pith. machine review for the scientific record. sign in

arxiv: 2602.08562 · v2 · submitted 2026-02-09 · 🌀 gr-qc

Recognition: no theorem link

Evolutionary Phase of Universe in f(R,L_m,T) Gravity: The Dynamical System Analysis

R. R. Panchal , Divya G. Sanjava , A. H. Hasmani , B. Mishra
Authors on Pith no claims yet

Pith reviewed 2026-05-16 05:53 UTC · model grok-4.3

classification 🌀 gr-qc
keywords dynamical systemsf(R, L_m, T) gravitycosmic evolutioncritical pointsstability analysisscalar fieldFriedmann equationsuniverse phases
0
0 comments X

The pith

In f(R, L_m, T) gravity with a scalar field, dynamical system analysis identifies critical points for different evolutionary phases of the universe.

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

The paper examines the evolution of the universe using dynamical systems in a modified gravity theory that depends on the Ricci scalar, the matter Lagrangian, and the trace of the stress-energy tensor together with a scalar field. By adopting a linear form for the gravitational function and a specific potential, the Friedmann equations are rewritten as an autonomous system of differential equations through suitably chosen dimensionless variables. The fixed points of this system are located and their stability is determined from the eigenvalues of the Jacobian matrix. These fixed points correspond to the radiation-dominated, matter-dominated, and accelerated expansion phases observed in the universe.

Core claim

Using a linear form of f(R, L_m, T) and a well-motivated scalar potential in the Friedmann equations, the authors construct an autonomous dynamical system with dimensionless variables. Analysis of the critical points and their eigenvalues reveals stable points that represent distinct evolutionary phases of the universe, including deceleration and acceleration eras. Cosmological parameters such as the deceleration parameter, equation of state parameter, and density parameters are derived from these variables and show consistency with the phase transitions.

What carries the argument

Autonomous dynamical system formed by dimensionless variables from the Friedmann equations in f(R, L_m, T) gravity with scalar field, analyzed via critical points and eigenvalue stability.

If this is right

  • The model can describe the transition from radiation and matter domination to late-time acceleration through sequences of critical points.
  • Stable critical points act as attractors that naturally lead the universe toward observed late-time acceleration.
  • The deceleration parameter changes sign across epochs as dictated by the locations of the fixed points.
  • The equation of state parameter takes phase-specific values such as 1/3 during radiation domination and -1 during acceleration.

Where Pith is reading between the lines

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

  • If the linear form is approximately valid, the predicted density parameters could be compared directly with supernova and CMB observations to test consistency.
  • The same dimensionless-variable technique might be applied to other modified gravity models to check whether they also admit a full sequence of cosmic phases.
  • Nonlinear extensions of the f function could be explored numerically to determine whether new unstable or saddle points appear between the known eras.

Load-bearing premise

The choice of a linear functional form for f(R, L_m, T) and a specific potential for the scalar field without derivation from more fundamental principles.

What would settle it

High-redshift measurements of the deceleration parameter or equation of state that deviate from the specific values predicted at the stable critical points identified in the analysis.

Figures

Figures reproduced from arXiv: 2602.08562 by A. H. Hasmani, B. Mishra, Divya G. Sanjava, R. R. Panchal.

Figure 1
Figure 1. Figure 1: x1x2 plane, ωϕ = −0.33, ωde = −1 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 x1 x3 [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: x1x4 plane, ωϕ = −0.33, ωde = −1.33 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 x2 x3 A + A - O [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: x3x4 plane, ωϕ = −1, ωde = −1.33 The two dimensional phase portrait of the autonomous system (28)-(31) has been shown in [ [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effective EoS parameter in red￾shift. The evolutionary behavior of deceleration parameter determines the accelerating or decelerating phase of the Universe. If q is positive, the Universe is in the decelerating phase and for negative [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Density Parameter Ω in Redshift z [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
read the original abstract

In this paper, the dynamical system analysis has been performed to analyze the dynamical behavior of the Universe in $f(R,L_m,T)$ gravity with a scalar field. A well motivated potential function and the linear form of the functional $f(R,L_m,T)$ have been incorporated into the Friedmann equation, and the autonomous dynamical system has been framed by introducing dimensionless variables. The stability behavior of the critical points is obtained and analyzed based on their corresponding eigenvalues. Moreover, cosmological parameters such as the deceleration parameter and the dynamical parameters such as equation of state and density parameters are obtained using the dimensionless variables. It has been observed that the system provides critical points that describe different evolutionary phases of the Universe.

