pith. machine review for the scientific record. sign in

arxiv: 2605.04123 · v1 · submitted 2026-05-05 · 🌀 gr-qc

Recognition: 4 theorem links

· Lean Theorem

Testing an anisotropic spinor field--based Modified Chaplygin Gas model in Kantowski--Sachs spacetime with observational constraints

Mahendra Goray , Bijan Saha
Authors on Pith no claims yet

Pith reviewed 2026-05-08 18:33 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Kantowski-Sachs spacetimeModified Chaplygin Gasnonlinear spinor fieldanisotropic cosmologyunified dark sectorobservational constraintsMCMC analysislate-time isotropization
0
0 comments X

The pith

The spinor field Modified Chaplygin Gas model in Kantowski-Sachs spacetime fits current observations while naturally incorporating early anisotropy that vanishes today.

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

The paper examines a cosmological model that couples a massless nonlinear spinor field to a Modified Chaplygin Gas inside an anisotropic Kantowski-Sachs spacetime. It constrains the free parameters with a Markov Chain Monte Carlo analysis of Pantheon+ supernovae, cosmic chronometers, DESI DR2 baryon acoustic oscillations, and CMB distance priors. The resulting best-fit values show late-time acceleration, a Hubble constant near 67-68 km/s/Mpc, and a shear parameter statistically consistent with zero. The model returns a lower chi-squared than Lambda CDM and is preferred by the Akaike Information Criterion, supporting the claim that this framework can unify dark matter and dark energy while allowing for transient anisotropy.

Core claim

The spinor field-based Modified Chaplygin Gas model in Kantowski-Sachs spacetime offers a viable framework that naturally incorporates anisotropy and a unified description of dark matter and dark energy, consistent with current observations, with the shear parameter becoming negligible at late times.

What carries the argument

The coupling of a massless nonlinear spinor field to the Modified Chaplygin Gas equation of state inside the Kantowski-Sachs metric, which evolves the anisotropy and the unified dark sector simultaneously.

If this is right

  • The model reproduces late-time acceleration with a present-day deceleration parameter near -0.49.
  • The shear parameter is driven to zero at late times, recovering an effectively isotropic universe.
  • The model yields a Hubble constant of 67-68 km/s/Mpc while fitting the combined supernova, chronometer, and baryon acoustic oscillation data.
  • It returns a lower minimum chi-squared and is favored by the Akaike Information Criterion over Lambda CDM.
  • The Modified Chaplygin Gas component supplies a single fluid description of both dark matter and dark energy.

Where Pith is reading between the lines

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

  • High-precision future surveys sensitive to shear at intermediate redshifts could directly test whether early anisotropy decays exactly as the spinor-MCG dynamics predict.
  • The same spinor coupling might be applied to other anisotropic metrics to explore whether the isotropization mechanism is generic or specific to Kantowski-Sachs geometry.
  • Because the model prefers a lower H0 value, it could be combined with additional early-universe physics to explore solutions to the Hubble tension without reintroducing large late-time anisotropy.

Load-bearing premise

The assumption that a massless nonlinear spinor field can be consistently coupled to the Modified Chaplygin Gas in Kantowski-Sachs spacetime to produce a physically motivated unified dark sector whose parameters remain stable under observational constraints.

What would settle it

A future measurement showing a statistically significant non-zero shear parameter at low redshift, or a Hubble constant firmly outside the 67-68 km/s/Mpc range from independent probes, would falsify the model's viability.

Figures

Figures reproduced from arXiv: 2605.04123 by Bijan Saha, Mahendra Goray.

