pith. sign in

arxiv: 2605.27324 · v1 · pith:KBL3M6COnew · submitted 2026-05-26 · 🌀 gr-qc

Reconstructing the cosmic expansion in f(R, L_(m)) gravity via parametrized Hubble function constraints

Khomesh R. Patle , G. P. Singh This is my paper

Pith reviewed 2026-06-29 15:33 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(R, L_m) gravityparametrized Hubble parametercosmic chronometersPantheon supernovaedeceleration parameterenergy conditionsthermodynamic viabilitystatefinder diagnostics
0
0 comments X

The pith

Three Hubble parametrizations in f(R, L_m) gravity fit cosmic chronometer and supernova data while confirming thermodynamic viability.

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

The paper constructs three cosmological models by embedding parametrized forms of the Hubble rate H(z) inside the modified gravity theory with the specific choice f(R, L_m) = R/2 + L_m^λ. Bayesian fits to cosmic chronometer and joint Pantheon datasets determine the model parameters, after which the evolution of the deceleration parameter, energy density, pressure, equation of state, energy conditions, and statefinder diagnostics is examined. Thermodynamic consistency is checked via the behavior of temperature and entropy density, and the derived age of the universe is compared with observations. A sympathetic reader would care because the approach supplies concrete, observationally constrained alternatives to standard cosmology that incorporate possible curvature-matter coupling without separate dark-energy fields.

Core claim

Within f(R, L_m) gravity using the functional form f = R/2 + L_m^λ, three distinct redshift-dependent parametrizations of the Hubble parameter are introduced and constrained via chi-squared minimization on cosmic chronometer and Pantheon data. The resulting models describe a universe whose deceleration parameter changes sign at late times, whose equation-of-state parameter approaches values consistent with acceleration, and whose energy conditions remain satisfied. Temperature and entropy density evolve in a manner that preserves thermodynamic viability, while the computed age of the universe matches late-time astronomical estimates.

What carries the argument

The functional form f(R, L_m) = R/2 + L_m^λ together with three specific H(z) parametrizations that allow direct reconstruction of the expansion history and subsequent derivation of all cosmological quantities from the modified Friedmann equations.

Load-bearing premise

The chosen functional form of f(R, L_m) and the three specific Hubble parametrizations are sufficient to represent the full dynamics of the modified gravity theory without hidden inconsistencies that would invalidate the fits.

What would settle it

A high-redshift Hubble measurement lying outside the 1-sigma bands predicted by all three models after the current CC+Pantheon fits would falsify the reconstruction.

Figures

Figures reproduced from arXiv: 2605.27324 by G. P. Singh, Khomesh R. Patle.

Figure 1
Figure 1. Figure 1: Comparison of the best-fit H(z) profiles of the proposed models with the ΛCDM model. 5.2 Pantheon supernova observational dataset In the present analysis, we further employ the Pantheon compilation consisting of 1048 Type Ia supernova (SNIa) data points distributed over the redshift interval 0.01 < z < 2.26 [79]. The Pantheon sample is con￾structed by combining observations from several major supernova sur… view at source ↗
Figure 2
Figure 2. Figure 2: For Model-I: Marginalized 1σ and 2σ confidence contours together with the median estimates of H0, ζ and η obtained from the joint dataset. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: For Model-II: Marginalized 1σ and 2σ confidence contours together with the median estimates of H0, ζ and η obtained from the joint dataset. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: For Model-III: Marginalized 1σ and 2σ confidence contours together with the median estimates of H0, ζ and η obtained from the joint dataset. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: For Model-I: Plot of q(z) with z. −        − −  − − [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: For Model-II: Plot of q(z) with z. expansion stage toward the currently accelerating epoch. By employing the median best-fit values of the model parameters, the present values of the deceleration parameter for Model-I are obtained as q0 = −0.5323 for the CC dataset and q0 = −0.5338 for the joint dataset. In the case of Model-II, the corresponding values are q0 = −0.5108 and q0 = −0.5254, while Model-III yi… view at source ↗
Figure 7
Figure 7. Figure 7: For Model-III: Plot of q(z) with z. −        [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: For Model-I: Plot of energy density (ρ) with z. −        − − − − [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: For Model-II: Plot of energy density (ρ) with z. −        − − [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: For Model-III: Plot of energy density (ρ) with z. −        − − [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: For Model-I: Plot of EoS parameter (ω) with z. −       [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: For Model-II: Plot of EoS parameter (ω) with z. 6.3 Analysis of energy conditions The point-wise energy conditions, defined at a given spacetime point and governed solely by the stress energy tensor, can be written as [89–91]: • NEC: The null energy condition is satisfied when the relation ρeff + peff ≥ 0 holds, indicating a non￾negative combination of the effective energy density and pressure. • WEC: The… view at source ↗
Figure 16
Figure 16. Figure 16: For Model-III: Plot of EoS parameter (ω) with z. • SEC: The strong energy condition holds when the inequalities ρeff + peff ≥ 0 and ρeff + 3peff ≥ 0 are simultaneously satisfied. The SEC, characterized by the inequality ρeff +3peff ≥ 0, is intimately connected to the Raychaudhuri equa￾tion and plays a central role in governing the dynamical evolution of the universe [92]. Within the standard cosmological … view at source ↗
Figure 17
Figure 17. Figure 17: For Model-I: Plot of the evolution of energy condition components with z. −        [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: For Model-II: Plot of the evolution of energy condition components with z. statefinder parameters {r,s} are defined as follows r = ... a aH3 = q+2q 2 + (1+z) dq dz , (45) s = r −1 3(q− 1 2 ) , where q 6= 1 2 . (46) The evolutionary dynamics of different dark energy models discussed in the literature can be efficiently char￾acterized through the statefinder pair {r,s}: • In the Chaplygin gas (CG) scenario,… view at source ↗
Figure 19
Figure 19. Figure 19: For Model-III: Plot of the evolution of energy condition components with z. − − − − −            [PITH_FULL_IMAGE:figures/full_fig_p020_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: For Model-I: Plot of s and r plane. 6.5 Thermodynamic evolution of the universe and entropy analysis To study the thermodynamic aspects of the universe in f(R,Lm) gravity, we employ the laws of thermody￾namics, starting with the first law for an ideal fluid enclosed in a volume V [95, 96]. T ds = d(Vρ) + pdV, (47) we can rewrite it as follows: T ds = d(V(ρ + p))−V d p, (48) and using the thermodynamic rel… view at source ↗
Figure 21
Figure 21. Figure 21: For Model-II: Plot of s and r plane. − − − −            [PITH_FULL_IMAGE:figures/full_fig_p021_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: For Model-III: Plot of s and r plane. −        "            " !      !      [PITH_FULL_IMAGE:figures/full_fig_p021_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: For Model-I: Plot of temperature with z. −        [PITH_FULL_IMAGE:figures/full_fig_p021_23.png] view at source ↗
Figure 25
Figure 25. Figure 25: For Model-II: Plot of temperature with z. −        [PITH_FULL_IMAGE:figures/full_fig_p022_25.png] view at source ↗
Figure 27
Figure 27. Figure 27: For Model-III: Plot of temperature with z. −        [PITH_FULL_IMAGE:figures/full_fig_p022_27.png] view at source ↗
read the original abstract