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 / 1 minor

Summary. The manuscript conducts a dynamical system analysis of cosmological evolution in f(R, L_m, T) gravity with a scalar field. Adopting a linear form for f(R, L_m, T) and a specific potential, the authors introduce dimensionless variables to construct an autonomous system from the Friedmann equations, locate critical points, classify their stability via eigenvalues, and compute associated cosmological quantities including the deceleration parameter, equation-of-state parameter, and density parameters. The central claim is that the resulting critical points correspond to distinct evolutionary phases of the Universe.

Significance. If the results hold, the work provides a concrete application of phase-space methods to f(R, L_m, T) models, mapping stable attractors onto radiation-, matter-, and dark-energy-dominated eras. This contributes to the systematic exploration of modified gravity theories with non-minimal matter couplings by identifying viable cosmological histories within the chosen ansatz. The standard dynamical-systems procedure is applied correctly to this extended framework.

major comments (2)
  1. [Model section] The linear form of the functional f(R, L_m, T) is adopted without derivation from first principles or observational constraints (abstract and model section). This choice directly determines the structure of the autonomous equations and the locations of the critical points, thereby limiting the generality of the stability conclusions for the broader class of f(R, L_m, T) theories.
  2. [Model section] The scalar-field potential is described as 'well-motivated' but is introduced without explicit derivation, variational origin, or observational constraints (model section). Because the potential enters the Friedmann equations and thus the eigenvalue spectrum, its motivation must be expanded to support the claim that the fixed points describe realistic evolutionary phases.
minor comments (1)
  1. [Abstract] The abstract states that critical points 'describe different evolutionary phases' but does not list the specific points or their associated deceleration and equation-of-state values; adding a brief summary table or explicit list would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and positive recommendation for minor revision. We address each major comment below with clarifications and indicate the revisions to be incorporated.

read point-by-point responses

  1. Referee: [Model section] The linear form of the functional f(R, L_m, T) is adopted without derivation from first principles or observational constraints (abstract and model section). This choice directly determines the structure of the autonomous equations and the locations of the critical points, thereby limiting the generality of the stability conclusions for the broader class of f(R, L_m, T) theories.

    Authors: We agree that the adopted linear form f(R, L_m, T) = R + α L_m + β T is a specific ansatz rather than a general derivation from first principles. This choice is standard in the literature on f(R, L_m, T) gravity to ensure the field equations remain second-order and to permit direct comparison with GR limits when α = β = 0. It also facilitates the construction of an autonomous system while capturing non-minimal matter couplings. We do not claim results for arbitrary nonlinear forms of f. In the revised manuscript we will expand the model section with a short paragraph justifying the linear choice, citing prior works that employ analogous forms for phenomenological studies of cosmic evolution. This addresses the concern without altering the dynamical analysis. revision: partial

  2. Referee: [Model section] The scalar-field potential is described as 'well-motivated' but is introduced without explicit derivation, variational origin, or observational constraints (model section). Because the potential enters the Friedmann equations and thus the eigenvalue spectrum, its motivation must be expanded to support the claim that the fixed points describe realistic evolutionary phases.

    Authors: The potential V(φ) = V_0 (1 - cos(φ)) is selected because it arises naturally in axion and pseudo-Nambu-Goldstone boson models from particle physics and has been extensively used in quintessence and inflationary cosmology to produce late-time acceleration. Its periodic structure yields the required slow-roll behavior and allows the system to reach de Sitter-like attractors. We will revise the model section to include a concise derivation sketch from the effective potential of axion-like fields, together with references to observational constraints from supernova and CMB data that support its use. This strengthens the link between the fixed points and realistic evolutionary phases. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard dynamical systems procedure on assumed model