Figure 1
Figure 1. Figure 1: Marginalized posterior distributions of the KS+Spinor MCG model parameters for the view at source ↗
Figure 2
Figure 2. Figure 2: Marginalized posterior distributions of the curved ΛCDM model parameters for the com view at source ↗
Figure 3
Figure 3. Figure 3: Marginalized posterior distributions of the flat ΛCDM model parameters for the combined view at source ↗
Figure 4
Figure 4. Figure 4: Bar plot comparing KS+Spinor MCG, curved ΛCDM, and flat ΛCDM models using view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of the Hubble parameter H(z) as a function of redshift z. The best-fit curves for the KS+Spinor MCG, curved ΛCDM, and flat ΛCDM models are compared with observational cosmic chronometer (CC) data points. approaches them from higher redshift and overlaps with the flat ΛCDM model near the transition redshift zt ≈ 0.61. 12 view at source ↗
Figure 6
Figure 6. Figure 6: Distance modulus µ(z) versus redshift z for KS+Spinor MCG and ΛCDM models, compared with Pantheon+ supernova data. 0.0 0.5 1.0 1.5 2.0 Redshift z 1.0 0.5 0.0 0.5 1.0 = o bs m o del KS+ Spinor MCG Curved CDM Flat CDM view at source ↗
Figure 7
Figure 7. Figure 7: Distance modulus residuals ∆µ versus redshift z for KS+Spinor MCG and ΛCDM models using Pantheon+ data. VI. Conclusion In this work, we investigated a massless nonlinear spinor field based Modified Chaplygin Gas (MCG) dark energy model in Kantowski–Sachs spacetime and constrained its parameters using recent cos￾13 view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of the effective equation of state parameter view at source ↗
Figure 9
Figure 9. Figure 9: Evolution of the deceleration parameter q(z) as a function of redshift z for the KS+Spinor MCG, curved ΛCDM, and flat ΛCDM models. mological data sets, namely Pantheon+, CC, DESI DR2, and CMB, across three different data combinations. For comparison, we also analyzed the curved and flat ΛCDM models using the same observational data. The MCMC analysis demonstrates that the KS + Spinor MCG model successfully… view at source ↗
read the original abstract

We investigate a cosmological model based on a massless nonlinear spinor field coupled to a Modified Chaplygin Gas (MCG) in the Kantowski--Sachs spacetime, aiming to probe anisotropies and unified dark sector dynamics. The model parameters are constrained using recent observational data, including Pantheon+, cosmic chronometers, DESI DR2, and CMB distance priors, via a Markov Chain Monte Carlo analysis. We find $H_0 \sim 67$--$68~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, while the shear parameter is consistent with zero, indicating an effectively isotropic Universe at late times. The model reproduces late-time cosmic acceleration with a present-day deceleration parameter $q_0 \sim -0.49$, and provides a good fit to the data, yielding a lower minimum $\chi^2$ than $\Lambda$CDM, and is favored by the Akaike Information Criterion. Overall, the spinor field MCG model in Kantowski--Sachs spacetime offers a viable framework that naturally incorporates anisotropy and a unified description of dark matter and dark energy, consistent with current observations.

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 investigates a cosmological model based on a massless nonlinear spinor field coupled to Modified Chaplygin Gas in Kantowski-Sachs spacetime. It performs MCMC constraints on the free parameters (MCG parameters A, B, alpha; spinor coupling; initial shear/anisotropy) using Pantheon+, cosmic chronometers, DESI DR2, and CMB distance priors. The reported results include H0 ~67-68 km/s/Mpc, shear consistent with zero at late times, q0 ~ -0.49, lower minimum chi^2 than LambdaCDM, and AIC preference for the model, leading to the claim that the framework naturally incorporates anisotropy and provides a unified dark sector description consistent with observations.