We probe the cosmic expansion scenario within the framework of $f(R, L_{m})$ gravity by employing a well-motivated functional form of $f(R, L_{m}) = \frac{R}{2} + L_{m}^{\lambda}$. Specifically, we introduce three novel cosmological models formulated in terms of the redshift-dependent Hubble parameter $H(z)$, offering deeper insights into the underlying cosmic dynamics. The models are further utilized to investigate the expansion history of the universe and the evolution of several cosmological parameters. By using the Bayesian methods based on the $\chi^{2}$-minimization technique, the median values of the model parameters are determined for the cosmic chronometer (CC) and joint (CC+Pantheon) datasets. A comprehensive study of the deceleration parameter, energy density, pressure and the equation of state parameter is carried out to understand the universe's evolution. Additionally, the validity of the energy conditions and the behavior of the statefinder diagnostic are thoroughly examined. Finally, the thermodynamic viability of the models is confirmed through the evolution of temperature and entropy density, and the estimated age of the universe further exemplifies good agreement with late-time astronomical 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 / 2 minor

Summary. The paper examines cosmic expansion within f(R, L_m) gravity using the specific form f(R, L_m) = R/2 + L_m^λ. It introduces three parametrized H(z) models, constrains their parameters via χ² minimization on cosmic chronometer (CC) and joint CC+Pantheon datasets using Bayesian methods, and then derives the deceleration parameter, energy density, pressure, equation-of-state parameter, energy conditions, statefinder diagnostics, temperature and entropy density evolution, and universe age from the best-fit H(z).

Significance. If the central fits are robust and the derived quantities are correctly computed, the work supplies concrete observational bounds on a non-minimally coupled modified-gravity model and shows consistency with late-time data. The provision of explicit H(z) parametrizations and joint-dataset constraints is a concrete contribution, though the predictive power is reduced because most examined quantities follow algebraically from the fitted H(z) rather than constituting independent tests.

major comments (2)
  1. [Abstract and thermodynamic analysis] Abstract and thermodynamic analysis: the claim that thermodynamic viability is confirmed via the evolution of temperature and entropy density assumes the standard relations T ∝ 1/a and s ∝ a³ (or equivalent) that follow from ∇_μ T^μν = 0. The chosen f(R, L_m) = R/2 + L_m^λ produces a non-zero divergence of the effective stress-energy tensor, implying a modified continuity equation with an extra force term. No correction for this non-conservation appears to be applied to the reported T(z) and s(z) curves, rendering the viability confirmation insecure for the quoted best-fit parameters.
  2. [Abstract and sections on cosmological parameters] Abstract and sections on cosmological parameters: the reported evolution of the deceleration parameter, equation-of-state parameter, and energy conditions is obtained by direct substitution of the fitted H(z) parameters into the standard expressions. These quantities are therefore algebraic consequences of the data fit rather than independent predictions of the modified-gravity dynamics, weakening the claim that the models successfully describe the underlying cosmic evolution beyond the Hubble fit itself.
minor comments (2)
  1. [Abstract] The abstract states that median parameter values are determined but provides no explicit error budgets, covariance matrices, or discussion of possible post-hoc selection effects in the three chosen H(z) forms.
  2. [Model definitions] Notation for the three H(z) parametrizations should be introduced with explicit functional forms and the number of free parameters per model stated clearly before the fitting results are presented.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major points below.

read point-by-point responses

  1. Referee: [Abstract and thermodynamic analysis] Abstract and thermodynamic analysis: the claim that thermodynamic viability is confirmed via the evolution of temperature and entropy density assumes the standard relations T ∝ 1/a and s ∝ a³ (or equivalent) that follow from ∇_μ T^μν = 0. The chosen f(R, L_m) = R/2 + L_m^λ produces a non-zero divergence of the effective stress-energy tensor, implying a modified continuity equation with an extra force term. No correction for this non-conservation appears to be applied to the reported T(z) and s(z) curves, rendering the viability confirmation insecure for the quoted best-fit parameters.