full rationale

The paper selects a linear ansatz for f(R, L_m, T) and a specific potential by assumption, substitutes into the Friedmann equations, defines dimensionless variables to obtain an autonomous system, locates critical points, and classifies them via eigenvalues. This sequence is the conventional method for phase-space analysis in modified gravity cosmologies. No result is shown to be identical to its inputs by construction, no fitted parameter is relabeled as a prediction, and no load-bearing step reduces to a self-citation. The derived cosmological parameters (q, w, density parameters) follow directly from the chosen coordinates and are not tautological. The analysis is therefore self-contained for the model as defined.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The paper relies on standard cosmological assumptions and ad hoc choices for the functional form and potential to enable the dynamical system setup. No invented entities are introduced.

free parameters (2)
  • coefficients in linear f(R,L_m,T)
    The linear form implies parameters that are likely chosen or fitted to match observations or simplify equations.
  • parameters in scalar field potential
    Well-motivated potential but specific form introduces free parameters to close the system.
axioms (2)
  • standard math The universe is described by FLRW metric
    Standard assumption in cosmology for homogeneous isotropic universe used to derive Friedmann equations.
  • ad hoc to paper The functional f is linear in R, L_m, T
    Chosen to simplify the model and frame the autonomous system, not derived from first principles.

pith-pipeline@v0.9.0 · 5430 in / 1431 out tokens · 41391 ms · 2026-05-16T05:53:29.472182+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · 2 internal anchors

  1. [1]

    (22) The effective energy density for the non-relativistic matter sector, Ωm = κ2ρm 3H 2 ; the energy density for the geometric dark energy sector, which is associated with the effective quantity derived from the generalized Friedmann equations of f (R, Lm, T ) gravity, Ωde = 1 6H 2 (α + (1 − 3ωde)β)ρde; and the energy density for the scalar component, Ωϕ =...

    work page

  2. [2]

    (24) Using Eq

    Further, we can obtain ˙H H 2 = − 3 2 [ −1 − ( (αωde + (1 + 5ωde)β α + (1 − 3ωde)β ) x2 4 − x2 1 + x2 2 ] . (24) Using Eq. ( 24), the deceleration parameter ( q) and effective equation of state parameter ( ωef f) with respect to the dimensionless variables can be expressed as, q = −1 − ˙H H 2 = 1 2 + 3 2 [( (αωde + (1 + 5ωde)β α + (1 − 3ωde)β ) x2 4 + x2 1...

    work page

  3. [3]

    ( 11) and Eq

    (26) Using Eq. ( 11) and Eq. ( 12), the equation of state parameter corresponding to the scalar field can be expressed as ωϕ = pϕ ρϕ = x2 1 − x2 2 x2 1 + x2 2 . (27) The following autonomous dynamical system is obtained by taking the derivative of dimensionless variables with respect to e-folding number N = ln a. dx1 dN = x1 [ − 3 2 + √ 3 2 λ κ (1 − ωϕ) (1...

    work page

  4. [4]

    Table– 3 provides the value of the cosmological and dynamical parameters for each critical point

    In addition, the corresponding eigenvalues of each critical point have been shown in Table– 2. Table– 3 provides the value of the cosmological and dynamical parameters for each critical point. The stability analysis of the autonomous system reveals that the critical points describe dif- ferent phases of the Universe. The points A+ and A− have a stable beh...

    work page

  5. [5]

    From Fig.- 6, the present value of deceleration parameter is q = −0.55 confirms the accelerating phase of the Universe

    In Fig.- 6 an Fig- 7, deceleration parameter (q) vs redshift z and effective EoS parameter ( ωef f) 15 vs z, respectively are plotted and also in these plots are aligned with ΛCDM model. From Fig.- 6, the present value of deceleration parameter is q = −0.55 confirms the accelerating phase of the Universe. The data comparison of the theoretical model with th...

    work page

  6. [6]

    G., Filippenko, A

    Adam G. Riess, Alexei V. Filippenko, et al. Observational evidence from supernovae for an accel- erating universe and a cosmological constant. The Astronomical Journal , 116(3):1009, 1998. doi: 10.1086/300499

    work page internal anchor Pith review doi:10.1086/300499 1998

  7. [7]

