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arxiv: 2605.11623 · v1 · submitted 2026-05-12 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Cosmology of f(Q,L_m) gravity with Holographic Ricci Dark Energy: Early-Time Inflation and Late-Time Acceleration and RGUP Corrected Observables

Khandro K Chokyi , Abdel Nasser Tawfik , Surajit Chattopadhyay
Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:13 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(Q,L_m) gravityholographic Ricci dark energyStarobinsky inflationRGUP correctionsearly-time accelerationlate-time accelerationmodified gravity cosmologycosmic expansion
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The pith

A single polynomial form of f(Q, L_m) gravity produces both early Starobinsky-like inflation from its quadratic term and late-time acceleration when paired with holographic Ricci dark energy.

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

The paper examines whether one geometric theory can replace separate mechanisms for the two accelerated epochs of the universe. It adopts a specific polynomial f(Q, L_m) that lets the quadratic piece dominate at high curvature to drive inflation while the linear and coupling terms, together with an added holographic dark-energy fluid, govern the late expansion. Background equations are solved to show smooth Hubble evolution and an equation of state that settles near minus one. Constraints from supernova, cosmic-chronometer and BAO data leave the matter-geometry coupling weakly bounded and compatible with no extra coupling. In the early universe the same function yields a Starobinsky-like phase whose spectral index and tensor ratio match Planck limits, with only small further shifts from relativistic generalized-uncertainty corrections.

Core claim

Within the chosen f(Q, L_m) = -Q + alpha Q^2 + 2 L_m + beta Q L_m, the quadratic non-metricity term alone supplies a Starobinsky-like inflationary background whose predicted n_s and r lie inside Planck 2018 bounds; at late times the same function, supplemented by holographic Ricci dark energy, produces stable accelerated expansion whose effective equation of state approaches the de Sitter value; the matter-geometry coupling beta remains consistent with zero under current data, and relativistic generalized-uncertainty corrections induce only sub-leading changes to the running of the spectral index.

What carries the argument

The minimal polynomial f(Q, L_m) = -Q + alpha Q^2 + 2 L_m + beta Q L_m, whose quadratic piece dominates at early high-curvature epochs while the remaining terms plus holographic Ricci dark energy control late-time dynamics.

If this is right

  • The quadratic term supplies a purely geometric inflationary phase without an extra inflaton field.
  • Late-time acceleration emerges from the interplay of the linear non-metricity term, the matter coupling and the holographic dark-energy density.
  • Bayesian constraints show beta is consistent with the Lambda-CDM limit, implying the extra coupling is not required by current observations.
  • RGUP momentum corrections leave the background expansion intact but shift the running of the spectral index by a small amount.
  • The effective equation of state evolves smoothly toward minus one at late times.

Where Pith is reading between the lines

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

  • If the same function works across both epochs, separate scalar-field sectors for inflation and dark energy could become unnecessary in this class of models.
  • Future CMB experiments that tighten the running of the spectral index could directly test the size of the RGUP correction.
  • Analogous curvature-dependent dominance might be explored in other non-metricity or teleparallel extensions to see whether the two-epoch unification persists.

Load-bearing premise

The specific polynomial dependence chosen for f(Q, L_m) is assumed to capture the relevant physics across all curvature regimes.

What would settle it

A future measurement of the running of the spectral index that lies outside the narrow band allowed by the RGUP-corrected Starobinsky-like phase, or a failure of the late-time Hubble evolution to fit the combined Pantheon, cosmic-chronometer and DESI BAO data when alpha and beta are varied.

Figures

Figures reproduced from arXiv: 2605.11623 by Abdel Nasser Tawfik, Khandro K Chokyi, Surajit Chattopadhyay.

Figure 1
Figure 1. Figure 1: Time evolution of key cosmological quantities in the reconstructed [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The behaviour of EoS parameter with respect to cosmic time [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Corner plot for the parameters (β, M). The posterior shows strong degeneracy in β, which accumulates at the lower prior boundary, while M remains sharply constrained. This behaviour indicates that current late-time data do not meaningfully constrain the matter–geometry coupling. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Constraints in the (ns, r) plane at k = 0.002 Mpc−1 from Planck, BK14, and BAO datasets. The black points denote the predictions of the high-curvature f(Q, Lm) model for N∗ = 50, 55, 60. • a geometrically motivated trigger for inflation; • predictions that match well with the outcomes of Planck 2018 [124] and BK14 [94] observational studies; • a single framework in which inflation and late-time acceleratio… view at source ↗
Figure 5
Figure 5. Figure 5: Constraints on ns and r from Planck 2018 and BK18 (68% and 95% CL). We compare the RGUP model (purple square, β = 0.05) against standard Starobinsky inflation (orange triangle) and other benchmark models at N = 60. The inset highlights the suppression of the tensor ratio in the RGUP model relative to the standard Starobinsky attractor. 32 [PITH_FULL_IMAGE:figures/full_fig_p032_5.png] view at source ↗
read the original abstract