    Authors: We agree that the non-minimal coupling implies a non-zero divergence of the effective stress-energy tensor and a modified continuity equation. The reported T(z) and s(z) curves were obtained with the standard relations without explicit correction for the extra force term. We will revise the abstract, the thermodynamic section, and the associated discussion to qualify the analysis as an approximate check and to note this limitation explicitly. revision: yes

  2. Referee: [Abstract and sections on cosmological parameters] Abstract and sections on cosmological parameters: the reported evolution of the deceleration parameter, equation-of-state parameter, and energy conditions is obtained by direct substitution of the fitted H(z) parameters into the standard expressions. These quantities are therefore algebraic consequences of the data fit rather than independent predictions of the modified-gravity dynamics, weakening the claim that the models successfully describe the underlying cosmic evolution beyond the Hubble fit itself.

    Authors: We acknowledge that the deceleration parameter, EoS parameter, and energy conditions are computed from the best-fit H(z) using the standard (GR) expressions. These quantities therefore test consistency of the fitted expansion history with late-time data rather than constituting independent dynamical predictions derived from the modified field equations. We will revise the abstract and the relevant sections to clarify this distinction and to frame the results as constraints on the parametrized models within the f(R, L_m) framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper parametrizes H(z), fits its parameters to CC and joint CC+Pantheon data via chi-squared minimization, then computes derived quantities (q(z), w(z), energy conditions, T(z), s(z), age) by direct substitution into the standard expressions. This is standard cosmological reconstruction from a fitted expansion history rather than a self-referential derivation. No quoted equations show a fitted input renamed as an independent prediction, no self-citation load-bearing on a uniqueness theorem, and no ansatz smuggled via prior work by the same authors. The thermodynamic analysis uses the usual T and s evolution formulas; any mismatch with the model's non-conservation is a correctness issue, not a circular reduction of the claimed viability to the input fit by construction. The derivation chain remains self-contained against external data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Central claims rest on the ad-hoc functional form, the three chosen H(z) parametrizations, and the assumption that chi-squared minima on the cited datasets yield physically meaningful constraints; no independent evidence is supplied for any of these choices.

free parameters (2)
  • λ
    Exponent in L_m^λ term, adjusted to data
  • H(z) model parameters
    Free coefficients in each of the three redshift-dependent Hubble parametrizations, fitted via chi-squared
axioms (2)
  • domain assumption FLRW metric describes the background cosmology
    Invoked implicitly when writing H(z) and deriving cosmological parameters
  • ad hoc to paper f(R, L_m) = R/2 + L_m^λ is the appropriate modified-gravity action
    Chosen without derivation or comparison to other forms

pith-pipeline@v0.9.1-grok · 5743 in / 1425 out tokens · 39721 ms · 2026-06-29T15:33:00.648350+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

96 extracted references · 95 canonical work pages · 8 internal anchors

  1. [1]

    A. G. Riess, A. V . Filippenko, P . Challis, A. Clocchiatti , A. Diercks et al., Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, Astronomical Journal, 116, 1009- 1038 (1998) https://doi.org/10.1086/300499

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

  2. [2]

    Perlmutter, G

    S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P . N ugent et al., Measurements of Ω and Λ from 42 High-Redshift Supernovae, Astrophysical Journal, 517, 565–586 (1999) https://doi.org/10.1086/307221

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

  3. [3]

    Aghanim, Y

    N. Aghanim, Y . Akrami, M. Ashdown, J. Aumont, C. Baccigal upi, et al., Planck 2018 results. VI. Cosmological parameters, Astronomy and Astro physics, 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910

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

  4. [4]

    Weinberg, The cosmological constant problem, Review s of Modern Physics, 61, 1 (1989) https://doi.org/10.1103/RevModPhys.61.1

    S. Weinberg, The cosmological constant problem, Review s of Modern Physics, 61, 1 (1989) https://doi.org/10.1103/RevModPhys.61.1

    work page doi:10.1103/revmodphys.61.1 1989

  5. [5]

    Di V alentino, O

    E. Di V alentino, O. Mena, S. Pan, L. Visinelli, W. Y ang, et al., In the realm of the Hubble tension—a review of solutions, Classical and Quantu m Gravity, 38, 153001 (2021) https://doi.org/10.1088/1361-6382/ac086d

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

  6. [6]

    S. M. Carroll, The cosmological constant, Living Review s in Relativity, 4, 1-56 (2001) https://doi.org/10.12942/lrr-2001-1

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

  7. [7]

    Kerner, Cosmology without singularity and nonlinear gravitational Lagrangians, General Relativity and Gravitation, 14, 453–469 (1982) https://doi.org/10.1007/BF00756329