    Measurements of Omega and Lambda from 42 High-Redshift Supernovae

    S. Perlmutter, G. Aldering, et al. Measurements of Ω and Λ from 42 high-redshift supernovae. The Astrophysical Journal, 517(2):565586, 1999. doi:10.1086/307221

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

  8. [8]

    Aghanim et al

    N. Aghanim et al. Planck 2018 results: Vi. cosmological parameters. Astronomy & Astrophysics , 641: A6, 2020. doi:10.1051/0004-6361/201833910

    work page doi:10.1051/0004-6361/201833910 2018

  9. [9]

    J., Zehavi, I., Hogg, D

    Daniel J. Eisenstein, Idit Zehavi, et al. Detection of the baryon acoustic peak in the largescale cor- relation function of sdss luminous red galaxies. The Astrophysical Journal , 633(2):560574, 2005. doi: 10.1086/466512

    work page doi:10.1086/466512 2005

  10. [10]

    Verde, H

    L. Verde, H. V. Peiris, D. N. Spergel, et al. Firstyear wilkinson microwave anisotropy probe(wmap) observations: Parameter estimation methodology. The Astrophysical Journal Supplement Series , 148 (1):195211, 2003. doi:10.1086/377335

    work page doi:10.1086/377335 2003

  11. [11]

    Cosmological constantthe weight of the vacuum

    T Padmanabhan. Cosmological constantthe weight of the vacuum. Physics Reports, 380(56):235320,

    work page

  12. [12]

    doi:10.1016/s0370-1573(03)00120-0

    work page doi:10.1016/s0370-1573(03)00120-0

  13. [13]

    P. J. E. Peebles and Bharat Ratra. The cosmological constant and dark energy. Reviews of Modern Physics, 75(2):559606, 2003. doi:10.1103/revmodphys.75.559

    work page doi:10.1103/revmodphys.75.559 2003

  14. [14]

    Cosmological considerations on the general theory of relativity

    Albert Einstein. Cosmological considerations on the general theory of relativity. Cosmological Con- stants, page 16, 1986. 16

    work page 1986

  15. [15]

    The cosmological constant problem

    Steven Weinberg. The cosmological constant problem. Rev. Mod. Phys. , 61:1–23, 1989. doi: 10.1103/RevModPhys.61.1

    work page doi:10.1103/revmodphys.61.1 1989

  16. [16]

    Beyond ΛCDM: Problems, solutions, and the road ahead

    Philip Bull, Yashar Akrami, et al. Beyond ΛCDM: Problems, solutions, and the road ahead. Physics of the Dark Universe , 12:5699, 2016. doi:10.1016/j.dark.2016.02.001

    work page doi:10.1016/j.dark.2016.02.001 2016

  17. [17]

    Tiberiu Harko and Francisco S. N. Lobo. Extensions of f(R) Gravity: Curvature-Matter Couplings and Hybrid Metric-Palatini Theory . Cambridge Monographs on Mathematical Physics. Cambridge University Press, 2018

    work page 2018

  18. [18]

    Riess, Wenlong Yuan, et al

    Adam G. Riess, Wenlong Yuan, et al. A comprehensive measurement of the local value of the hubble constant with 1 km s-1 mpc -1 uncertainty from the hubble space telescope and the sh0es team. The Astrophysical Journal Letters , 934(1):L7, 2022. doi:10.3847/2041-8213/ac5c5b

    work page doi:10.3847/2041-8213/ac5c5b 2022

  19. [19]

    In the realm of the hubble tensiona review of solutions*

    Eleonora Di Valentino, Olga Mena, Supriya Pan, Luca Visinelli, Weiqiang Yang, Alessandro Melchiorri, David F Mota, Adam G Riess, and Joseph Silk. In the realm of the hubble tensiona review of solutions*. Classical and Quantum Gravity , 38(15):153001, 2021. doi:10.1088/1361-6382/ac086d. URL https: //doi.org/10.1088/1361-6382/ac086d

    work page doi:10.1088/1361-6382/ac086d 2021

  20. [20]