Significance. If the central claims hold after addressing the issues below, the work would demonstrate an observationally viable unified DM+DE model in an anisotropic background, with standard MCMC methodology applied to recent datasets. However, the reported consistency of shear with zero limits the demonstrated advantage of the Kantowski-Sachs choice over isotropic MCG models, reducing the novelty of the anisotropic incorporation.

major comments (2)
  1. [Abstract and MCMC analysis section] Abstract and results on MCMC constraints: the finding that the shear parameter is consistent with zero at late times directly undermines the central claim that the model 'naturally incorporates anisotropy' in a physically meaningful way. The Kantowski-Sachs metric introduces two independent scale factors, yet the data (Pantheon+, chronometers, DESI DR2, CMB priors) force the anisotropic degrees of freedom to vanish, reducing the dynamics to the isotropic limit without shown advantage for the unified spinor-MCG description.
  2. [Abstract and observational constraints section] MCMC analysis and abstract: no error budgets, covariance matrices, or explicit checks for parameter degeneracies are supplied. This leaves the claims of a 'good fit' and 'lower chi^2' only partially verifiable, as the circularity burden (all reported H0, q0, shear values obtained by direct fitting to the same datasets) cannot be fully assessed without these diagnostics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We have carefully addressed each major point below, providing clarifications and indicating revisions where the manuscript requires strengthening for verifiability and precision.

read point-by-point responses

  1. Referee: [Abstract and MCMC analysis section] Abstract and results on MCMC constraints: the finding that the shear parameter is consistent with zero at late times directly undermines the central claim that the model 'naturally incorporates anisotropy' in a physically meaningful way. The Kantowski-Sachs metric introduces two independent scale factors, yet the data (Pantheon+, chronometers, DESI DR2, CMB priors) force the anisotropic degrees of freedom to vanish, reducing the dynamics to the isotropic limit without shown advantage for the unified spinor-MCG description.

    Authors: We acknowledge that the posterior on the shear parameter being consistent with zero at late times indicates the model evolves toward an effectively isotropic state, in line with observational expectations. The Kantowski-Sachs setup nevertheless provides a general anisotropic background in which the spinor-MCG dynamics are solved; the MCMC results demonstrate that non-zero initial shear is allowed by the parameter space and decays naturally due to the field equations. This constitutes a built-in mechanism for anisotropy that is absent in purely isotropic MCG models. We have revised the abstract and the discussion section to qualify the claim as 'permits a natural incorporation of anisotropy that is consistent with late-time isotropy,' and we have added a brief comparison of the shear evolution against the corresponding isotropic MCG case to illustrate the dynamical distinction, even though the late-time limit coincides. revision: partial

  2. Referee: [Abstract and observational constraints section] MCMC analysis and abstract: no error budgets, covariance matrices, or explicit checks for parameter degeneracies are supplied. This leaves the claims of a 'good fit' and 'lower chi^2' only partially verifiable, as the circularity burden (all reported H0, q0, shear values obtained by direct fitting to the same datasets) cannot be fully assessed without these diagnostics.

    Authors: We agree that the absence of these diagnostics limits the transparency of the fit-quality claims. In the revised manuscript we now supply the full covariance matrix of the MCMC chains, one-sigma error budgets on all parameters (including A, B, α, the spinor coupling, and initial shear), and explicit degeneracy plots together with a short discussion of the principal correlations. While any cosmological parameter estimation is performed on the same datasets by construction, we have added a note on the use of independent data subsets (e.g., Pantheon+ alone versus the full combination) to assess robustness and reduce circularity concerns. revision: yes

Circularity Check

1 steps flagged

Fitted parameters to Pantheon+ and other datasets presented as model 'predictions' and 'findings' of anisotropy incorporation

specific steps
  1. fitted input called prediction [Abstract]
    "We find H_0 ∼ 67--68 km s^{-1} Mpc^{-1}, while the shear parameter is consistent with zero, indicating an effectively isotropic Universe at late times. The model reproduces late-time cosmic acceleration with a present-day deceleration parameter q_0 ∼ -0.49, and provides a good fit to the data, yielding a lower minimum χ² than ΛCDM, and is favored by the Akaike Information Criterion."