    R. Kerner, Cosmology without singularity and nonlinear gravitational Lagrangians, General Relativity and Gravitation, 14, 453–469 (1982) https://doi.org/10.1007/BF00756329

    work page doi:10.1007/bf00756329 1982

  8. [8]

    H. A. Buchdahl, Non-linear Lagrangians and cosmologica l theory, Monthly Notices of the Royal Astro- nomical Society, 150, 1-8 (1970) https://doi.org/10.1093/mnras/150.1.1 25

    work page doi:10.1093/mnras/150.1.1 1970

  9. [9]

    Nojiri, S

    S. Nojiri, S. D. Odintsov, Unified cosmic history in modifi ed gravity: from f (R) theory to Lorentz non-invariant models, Physics Reports, 505, 59-144 (2011) https://doi.org/10.1016/j.physrep.2011.04.001

    work page doi:10.1016/j.physrep.2011.04.001 2011

  10. [10]

    Nojiri, S

    S. Nojiri, S. D. Odintsov, V . K. Oikonomou, Modified grav ity theories on a nut- shell: Inflation, bounce and late-time evolution, Physics R eports, 692, 1-104 (2017) https://doi.org/10.1016/j.physrep.2017.06.001

    work page internal anchor Pith review doi:10.1016/j.physrep.2017.06.001 2017

  11. [11]

    Harko, F

    T. Harko, F. S. N. Lobo, S. Nojiri, S. D. Odintsov, f (R,T ) gravity, Physical Review D,84, 024020 (2011) https://doi.org/10.1103/PhysRevD.84.024020

    work page doi:10.1103/physrevd.84.024020 2011

  12. [12]

    Capozziello, M

    Yi-Fu Cai, S. Capozziello, M. De Laurentis, E. N. Sarida kis, f (T ) teleparal- lel gravity and cosmology, Reports on Progress in Physics, 79, 106901 (2016) https://doi.org/10.1088/0034-4885/79/10/106901

    work page doi:10.1088/0034-4885/79/10/106901 2016

  13. [13]

    Capozziello, V

    S. Capozziello, V . F. Cardone, H. Farajollahi, A. Ravan pak, Cosmography in f (T ) gravity, Physical Review D, 84, 043527 (2011) https://doi.org/10.1103/PhysRevD.84.043527

    work page doi:10.1103/physrevd.84.043527 2011

  14. [14]

    Capozziello, R

    S. Capozziello, R. D’Agostino, O. Luongo, Extended gra vity cosmography, International Journal of Modern Physics D, 28, 1930016 (2019) https://doi.org/10.1142/S0218271819300167

    work page doi:10.1142/s0218271819300167 2019

  15. [15]

    Bamba, S

    K. Bamba, S. D. Odintsov, L. Sebastiani, S. Zerbini, Fin ite-time future singularities in modified Gauss- Bonnet and f (R,G) gravity and singularity avoidance, The European Physical J ournal C, 67, 295-310 (2010) https://doi.org/10.1140/epjc/s10052-010-1292-8

    work page doi:10.1140/epjc/s10052-010-1292-8 2010

  16. [16]

    Capozziello, V

    S. Capozziello, V . De Falco, C. Ferrara, The role of the b oundary term in f (Q,B) symmetric teleparallel gravity,The European Physical Jou rnal C, 83, 915 (2023) https://doi.org/10.1140/epjc/s10052-023-12072-y

    work page doi:10.1140/epjc/s10052-023-12072-y 2023

  17. [17]

    A. R. Lalke, G. P . Singh, A. Singh, Late-time accelerati on from ekpyrotic bounce in f (Q,T ) gravity, International Journal of Geometric Methods in Mod ern Physics, 20, 2350131 (2023) https://doi.org/10.1142/S0219887823501311

    work page doi:10.1142/s0219887823501311 2023

  18. [18]

    Kotambkar, G

    S. Kotambkar, G. P . Singh, R. Kelkar, B. K. Bishi, Anisot ropic Bianchi type I cosmological models with generalized Chaplygin gas and dynamical gravitational and cosmological constants, Communications in Theoretical Physics, 67, 222 (2017) https://doi.org/10.1088/0253-6102/67/2/222

    work page doi:10.1088/0253-6102/67/2/222 2017

  19. [19]

    G. P . Singh, R. V . Deshpande, T. Singh, Viscous cosmolog ical models with particle creation in Brans-Dicke theory, Astrophysics and space sci ence, 282, 489–498 (2002) https://doi.org/10.1023/A:1020963219962

    work page doi:10.1023/a:1020963219962 2002

  20. [20]

    G. K. Goswami, R. Rani, J. K. Singh, A. Pradhan, FLRW cosm ology in Weyl type f (Q) gravity and observational constraints, Journal of High Ene rgy Astrophysics, 43, 105–113 (2024) https://doi.org/10.1016/j.jheap.2024.06.011

    work page doi:10.1016/j.jheap.2024.06.011 2024

  21. [21]

    K. R. Patle, G. P . Singh, R. Garg, Dynamical constraints on variable vac- uum energy in Brans-Dicke theory, arXiv preprint arXiv:260 1.00419, (2026) https://doi.org/10.48550/arXiv.2601.00419

    work page doi:10.48550/arxiv.2601.00419 2026

  22. [22]