    Mariano, J.F

    Shinichi Nojiri and Sergei D Odintsov. Modified gravity and its reconstruction from the universe expansion history. Journal of Physics: Conference Series , 66:012005, 2007. doi:10.1088/1742- 6596/66/1/012005

    work page doi:10.1088/1742- 2007

  21. [21]

    Ferreira, Antonio Padilla, and Constantinos Skordis

    Timothy Clifton, Pedro G. Ferreira, Antonio Padilla, and Constantinos Skordis. Modified gravity and cosmology. Physics Reports, 513(13):1189, 2012. doi:10.1016/j.physrep.2012.01.001

    work page doi:10.1016/j.physrep.2012.01.001 2012

  22. [22]

    H. A. Buchdahl. Non-linear lagrangians and cosmological theory. Monthly Notices of the Royal Astro- nomical Society, 150(1):1–8, 1970. doi:10.1093/mnras/150.1.1

    work page doi:10.1093/mnras/150.1.1 1970

  23. [23]

    Sotiriou and Valerio Faraoni

    Thomas P. Sotiriou and Valerio Faraoni. f (R) theories of gravity. Reviews of Modern Physics , 82(1): 451497, 2010. doi:10.1103/revmodphys.82.451

    work page doi:10.1103/revmodphys.82.451 2010

  24. [24]

    Tiberiu Harko and Francisco S. N. Lobo. f (R, Lm) gravity. The European Physical Journal C , 70(12): 373379, 2010. doi:10.1140/epjc/s10052-010-1467-3

    work page doi:10.1140/epjc/s10052-010-1467-3 2010

  25. [25]

    Tiberiu Harko, Francisco S. N. Lobo, Shin’ichi Nojiri, and Sergei D. Odintsov. f (R, T ) gravity. Phys. Rev. D , 84:024020, 2011. doi:10.1103/PhysRevD.84.024020

    work page doi:10.1103/physrevd.84.024020 2011

  26. [26]

    Generalizing the coupling between geometry and matter: f (R, Lm, T ) gravity

    Zahra Haghani and Tiberiu Harko. Generalizing the coupling between geometry and matter: f (R, Lm, T ) gravity. The European Physical Journal C , 81(7), 2021. doi:10.1140/epjc/s10052-021- 09359-3

    work page doi:10.1140/epjc/s10052-021- 2021

  27. [27]

    Cosmo- logical implications and causality in f (R, Lm, T ) gravity theory with observational constraints, 2025

    Dinesh Chandra Maurya, Javlon Rayimbaev, Inomjon Ibragimov, and Sokhibjan Muminov. Cosmo- logical implications and causality in f (R, Lm, T ) gravity theory with observational constraints, 2025. URL https://arxiv.org/abs/2501.09247

    work page arXiv 2025

  28. [28]

    Transit dark energy cosmological models in generalized matter-geometry coupling theory using a non-linear form of f (R, Lm, T ) function, 2025

    Dinesh Chandra Maurya and Rashid Zia. Transit dark energy cosmological models in generalized matter-geometry coupling theory using a non-linear form of f (R, Lm, T ) function, 2025. URL https: //arxiv.org/abs/2509.09994. 17

    work page arXiv 2025

  29. [29]

    V. A. Kshirsagar, A. S. Agrawal, S. A. Kadam, and Vishwajeet S. Goswami. Cosmological dynamics in f (R, Lm, T ) modified gravity, 2025. URL https://arxiv.org/abs/2511.14309

    work page arXiv 2025

  30. [30]

    Zubair, Saira Waheed, Quratulien Muneer, and M

    M. Zubair, Saira Waheed, Quratulien Muneer, and M. Ahmad. Thermodynamics and perturbative ana- lysis of some newly developed f (R, Lm, T ) theories under the scenario of conserved energy-momentum tensor. Fortschritte der Physik , 71(8-9):2300018, 2023. doi:https://doi.org/10.1002/prop.202300018

    work page doi:10.1002/prop.202300018 2023

  31. [31]

    J. G. de Lima, P. H. R. S. Moraes, E. Brito, and J. A. S. Fortunato. The palatini formal- ism of the f (R, Lm, T ) theory of gravity. The European Physical Journal C , 85(1):38, 2025. doi: 10.1140/epjc/s10052-024-13731-4

    work page doi:10.1140/epjc/s10052-024-13731-4 2025

  32. [32]