    H0, shear, q0 and χ² values are the direct output of MCMC parameter fitting to Pantheon+, cosmic chronometers, DESI DR2 and CMB priors. Reporting them as 'findings' and 'reproduces' makes the quoted results equivalent to the fitted inputs by construction rather than independent predictions from the spinor-MCG-KS dynamics.

full rationale

The paper derives the field equations for the massless nonlinear spinor coupled to MCG in Kantowski-Sachs metric independently. However, the central results (H0, q0, shear~0, χ² comparison) are obtained by MCMC fitting of free parameters directly to the same observational datasets used for constraints. These are then reported as 'we find' and 'reproduces' without independent verification, reducing the viability claims to the input data by construction. The anisotropy claim is further undercut as data force shear to zero, but no separate circularity in the metric setup itself.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on several fitted parameters whose values are not derived from first principles and on the assumption that the chosen coupling between spinor and MCG produces a stable unified fluid. No machine-checked proofs or external benchmarks are mentioned.

free parameters (3)
  • MCG parameters (A, B, alpha)
    Standard Modified Chaplygin Gas equation-of-state parameters fitted to data.
  • spinor coupling constant
    Strength of the nonlinear spinor interaction, adjusted to match observations.
  • initial shear and anisotropy parameters
    Kantowski-Sachs metric parameters whose late-time values are constrained by data.
axioms (2)
  • domain assumption The spinor field is massless and nonlinear.
    Stated in the model setup; required for the field to source the unified dark sector.
  • domain assumption Kantowski-Sachs metric is an appropriate background for late-time cosmology.
    Assumed to allow controlled anisotropy that can be tested against isotropy data.

pith-pipeline@v0.9.0 · 5506 in / 1554 out tokens · 63551 ms · 2026-05-08T18:33:06.991761+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

54 extracted references · 47 canonical work pages · 2 internal anchors

  1. [1]

    Heavens, The Cosmological Model: an overview and an outlook, J

    A. Heavens, The Cosmological Model: an overview and an outlook, J. Phys. Conf. Ser.120, 022001 (2008), doi:10.1088/1742-6596/120/2/022001

    work page doi:10.1088/1742-6596/120/2/022001 2008

  2. [2]

    Weinberg,Cosmology(Oxford University Press, Oxford, 2008)

    S. Weinberg,Cosmology(Oxford University Press, Oxford, 2008)

    2008

  3. [3]

    Dodelson,Modern Cosmology(Academic Press, San Diego, 2003)

    S. Dodelson,Modern Cosmology(Academic Press, San Diego, 2003)

    2003

  4. [4]

    2020a, Astron

    N. Aghanimet al.(Planck Collaboration), Astron. Astrophys.641, A6 (2020), doi:10.1051/0004-6361/201833910, arXiv:1807.06209

    work page doi:10.1051/0004-6361/201833910 2020

  5. [5]

    P. J. E. Peebles and B. Ratra, Rev. Mod. Phys.75, 559 (2003), doi:10.1103/RevModPhys.75.559, arXiv:astro-ph/0207347

    work page doi:10.1103/revmodphys.75.559 2003

  6. [6]

    Heavens,Statistical Techniques in Cosmology(Springer, 2009)

    A. Heavens,Statistical Techniques in Cosmology(Springer, 2009)

    2009

  7. [7]

    A. G. Riesset al., Astron. J.116, 1009 (1998), doi:10.1086/300499, arXiv:astro-ph/9805201

    work page Pith review doi:10.1086/300499 1998

  8. [8]

    1999, apj, 517, 565, doi: 10.1086/307221

    S. Perlmutteret al., Astrophys. J.517, 565 (1999), doi:10.1086/307221, arXiv:astro- ph/9812133

    work page internal anchor Pith review doi:10.1086/307221 1999

  9. [9]

    M., Jones , D

    D.M. Scolnic et al., Astrophys. J.859, 101 (2018), doi:10.3847/1538-4357/aab9bb, arXiv:1710.00845. 15

    work page doi:10.3847/1538-4357/aab9bb 2018

  10. [10]

    and Carr, Anthony and Zuntz, Joe and Kessler, Rick and Davis, Tamara M

    D. Brout et al., Astrophys. J.938, 110 (2022), doi:10.3847/1538-4357/ac8e04, arXiv:2202.04077

    work page doi:10.3847/1538-4357/ac8e04 2022

  11. [11]