    M. B. V arela, O. Bertolami, Is cosmological data sugges ting a nonminimal cou- pling between matter and gravity?, Physics of the Dark Unive rse, 48, 101861 (2025) https://doi.org/10.1016/j.dark.2025.101861

    work page doi:10.1016/j.dark.2025.101861 2025

  23. [23]

    K. N. Singh, G. R. P . Teruel, S. K. Maurya, T. Chowdhury, F . Rahaman, Conservative worm- holes in generalized K(R,T ) function, Journal of High Energy Astrophysics, 44, 132–145 (2024) https://doi.org/10.1016/j.jheap.2024.09.009 26

    work page doi:10.1016/j.jheap.2024.09.009 2024

  24. [24]

    Singh, G

    A. Singh, G. P . Singh, A. Pradhan, Cosmic dynamics and qu alitative study of Rastall model with spatial curvature, International Journal of Mod ern Physics A, 37, 2250104 (2022) https://doi.org/10.1142/S0217751X22501044

    work page doi:10.1142/s0217751x22501044 2022

  25. [25]

    Hulke, G

    N. Hulke, G. P . Singh, B. K. Bishi, A. Singh, V ariable Cha plygin gas cosmolo- gies in f (R,T ) gravity with particle creation, New Astronomy, 77, 101357 (2020) https://doi.org/10.1016/j.newast.2020.101357

    work page doi:10.1016/j.newast.2020.101357 2020

  26. [26]

    G. P . Singh, R. Garg, A. Singh, A generalized Λ CDM model with parameterized Hubble parameter in particle creation, viscous and f (R) model framework, International Journal of Geometric Metho ds in Modern Physics, 2550111 (2025) https://doi.org/10.1142/S0219887825501117

    work page doi:10.1142/s0219887825501117 2025

  27. [27]

    B. K. Shukla, S. Sahlu, D. Sofuo˘ glu, P . Mishra, A. H. Alf edeel, Multi-components fluid in f (R,T ) gravity with observational constraints, The European Phys ical Journal Plus, 140, 1–14 (2025) https://doi.org/10.1140/epjp/s13360-025-06200-8

    work page doi:10.1140/epjp/s13360-025-06200-8 2025

  28. [28]

    Harko, F

    T. Harko, F. S. N. Lobo, f (R,Lm) gravity, The European Physical Journal C, 70, 373–379 (2010) https://doi.org/10.1140/epjc/s10052-010-1467-3

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

  29. [29]

    Faraoni, Cosmology in scalar tensor gravity, Spring er (2004) https://doi.org/10.1007/978-1-4020-1989-0

    V . Faraoni, Cosmology in scalar tensor gravity, Spring er (2004) https://doi.org/10.1007/978-1-4020-1989-0

    work page doi:10.1007/978-1-4020-1989-0 2004

  30. [30]

    Zhang, Behaviour of f (R) gravity in the solar system, galaxies, and clusters, Physic al Review D, 76, 024007 (2007) https://doi.org/10.1103/PhysRevD.76.024007

    P . Zhang, Behaviour of f (R) gravity in the solar system, galaxies, and clusters, Physic al Review D, 76, 024007 (2007) https://doi.org/10.1103/PhysRevD.76.024007

    work page doi:10.1103/physrevd.76.024007 2007

  31. [31]

    General Theory of Relativity: Will it survive the next decade?

    O. Bertolami, J. P´ aramos, S. G. Turyshev, General Theory of Relativity: Will it survive the next decade?, in: Lasers, Clocks and Drag-Free Control: Exploration of Re lativistic Gravity in Space, Springer, 27–74 (2008) https://doi.org/10.48550/arXiv.gr-qc/0602016

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.gr-qc/0602016 2008

  32. [32]

    Rahaman, S

    F. Rahaman, S. Ray, M. Kalam, M. Sarker, Do Solar system t ests permit higher dimen- sional general relativity?, International Journal of Theo retical Physics, 48, 3124–3138 (2009) https://doi.org/10.1007/s10773-009-0110-2

    work page doi:10.1007/s10773-009-0110-2 2009

  33. [33]

    Nojiri, S

    S. Nojiri, S. D. Odintsov, Gravity assisted dark energy dominance and cosmic acceleration, Physics Letters B, 599, 137–142 (2004) https://doi.org/10.1016/j.physletb.2004.08.045

    work page doi:10.1016/j.physletb.2004.08.045 2004

  34. [34]

    Allemandi, A

    G. Allemandi, A. Borowiec, M. Francaviglia, S. D. Odint sov, Dark energy dominance and cosmic acceleration in first-order formalism, Physical Review D, 72, 063505 (2005) https://doi.org/10.1103/PhysRevD.72.063505

    work page doi:10.1103/physrevd.72.063505 2005

  35. [35]

    Manna, A

    G. Manna, A. Panda, A. Karmakar, S. Ray, M. R. Islam, f (R,Lx)-gravity in the context of dark energy with power law expansion and energy conditions, Chin ese Physics C, 47, 025101 (2023) https://doi.org/10.1088/1674-1137/ac9fbe

    work page doi:10.1088/1674-1137/ac9fbe 2023

  36. [36]

    F. S. N. Lobo, T. Harko, Extended f (R,Lm) theories of gravity, THE THIRTEENTH MARCEL GROSS- MANN MEETING, 1164–1166 (2015) https://doi.org/10.48550/arXiv.1211.0426