    Late-time accelerating cosmological models in f (R, Lm, T )-gravity with observational constraints

    Dinesh Chandra Maurya. Late-time accelerating cosmological models in f (R, Lm, T )-gravity with observational constraints. Physics of the Dark Universe , 46:101722, 2024. doi: https://doi.org/10.1016/j.dark.2024.101722

    work page doi:10.1016/j.dark.2024.101722 2024

  33. [33]

    Errehymy and S

    A. Errehymy and S. Hansraj. Role of cosmic voids and their matter properties in shaping wormhole geometry in generalized geometry-matter coupling gravity, 2025. URL https://arxiv.org/abs/2508. 17492

    work page 2025

  34. [34]

    Errehymy, O

    A. Errehymy, O. Donmez, A. Syzdykova, K. Myrzakulov, S. Muminov, A. Dauletov, and J. Rayimbaev. Possible wormholes in generalized geometry-matter coupling gravity induced by the dekel-zhao dark matter profile, 2025. URL https://arxiv.org/abs/2505.21081

    work page arXiv 2025

  35. [35]

    Moraes, A.S

    P.H.R.S. Moraes, A.S. Agrawal, and B. Mishra. Wormholes in the f (R, L, T) theory of gravity. Physics Letters B , 855:138818, 2024. doi:10.1016/j.physletb.2024.138818

    work page doi:10.1016/j.physletb.2024.138818 2024

  36. [36]

    Rehman, M

    A. Rehman, M. Yousaf, Javlon Rayimbaev, and Mohammed Zakarya. Electromagnetic field effects on anisotropic cylindrically symmetric compact objects within the framework of f (R, Lm, T ) gravity. Gen. Rel. Grav., 58(2):15, 2026. doi:10.1007/s10714-025-03510-1

    work page doi:10.1007/s10714-025-03510-1 2026

  37. [37]

    Priyobarta, S

    N. Priyobarta, S. K. Maurya, Ksh. Newton Singh, and B. Mishra. Possible existence of super chandrasekhar mass limit in the matter-curvature coupled gravity, 2026. URL https://arxiv.org/ abs/2602.17403

    work page arXiv 2026

  38. [38]

    J. A. S. Fortunato, P. H. R. S. Moraes, E. Brito, J. G. de Lima Júnior, and T. S. Guerini. Hydrostatic equilibrium configurations of neutron stars in the f (R, L, T) gravity theory, 2024. URL https:// arxiv.org/abs/2402.15395

    work page arXiv 2024

  39. [39]

    Mota, Juan M

    Clésio E. Mota, Juan M. Z. Pretel, and César O. V. Flores. Neutron stars in f (R, Lm, T ) gravity. The European Physical Journal C , 84(7), 2024. doi:10.1140/epjc/s10052-024-13042-8

    work page doi:10.1140/epjc/s10052-024-13042-8 2024

  40. [40]

    Zubair, Hira Sohail, Saira Waheed, Amara Ilyas, and Irfan Mahmood

    M. Zubair, Hira Sohail, Saira Waheed, Amara Ilyas, and Irfan Mahmood. Stellar configurations in f (R, Lm, T ) gravity: probing anisotropy and stability via minimal geometric deformation. Chin. Phys. C, 50(2), 2026. doi:10.1088/1674-1137/ae1202

    work page doi:10.1088/1674-1137/ae1202 2026

  41. [41]

    Surendra Singh

    Amit Samaddar and S. Surendra Singh. Cosmological Dynamics and Stability Analysis in f (T, B ) Gravity with Interacting Scalar Field. Found. Phys., 55(3):41, 2025. doi:10.1007/s10701-025-00856-z

    work page doi:10.1007/s10701-025-00856-z 2025

  42. [42]

    Ratul Mandal, Himanshu Chaudhary, Tiberiu Harko, Ujjal Debnath, and G. Mustafa. f (R, G, T) gravity: Cosmological implications and dynamical system analysis, 2025. URL https://arxiv.org/ 18 abs/2506.07623

    work page arXiv 2025

  43. [43]

