    2014

  15. [23]

    Babichev, C

    E. Babichev, C. Charmousis, M. Hassaine, Charged Galileon black holes, JCAP 05, 031 (2015)

    2015

  16. [24]

    S. V. Sushkov, R. Korolev, Scalar wormholes with non- minimal derivative coupling, Class. Quant. Grav. 29, 085008 (2012)

    2012

  17. [25]

    R. V. Korolev,, S. V. Sushkov, Exact wormhole solu- tions with nonminimal kinetic coupling, Phys. Rev. D 90, 124025 (2014)

    2014

  18. [26]

    Cisterna, T

    A. Cisterna, T. Delsate, M. Rinaldi, Neutron stars in general second order scalar-tensor theory: The case of nonminimal derivative coupling, Phys. Rev. D 92, 044050 (2015)

    2015

  19. [27]

    Cisterna, T

    A. Cisterna, T. Delsate, L. Ducobu, and M. Rinaldi, Slowly rotating neutron stars in the nonminimal deriva- tive coupling sector of Horndeski gravity, Phys. Rev. D 93, 084046 (2016)

    2016

  20. [28]

    Maselli, H

    A. Maselli, H. O. Silva, M. Minamitsuji, E. Berti, Neu- tron stars in Horndeski gravity, Phys. Rev. D 93, 124056 (2016)

    2016

  21. [29]

    J. L. Bl´ azquez-Salcedo, K. Eickhoff, Axial quasinorma l modes of static neutron stars in the nonminimal deriva- tive coupling sector of Horndeski gravity: Spectrum and universal relations for realistic equations of state, Phys . Rev. D 97, 104002 (2018)

    2018

  22. [30]

    H. O. Silva, A. Maselli, M. Minamitsuji, E. Berti, Com- pact objects in Horndeski gravity, Int. J. Mod. Phys. D 25, 09, 1641006 (2016)

    2016

  23. [31]

    P. E. Kashargin, S. V. Sushkov, Anti-de Sitter neutron stars in the theory of gravity with non- minimal derivative coupling , JCAP 01, 005 (2023), [doi:10.1088/1475-7516/2023/01/005]

    2023 doi

  24. [32]

    S. V. Sushkov, Exact cosmological solutions with nonmin- imal derivative coupling , Phys. Rev. D80 (2009) 103505, [doi:10.1103/PhysRevD.80.103505]

    2009 doi

  25. [33]

    E. N. Saridakis and S. V. Sushkov, Quintessence and phantom cosmology with non-minimal derivative cou- pling, Phys. Rev. D81 (2010) 083510, [ arXiv:1002.3478], [doi:10.1103/PhysRevD.81.083510]

    2010 arXiv

  26. [34]

    S. V. Sushkov, Realistic cosmological scenario with non- minimal kinetic coupling , Phys. Rev. D85 (2012) 123520, [doi:10.1103/PhysRevD.85.123520]

    2012 doi

  27. [35]

    M. A. Skugoreva, S. V. Sushkov, A. V. Toporensky, Phys. Rev. D88 (2013) 083539

    2013

  28. [36]

    Matsumoto and S

    J. Matsumoto and S. V. Sushkov, JCAP 1511, no. 11, 047 (2015) [arXiv:1510.03264 [gr-qc]]

    2015 arXiv

  29. [37]

    A. A. Starobinsky, S. V. Sushkov, and M. S. Volkov, The screening Horndeski cosmologies , JCAP 1606 (2016), no. 06 007, [ doi:10.1088/1475-7516/2016/06/007]. 7

    2016 doi

  30. [38]

    A. A. Starobinsky, S. V. Sushkov, and M. S. Volkov, Anisotropy screening in Horndeski cosmologies , Phys. Rev. D 101 (2020), no. 6 064039, [ arXiv:1912.12320], [doi:10.1103/PhysRevD.101.064039]

    2020 arXiv

  31. [39]

    Galeev, R

    R. Galeev, R. Muharlyamov, A. A. Starobinsky, S. V. Sushkov, and M. S. Volkov, Anisotropic cosmological models in Horndeski gravity , Phys. Rev. D 103, 104015 (2021), [ arXiv:2102.10981], [doi:10.1103/PhysRevD.103.104015]

    2021 arXiv

  32. [40]

    S. V. Sushkov and R. Galeev, Cosmological models with arbitrary spatial curvature in the theory of grav- ity with nonminimal derivative coupling , Phys. Rev. D 108, 044028 (2023), doi:10.1103/PhysRevD.108.044028 [arXiv:2306.00611 [gr-qc]]

    2023 arXiv

  33. [41]

    Planck 2018 re- sults. VI. Cosmological parameters,

    N. Aghanim et al. [Planck], “Planck 2018 re- sults. VI. Cosmological parameters,” Astron. Astro- phys. 641, A6 (2020); [erratum: Astron. Astrophys. 652, C4 (2021)]. doi:10.1051/0004-6361/201833910, [arXiv:1807.06209 [astro-ph.CO]]

    2020 arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.