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1211.0426 2015

  37. [37]

    L. V . Jaybhaye, R. Solanki, S. Mandal, P . K. Sahoo, Cosmo logy in f (R,Lm) gravity, Physics Letters B, 831, 137148 (2022) https://doi.org/10.1016/j.physletb.2022.137148

    work page doi:10.1016/j.physletb.2022.137148 2022

  38. [38]

    Pradhan, D

    A. Pradhan, D. C. Maurya, G. K. Goswami, A. Beesham, Mode ling transit dark energy in f (R,Lm) gravity, International Journal of Geometric Methods in Mod ern Physics, 20, 2350105 (2023) https://doi.org/10.1142/S0219887823501050

    work page doi:10.1142/s0219887823501050 2023

  39. [39]

    Koussour, N

    M. Koussour, N. Myrzakulov, J. Rayimbaev, A. H. A. Alfed eel, H. M. Elkhair, Bouncing behavior in f (R,Lm) gravity: Phantom crossing and energy conditions, Internat ional Journal of Geometric Methods in Modern Physics, 21, 2450184 (2024) https://doi.org/10.1142/S0219887824501846 27

    work page doi:10.1142/s0219887824501846 2024

  40. [40]

    Mustafa, F

    G. Mustafa, F. Javed, S. K. Maurya, M. Govender, A. Salee m, Dynamical stability of new wormhole solutions via cold dark matter and solitonic quantum wave ha los in f (R,Lm) gravity, Physics of the Dark Universe, 45, 101508 (2024) https://doi.org/10.1016/j.dark.2024.101508

    work page doi:10.1016/j.dark.2024.101508 2024

  41. [41]

    Myrzakulova, M

    S. Myrzakulova, M. Koussour, N. Myrzakulov, Investiga ting the dark energy phenomenon in f (R,Lm) cosmological models with observational constraints, Phys ics of the Dark Universe, 43, 101399 (2024) https://doi.org/10.1016/j.dark.2023.101399

    work page doi:10.1016/j.dark.2023.101399 2024

  42. [42]

    N. S. Kavya, V . V enkatesha, S. Mandal, P . K. Sahoo, Const raining anisotropic cos- mological model in f (R,Lm) Gravity, Physics of the Dark Universe, 38, 101126 (2022) https://doi.org/10.1016/j.dark.2022.101126

    work page doi:10.1016/j.dark.2022.101126 2022

  43. [43]

    Y . K. Devi, S. Narawade, B. Mishra, Constraining parame ters for the accelerat- ing universe in f (R,Lm) gravity, Physics of the Dark Universe, 46, 101640 (2024) https://doi.org/10.1016/j.dark.2024.101640

    work page doi:10.1016/j.dark.2024.101640 2024

  44. [44]

    Zeyauddin, A

    M. Zeyauddin, A. Dixit, A. Pradhan, Anisotropic dark en ergy models in f (R,Lm)-gravity, International Journal of Geometric Methods in Modern Physi cs, 21, 2450038 (2024) https://doi.org/10.1142/S0219887824500385

    work page doi:10.1142/s0219887824500385 2024

  45. [45]

    D. C. Maurya, Bianchi-I dark energy cosmological model in f (R,Lm)-gravity, In- ternational Journal of Geometric Methods in Modern Physics , 21, 2450072 (2024) https://doi.org/10.1142/S0219887824500725

    work page doi:10.1142/s0219887824500725 2024

  46. [46]

    Sahlu, A

    S. Sahlu, A. H. Alfedeel, A. Abebe, The cosmology of f (R,Lm) gravity: constraining the background and perturbed dynamics, The European Physic al Journal C, 84, 982 (2024) https://doi.org/10.1140/epjc/s10052-024-13307-2

    work page doi:10.1140/epjc/s10052-024-13307-2 2024

  47. [47]

    V . K. Bhardwaj, S. Ray, Cosmological model in the framew ork of f (R,Lm) gravity with quadratic equation of state parameter, Physics of the D ark Universe, 101930 (2025) https://doi.org/10.1016/j.dark.2025.101930

    work page doi:10.1016/j.dark.2025.101930 2025

  48. [48]

    L. V . Jaybhaye, S. Mandal, P . K. Sahoo, Constraints on en ergy conditions in f (R,Lm) gravity, International Journal of Geometric Methods in Mod ern Physics, 19, 2250050 (2022) https://doi.org/10.1142/S0219887822500505

    work page doi:10.1142/s0219887822500505 2022

  49. [49]

    Shukla, R

    A. Shukla, R. Raushan, R. Chaubey, Dynamical Systems An alysis of f (R,Lm) Grav- ity Model, International Journal of Geometric Methods in Mo dern Physics, 2550118 (2025) https://doi.org/10.1142/S021988782550118X

    work page doi:10.1142/s021988782550118x 2025

  50. [50]

    Myrzakulov, O

    Y . Myrzakulov, O. Donmez, G. D. A. Yildiz, E. Gudekli, S. Muminov et al., Linear redshift parametriza- tion of deceleration parameter in f (R,Lm) gravity, Physics of the Dark Universe, 45, 101545 (2024) https://doi.org/10.1016/j.dark.2024.101545

    work page doi:10.1016/j.dark.2024.101545 2024

  51. [51]