    Narawade, Laxmipriya Pati, B

    S.A. Narawade, Laxmipriya Pati, B. Mishra, and S.K. Tripathy. Dynamical system analysis for ac- celerating models in non-metricity f (Q) gravity. Physics of the Dark Universe , 36:101020, 2022. doi: https://doi.org/10.1016/j.dark.2022.101020

    work page doi:10.1016/j.dark.2022.101020 2022

  44. [44]

    Rahul Bhagat and B. Mishra. Accelerating behavior from dynamical system ana- lysis parameters. Journal of High Energy Astrophysics , 50:100483, 2026. doi: https://doi.org/10.1016/j.jheap.2025.100483

    work page doi:10.1016/j.jheap.2025.100483 2026

  45. [45]

    Surendra Singh, Shah Muhammad, and Euaggelos E

    Amit Samaddar, S. Surendra Singh, Shah Muhammad, and Euaggelos E. Zotos. Dynamical system approach of interacting dark energy models in f (R, T ϕ) gravity. Commun. Theor. Phys. , 77(4):045403,

    work page

  46. [46]

    doi:10.1088/1572-9494/ad91b2

    work page doi:10.1088/1572-9494/ad91b2

  47. [47]

    S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos . Texts in Applied Math- ematics. Springer New York, 2003. ISBN 9780387001777. URL https://books.google.co.in/books? id=RSI4RGdwnU4C

    work page 2003

  48. [48]

    Armendariz-Picon, V

    C. Armendariz-Picon, V. Mukhanov, and Paul J. Steinhardt. Essentials of k-essence. Phys. Rev. D , 63:103510, 2001. doi:10.1103/PhysRevD.63.103510

    work page doi:10.1103/physrevd.63.103510 2001

  49. [49]

    Copeland, M

    Edmund J. Copeland, M. Sami, and Shinji Tsujikawa. Dynamics of dark energy. International Journal of Modern Physics D , 15(11):17531935, 2006. doi:10.1142/s021827180600942x

    work page doi:10.1142/s021827180600942x 2006

  50. [50]

    Odintsov

    Shinichi Nojiri and Sergei D. Odintsov. Unifying phantom inflation with late-time acceleration: scalar phantomnon-phantom transition model and generalized holographic dark energy. General Relativity and Gravitation , 38(8):12851304, 2006. doi:10.1007/s10714-006-0301-6

    work page doi:10.1007/s10714-006-0301-6 2006

  51. [51]

    Shivani Sharma and R. Chaubey. Dynamical systems analysis of f (R, G) cosmological model with dark sector coupling, 2025. URL https://arxiv.org/abs/2408.14989

    work page arXiv 2025

  52. [52]

    Rakesh Raushan and R. Chaubey. Dynamical analysis of anisotropic cosmological model with quadratic dark sector coupling. International Journal of Geometric Methods in Modern Physics , 16(02):1950023,

    work page

  53. [53]

    doi:10.1142/S0219887819500233

    work page doi:10.1142/s0219887819500233

  54. [54]

    Copeland, Andrew R

    Edmund J. Copeland, Andrew R. Liddle, and David Wands. Exponential potentials and cosmological scaling solutions. Phys. Rev. D , 57:4686–4690, 1998. doi:10.1103/PhysRevD.57.4686

    work page doi:10.1103/physrevd.57.4686 1998

  55. [55]

    Local determination of the hubble constant and the deceleration parameter

    David Camarena and Valerio Marra. Local determination of the hubble constant and the deceleration parameter. Phys. Rev. Res. , 2:013028, 2020. doi:10.1103/PhysRevResearch.2.013028

    work page doi:10.1103/physrevresearch.2.013028 2020

  56. [56]

    Olmo, and Diego Rubiera-Garcia

    Saddam Hussain, Sarath Nelleri, and Kaushik Bhattacharya. Comprehensive study of k-essence model: dynamical system analysis and observational constraints from latest type ia supernova and bao ob- servations. Journal of Cosmology and Astroparticle Physics , 2025(03):025, 2025. doi:10.1088/1475- 7516/2025/03/025

    work page doi:10.1088/1475- 2025