    Peißker, M

    Planck Collaboration, Astron. Astrophys.571, A16 (2014), doi:10.1051/0004- 6361/201321591, arXiv:1303.5076

    work page doi:10.1051/0004- 2014

  12. [12]

    and Blanton, Michael R

    M. Tegmarket al., Phys. Rev. D69, 103501 (2004), doi:10.1103/PhysRevD.69.103501, arXiv:astro-ph/0310723

    work page doi:10.1103/physrevd.69.103501 2004

  13. [13]

    2001, MNRAS, 322, 2,

    S. Coleet al., Mon. Not. R. Astron. Soc.362, 505 (2005), doi:10.1111/j.1365- 2966.2005.09318.x, arXiv:astro-ph/0501174

    work page doi:10.1111/j.1365- 2005

  14. [14]

    Buryak, P.D

    M. Bartelmann and P. Schneider, Phys. Rept.340, 291 (2001), doi:10.1016/S0370- 1573(00)00082-X, arXiv:astro-ph/9912508

    work page doi:10.1016/s0370- 2001

  15. [15]

    Cosmology with Cosmic Shear Observations: A Review , shorttitle =

    M. Kilbinger, Rept. Prog. Phys.78, 086901 (2015), doi:10.1088/0034-4885/78/8/086901, arXiv:1411.0115

    work page doi:10.1088/0034-4885/78/8/086901 2015

  16. [16]

    2021, prd, 103, 083533, doi: 10.1103/PhysRevD.103.083533

    S. Alamet al., Phys. Rev. D103, 083533 (2021), doi:10.1103/PhysRevD.103.083533, arXiv:2007.08991

    work page doi:10.1103/physrevd.103.083533 2021

  17. [17]

    J.947, 85 (2023), doi:10.3847/1538-4357/acbfb8, arXiv:2208.08512

    DESI Collaboration, Astrophys. J.947, 85 (2023), doi:10.3847/1538-4357/acbfb8, arXiv:2208.08512

    work page doi:10.3847/1538-4357/acbfb8 2023

  18. [18]

    DESI Collaboration, Mon. Not. R. Astron. Soc.522, 2038 (2023), doi:10.1093/mnras/stad1136, arXiv:2306.06308

    work page doi:10.1093/mnras/stad1136 2038

  19. [19]

    DESI Collaboration et al.,(2025), https://doi.org/10.48550/arXiv.2503.14745

    work page internal anchor Pith review doi:10.48550/arxiv.2503.14745 2025

  20. [20]

    DESI Collaboration et al., Phys. Rev. D112, 083515 (2025), https://doi.org/10.1103/tr6y- kpc6, arXiv:2404.03000

    work page doi:10.1103/tr6y- 2025

  21. [21]

    1989, Reviews of Modern Physics, 61, 1, doi: 10.1103/RevModPhys.61.1

    S. Weinberg, Rev. Mod. Phys.61, 1 (1989), doi:10.1103/RevModPhys.61.1

    work page doi:10.1103/revmodphys.61.1 1989

  22. [22]

    S. M. Carroll, Living Rev. Relativ.4, 1 (2001), doi:10.12942/lrr-2001-1, arXiv:astro- ph/0004075

    work page doi:10.12942/lrr-2001-1 2001

  23. [23]

    A. G. Riesset al., Astrophys. J.876, 85 (2019), doi:10.3847/1538-4357/ab1422, arXiv:1903.07603

    work page Pith review doi:10.3847/1538-4357/ab1422 2019

  24. [24]

    Martínez et al., Prevalence of non-aromatic carbonaceous molecules in the inner regions of circumstellar envelopes, Nature Astronomy, 4, 97 (2020)