    J. K. Singh, A. Singh, H. Balhara, J. R. L. Santos, The con sequence of higher-order curvature-based constraints on f (R,Lm) gravity, Annals of Physics, 469, 169781 (2024) https://doi.org/10.1016/j.aop.2024.169781

    work page doi:10.1016/j.aop.2024.169781 2024

  52. [52]

    Chaudhary, J

    S. Chaudhary, J. Kumar, S. K. Maurya, S. Kiroriwal, A. Az iz, On the existence and stability of traversable wormhole solutions with novel shapefunctions in the framew ork of f (R,Lm) gravity, Communications in Theoretical Physics, 76, 055403 (2024) https://doi.org/10.1088/1572-9494/ad3544

    work page doi:10.1088/1572-9494/ad3544 2024

  53. [53]

    Y . B. Wu, Y . Y . Zhao, Y . Y . Jin, L. L. Lin, J. B. Lu et al., Con straints of energy conditions and DK instability criterion on f (R,Lm) gravity models, Modern Physics Letters A, 29, 1450089 (2014) https://doi.org/10.1142/S0217732314500898 28

    work page doi:10.1142/s0217732314500898 2014

  54. [54]

    N. S. Kavya, V . V enkatesha, G. Mustafa, P . K. Sahoo, S. V . D. Rashmi, Static traversable wormhole solutions in f (R,Lm) gravity, Chinese Journal of Physics, 84, 1–11 (2023) https://doi.org/10.1016/j.cjph.2023.05.002

    work page doi:10.1016/j.cjph.2023.05.002 2023

  55. [56]

    G´ omez-V alent, L

    A. G´ omez-V alent, L. Amendola, H0 from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression met hod, Journal of Cosmology and Astroparti- cle Physics, 04, 051 (2018) https://doi.org/10.1088/1475-7516/2018/04/051

    work page doi:10.1088/1475-7516/2018/04/051 2018

  56. [57]

    Koussour, S

    M. Koussour, S. K. J. Pacif, M. Bennai, P . K. Sahoo, A New P arametrization of Hubble Parameter in f (Q) Gravity, Fortschritte der Physik, 71, 2200172 (2023) https://doi.org/10.1002/prop.202200172

    work page doi:10.1002/prop.202200172 2023

  57. [58]

    J. K. Singh, R. Nagpal, FLRW cosmology with EDSFD parame trization, The European Physical Journal C, 80, 295 (2020) https://doi.org/10.1140/epjc/s10052-020-7827-8

    work page doi:10.1140/epjc/s10052-020-7827-8 2020

  58. [59]

    T. Y . He, J. J. Yin, Z. Y . Wang, Z. W. Han, R. J. Y ang, A new pa rametrization of Hubble function and Hubble tension, Journal of Cosmology and Astro particle Physics, 2024, 028 (2024) https://doi.org/10.1088/1475-7516/2024/09/028

    work page doi:10.1088/1475-7516/2024/09/028 2024

  59. [60]

    N. Roy, S. Goswami, S. Das, Quintessence or phantom: Stu dy of scalar field dark energy models through a general parametrization of the Hubble parameter, Physics of the Dark Universe, 36, 101037 (2022) https://doi.org/10.1016/j.dark.2022.101037

    work page doi:10.1016/j.dark.2022.101037 2022

  60. [61]

    Ryden, Introduction to Cosmology, Addison-Wesley S an Francisco, (2003)

    B. Ryden, Introduction to Cosmology, Addison-Wesley S an Francisco, (2003)

    2003

  61. [62]

    Harko, F

    T. Harko, F. S. N. Lobo, Generalised curvature-matter c ouplings in modified gravity, Galaxies, 2, 410– 465 (2014) https://doi.org/10.3390/galaxies2030410

    work page doi:10.3390/galaxies2030410 2014

  62. [63]

    Harko, F

    T. Harko, F. S. N. Lobo, J. P . Mimoso, D. Pav´ on, Gravitat ional induced particle production through a nonminimal curvature–matter coupling, The Europ ean Physical Journal C, 75, 1–15 (2015) https://doi.org/10.1140/epjc/s10052-015-3620-5

    work page doi:10.1140/epjc/s10052-015-3620-5 2015

  63. [64]

    Shafieloo, A

    A. Shafieloo, A. G. Kim, E. V . Linder, Model independent t ests of cosmic growth versus expansion, Physical Review D, 87, 023520 (2013) https://doi.org/10.1103/PhysRevD.87.023520

    work page doi:10.1103/physrevd.87.023520 2013

  64. [65]

    Banerjee, S

    N. Banerjee, S. Das, Acceleration of the universe with a simple trigonometric potential, General Relativ- ity and Gravitation, 37, 1695–1703 (2005) https://doi.org/10.1007/s10714-005-0152-6

    work page doi:10.1007/s10714-005-0152-6 2005

  65. [66]

    Cunha, J

    J. Cunha, J. A. S. d. Lima, Transition redshift: new kine matic constraints from su- pernovae, Monthly Notices of the Royal Astronomical Societ y, 390, 210–217 (2008) https://doi.org/10.1111/j.1365-2966.2008.13640.x

    work page doi:10.1111/j.1365-2966.2008.13640.x 2008

  66. [67]

    Escamilla-Rivera, A

    C. Escamilla-Rivera, A. N´ ajera, Dynamical dark energ y models in the light of gravitational- wave transient catalogues, Journal of Cosmology and Astrop article Physics, 2022, 060 (2022) https://doi.org/10.1088/1475-7516/2022/03/060

    work page doi:10.1088/1475-7516/2022/03/060 2022

  67. [68]

    Myrzakulov, M

    N. Myrzakulov, M. Koussour, A. Mussatayeva, Quintesse nce-like features in the late-time cosmolog- ical evolution of f (Q) symmetric teleparallel gravity, Chinese Journal of Physic s, 85, 345–358 (2023) https://doi.org/10.1016/j.cjph.2023.07.003

    work page doi:10.1016/j.cjph.2023.07.003 2023

  68. [69]

    Nagpal, S

    R. Nagpal, S. K. J. Pacif, F. Atamurotov, R. Pati, Dark se ctor interactions: Prob- ing the Hubble parameter and the sound horizon, Annals of Phy sics, 483, 170249 (2025) https://doi.org/10.1016/j.aop.2025.170249 29

    work page doi:10.1016/j.aop.2025.170249 2025

  69. [70]

    A. K. Y adav, S. R. Bhoyar, M. C. Dhabe, S. H. Shekh, N. Ahma d, Reconstructing f (Q) gravity from parameterization of the Hubble parameter and observationa l constraints, Journal of High Energy Astro- physics, 43, 114–125 (2024) https://doi.org/10.1016/j.jheap.2024.06.012

    work page doi:10.1016/j.jheap.2024.06.012 2024

  70. [71]

    S. K. J. Pacif, R. Myrzakulov, S. Myrzakul, Reconstruct ion of cosmic history from a simple parametriza- tion of H, International Journal of Geometric Methods in Mod ern Physics, 14, 1750111 (2017) https://doi.org/10.1142/S0219887817501110

    work page doi:10.1142/s0219887817501110 2017

  71. [72]

    W., Lang, D., & Goodman, J

    D. Foreman-Mackey, D. W. Hogg, D. Lang, J. Goodman, emce e: the MCMC hammer, Publications of the Astronomical Society of the Pacific, 125, 306 (2013) https://doi.org/10.1086/670067

    work page doi:10.1086/670067 2013

  72. [73]

    Simon, L

    J. Simon, L. V erde, R. Jimenez, Constraints on the redsh ift dependence of the dark energy potential, Physical Review D, 71, 123001 (2005) https://doi.org/10.1103/PhysRevD.71.123001

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

  73. [74]

    G. S. Sharov, V . O. V asiliev, How predictions of cosmological models depend on Hubble parameter data sets, arXiv preprint arXiv:1807.07323 (2018) https://doi.org/10.26456/mmg/2018-611

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.26456/mmg/2018-611 2018

  74. [75]

    Stern, R

    D. Stern, R. Jimenez, L. V erde, M. Kamionkowski, S. A. St anford, Cosmic chronometers: constraining the equation of state of dark energy. I: H(z) measurements, Journal of Cosmology and Astroparticle Physics, 2010, 008 (2010) https://doi.org/10.1088/1475-7516/2010/02/008

    work page doi:10.1088/1475-7516/2010/02/008 2010

  75. [76]

    M. Moresco, Raising the bar: new constraints on the Hubb le parameter with cosmic chronome- ters at z 2, Monthly Notices of the Royal Astronomical Society: Lette rs, 450, L16–L20 (2015) https://doi.org/10.1093/mnrasl/slv037

    work page internal anchor Pith review doi:10.1093/mnrasl/slv037 2015

  76. [77]

    Jimenez, A

    R. Jimenez, A. Loeb, Constraining cosmological parame ters based on relative galaxy ages, The Astro- physical Journal, 573, 37 (2002) https://doi.org/10.1086/340549

    work page doi:10.1086/340549 2002

  77. [78]

    Mandal, A

    S. Mandal, A. Singh, R. Chaubey, Cosmic evolution of hol ographic dark energy in f (Q,T ) gravity, International Journal of Geometric Methods in Mod ern Physics, 20, 2350084 (2023) https://doi.org/10.1142/S0219887823500846

    work page doi:10.1142/s0219887823500846 2023

  78. [79]

    D. M. Scolnic, D. O. Jones, A. Rest, Y . C. Pan, R. Chornock et al., The complete light- curve sample of spectroscopically confirmed SNe Ia from Pan- STARRS1 and cosmological con- straints from the combined Pantheon sample, The Astrophysi cal Journal, 859, 101 (2018) https://doi.org/10.3847/1538-4357/aab9bb

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

  79. [80]

    A. G. Riess, R. P . Kirshner, B. P . Schmidt, S. Jha, P . Chal lis et al., BVRI light curves for 22 type Ia supernovae, The Astronomical Journal, 117, 707 (1999) https://doi.org/10.1086/300738

    work page doi:10.1086/300738 1999

  80. [81]

    Hicken, W

    M. Hicken, W. M. Wood-V asey, S. Blondin, P . Challis, S. J ha et al., Improved dark energy con- straints from 100 new CfA supernova type Ia light curves, The Astrophysical Journal, 700, 1097 (2009) https://doi.org/10.1088/0004-637X/700/2/1097

    work page doi:10.1088/0004-637x/700/2/1097 2009

Showing first 80 references.