    L. Verde, T. Treu and A. G. Riess, Nature Astron.3, 891 (2019), doi:10.1038/s41550-019- 0902-0, arXiv:1907.10625

    work page doi:10.1038/s41550-019- 2019

  25. [25]

    E. J. Copeland, M. Sami and S. Tsujikawa, Int. J. Mod. Phys. D15, 1753 (2006), doi:10.1142/S021827180600942X, arXiv:hep-th/0603057

    work page doi:10.1142/s021827180600942x 2006

  26. [26]

    C. W. Misner, Astrophys. J.151, 431 (1968), doi:10.1086/149448

    work page doi:10.1086/149448 1968

  27. [27]

    G. F. R. Ellis and M. A. H. MacCallum, Commun. Math. Phys.12, 108 (1969), doi:10.1007/BF01645908

    work page doi:10.1007/bf01645908 1969

  28. [28]

    Saha, Phys

    B. Saha, Phys. Rev. D64, 123501 (2001), doi:10.1103/PhysRevD.64.123501, arXiv:gr- qc/0107013

    work page doi:10.1103/physrevd.64.123501 2001

  29. [29]

    P. A. R. Adeet al.(Planck Collaboration), Astron. Astrophys.594, A16 (2016), doi:10.1051/0004-6361/201526681, arXiv:1506.07135

    work page doi:10.1051/0004-6361/201526681 2016

  30. [30]

    Saadehet al., Phys

    D. Saadehet al., Phys. Rev. Lett.117, 131302 (2016), doi:10.1103/PhysRevLett.117.131302, arXiv:1605.07178. 16

    work page doi:10.1103/physrevlett.117.131302 2016

  31. [31]

    Kantowski and R

    R. Kantowski and R. K. Sachs, J. Math. Phys.7, 443 (1966), doi:10.1063/1.1704952

    work page doi:10.1063/1.1704952 1966

  32. [32]

    M. P. Ryan and L. C. Shepley,Homogeneous Relativistic Cosmologies(Princeton University Press, 1975)

    1975

  33. [33]

    Saha, Spinor field nonlinearity and space-time geometry, Phys

    B. Saha, Spinor field nonlinearity and space-time geometry, Phys. Part. Nucl.49, 146 (2018)

    2018

  34. [35]

    On consistency of the interacting (anti)holomorphic higher-spin sector

    M. Goray and B. Saha, Eur. Phys. J. C86, 19 (2026), https://doi.org/10.1140/epjc/s10052- 025-15230-6

    work page doi:10.1140/epjc/s10052- 2026

  35. [36]

    Saha, Nonlinear Spinor Fields in Bianchi type-Ispacetime: Problems and Possibilities, Astrophys

    B. Saha, Nonlinear Spinor Fields in Bianchi type-Ispacetime: Problems and Possibilities, Astrophys. Space Sci.357, 28 (2015), doi:10.1007/s10509-015-2271-9

    work page doi:10.1007/s10509-015-2271-9 2015

  36. [37]

    Fabbri, Conformal gravity with the most general ELKO matter, Phys

    L. Fabbri, Conformal gravity with the most general ELKO matter, Phys. Rev. D85, 047502 (2012), doi:10.1103/PhysRevD.85.047502, arXiv:1112.2404

    work page doi:10.1103/physrevd.85.047502 2012

  37. [38]

    N. J. Pop lawski, Nonsingular, big-bounce cosmology from spinor-torsion coupling, Phys. Rev. D85, 107502 (2012), doi:10.1103/PhysRevD.85.107502, arXiv:1111.4595

    work page doi:10.1103/physrevd.85.107502 2012

  38. [39]

    R. G. Torrence and W. E. Couch, Note on Kantowski-Sachs space-times, Gen. Relativ. Gravit. 20, 603 (1988), doi:10.1007/BF00758910

    work page doi:10.1007/bf00758910 1988

  39. [40]

    Krasnov, O

    M. Krasnov, O. Trivedi, and M. Khlopov, Kantowski-Sachs cosmological model with axion-like scalar field and dark energy, arXiv:2410.09571

    work page arXiv

  40. [41]

    Vinutha, K

    T. Vinutha, K. Niharika, and K. Sri Kavya, The study of Kantowski-Sachs perfect fluid cosmological model in modified gravity, arXiv:2301.01163

    work page arXiv

  41. [42]

    B. Saha, Spinor field in Kantowski-Sachs cosmology, inProceedings of the LXI All-Russian Conference on Problems in Dynamics, Particle Physics, Plasma Physics and Optoelectronics, RUDN University, Moscow, Russia, May 19–23 (2025), pp. 66–74

    2025

  42. [43]

    Ratra and P

    B. Ratra and P. J. E. Peebles, Phys. Rev. D37, 3406 (1988), doi:10.1103/PhysRevD.37.3406

    work page doi:10.1103/physrevd.37.3406 1988

  43. [44]

    R. R. Caldwell, R. Dave and P. J. Steinhardt, Phys. Rev. Lett.80, 1582 (1998), doi:10.1103/PhysRevLett.80.1582, arXiv:astro-ph/9708069

    work page doi:10.1103/physrevlett.80.1582 1998

  44. [45]

    A. Y. Kamenshchik, U. Moschella and V. Pasquier, Phys. Lett. B511, 265 (2001), doi:10.1016/S0370-2693(01)00571-8, arXiv:gr-qc/0103004

    work page doi:10.1016/s0370-2693(01)00571-8 2001

  45. [46]

    M. C. Bento, O. Bertolami and A. A. Sen, Phys. Rev. D66, 043507 (2002), doi:10.1103/PhysRevD.66.043507, arXiv:gr-qc/0202064

    work page doi:10.1103/physrevd.66.043507 2002

  46. [47]

    H. B. Benaoum, arXiv:hep-th/0205140

    work page arXiv

  47. [48]

    Debnath, A

    U. Debnath, A. Banerjee and S. Chakraborty, Class. Quant. Grav.21, 5609 (2004), doi:10.1088/0264-9381/21/23/019, arXiv:gr-qc/0411015

    work page doi:10.1088/0264-9381/21/23/019 2004

  48. [49]

    J. Lu, Y. Gui and X. Zhang, Eur. Phys. J. C63, 349 (2009), doi:10.1140/epjc/s10052-009- 1102-6, arXiv:0806.0676

    work page doi:10.1140/epjc/s10052-009- 2009

  49. [52]

    Saikawa, J

    M. Morescoet al., J. Cosmol. Astropart. Phys.05, 014 (2016), doi:10.1088/1475- 7516/2016/05/014, arXiv:1601.01701

    work page doi:10.1088/1475- 2016

  50. [53]

    Four New Observational $H(z)$ Data From Luminous Red Galaxies of Sloan Digital Sky Survey Data Release Seven

    C. Zhanget al., Res. Astron. Astrophys.14, 1221 (2014), doi:10.1088/1674-4527/14/10/002, arXiv:1207.4541

    work page Pith review doi:10.1088/1674-4527/14/10/002 2014

  51. [54]

    Constraints on the redshift dependence of the dark energy potential

    J. Simon, L. Verde and R. Jimenez, Phys. Rev. D71, 123001 (2005), doi:10.1103/PhysRevD.71.123001, arXiv:astro-ph/0412269

    work page Pith review doi:10.1103/physrevd.71.123001 2005

  52. [55]

    Baryon acoustic oscillations in the Ly forest of BOSS DR11 quasars

    T. Delubacet al., Astron. Astrophys.574, A59 (2015), doi:10.1051/0004-6361/201423969, arXiv:1404.1801

    work page doi:10.1051/0004-6361/201423969 2015

  53. [56]

    DESI Collaboration, Phys. Rev. D112, 083516 (2025)

    2025

  54. [57]

    DESI Collaboration, Phys. Rev. D112, 083514 (2025), arXiv:2503.14739. 18

    work page arXiv 2025