This study investigates a cosmological scenario within the f(Q,L_m) gravity framework to explore whether one geometric model can simultaneously describe the early and late-time accelerated epochs. Motivated by the recently proposed f(Q,L_m) gravity framework by Hazarika et al. [Phys. Dark Universe 50 (2025) 102092], we adopt a minimal polynomial form, f(Q,L_m) = -Q + alpha Q^2 + 2L_m + beta QL_m, and the late-time dynamics are reconstructed by introducing Holographic Ricci Dark Energy (HRDE) as an effective fluid. The resulting background evolution demonstrates smooth accelerated expansion, stable Hubble parameter behavior, and an effective equation of state that approaches the de Sitter regime. Bayesian analysis utilizing Pantheon supernovae, cosmic chronometer, and DESI BAO data reveals that the matter-geometry coupling parameter beta is weakly constrained and remains consistent with the LambdaCDM limit. In the high-curvature regime characteristic of the early Universe, the quadratic non-metricity term alpha Q^2 dominates the dynamics, resulting in a Starobinsky-like inflationary phase driven solely by geometric effects with predicted n_s and r values consistent with Planck 2018 observations. Furthermore, quantum-gravity-inspired corrections are examined through a Relativistic Generalized Uncertainty Principle (RGUP), implemented as a momentum-dependent deformation of the effective spacetime metric. These corrections maintain the geometric inflationary background while introducing minor perturbative shifts in higher-order inflationary observables, specifically the running of the spectral index. Overall, these findings indicate that the f(Q,L_m) framework offers a dynamically consistent geometric model in which early and late cosmic acceleration arise from distinct curvature regimes, with RGUP effects causing sub-leading modifications.

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

1 major / 2 minor

Summary. This paper investigates cosmology in the f(Q, L_m) gravity theory with the specific polynomial form f(Q, L_m) = -Q + α Q² + 2 L_m + β Q L_m. It reconstructs late-time acceleration by adding Holographic Ricci Dark Energy (HRDE) as an effective fluid, performs Bayesian analysis with Pantheon supernovae, cosmic chronometers, and DESI BAO data showing consistency with ΛCDM for the coupling parameter β, and demonstrates that the quadratic term α Q² drives a Starobinsky-like inflationary phase in the early universe with n_s and r values compatible with Planck 2018. Additionally, Relativistic Generalized Uncertainty Principle (RGUP) corrections are applied, leading to sub-leading modifications in inflationary observables.

Significance. Should the derivations and fits prove robust, the manuscript offers a framework in which distinct curvature regimes within a single modified gravity model account for both early and late cosmic acceleration, augmented by quantum gravity-inspired corrections. Credit is due for the multi-dataset Bayesian constraints and the explicit matching to observational benchmarks such as Planck 2018 and ΛCDM limits.

major comments (1)
  1. [Abstract] Abstract: The central claim that 'one geometric model can simultaneously describe the early and late-time accelerated epochs' and that the f(Q, L_m) framework is a 'dynamically consistent geometric model' in which accelerations 'arise from distinct curvature regimes' is undermined by the explicit statement that late-time dynamics are 'reconstructed by introducing Holographic Ricci Dark Energy (HRDE) as an effective fluid.' The manuscript does not demonstrate that the modified Friedmann equations derived from f(Q, L_m) = -Q + α Q² + 2 L_m + β Q L_m alone produce w_eff ≈ -1 at late times without the added HRDE component. This hybrid construction is load-bearing for the unification claim and requires either a derivation showing emergent de Sitter behavior from the geometry or a revised statement of the model's scope.
minor comments (2)
  1. [Model Setup] The definition of the matter Lagrangian L_m and its explicit coupling to the non-metricity scalar Q should be stated with the assumed matter content (e.g., perfect fluid form) to allow reproduction of the effective fluid equations.
  2. [Figures] Figure captions for the Hubble parameter evolution and effective equation of state should include the 1σ and 2σ bands from the Bayesian posteriors on α and β for direct visual assessment of consistency with data.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The major comment highlights an important point regarding the precise scope of our unification claim, which we address below by agreeing to revise the abstract and related statements for accuracy.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'one geometric model can simultaneously describe the early and late-time accelerated epochs' and that the f(Q, L_m) framework is a 'dynamically consistent geometric model' in which accelerations 'arise from distinct curvature regimes' is undermined by the explicit statement that late-time dynamics are 'reconstructed by introducing Holographic Ricci Dark Energy (HRDE) as an effective fluid.' The manuscript does not demonstrate that the modified Friedmann equations derived from f(Q, L_m) = -Q + α Q² + 2 L_m + β Q L_m alone produce w_eff ≈ -1 at late times without the added HRDE component. This hybrid construction is load-bearing for the unification claim and requires either a derivation showing emergent de Sitter behavior from the geometry or a revised statement of the model's scope.

    Authors: We agree with the referee that the late-time acceleration is not generated solely by the geometric f(Q, L_m) sector. In the manuscript, the modified Friedmann equations from the chosen polynomial form are supplemented by HRDE as an effective fluid to reconstruct the observed late-time expansion with w_eff approaching -1. The early-time Starobinsky-like inflation arises purely from the α Q² term at high curvature, while the β coupling term allows for matter-geometry interaction that is consistent with data. The 'unification' in our framework refers to employing a single f(Q, L_m) action that accommodates both regimes through distinct curvature scales, with HRDE providing the necessary late-time component. We do not claim or derive an emergent de Sitter solution from the geometry alone. To address this, we will revise the abstract and introduction to state more precisely that the model combines geometric inflation with HRDE-driven late-time acceleration within the f(Q, L_m) framework, while retaining the Bayesian constraints and RGUP analysis. This revision will be incorporated in the updated manuscript. revision: yes

Circularity Check

1 steps flagged

Late-time acceleration reconstructed via added HRDE fluid rather than emerging purely from f(Q,L_m) geometry

specific steps
  1. fitted input called prediction [Abstract]
    "the late-time dynamics are reconstructed by introducing Holographic Ricci Dark Energy (HRDE) as an effective fluid. The resulting background evolution demonstrates smooth accelerated expansion, stable Hubble parameter behavior, and an effective equation of state that approaches the de Sitter regime. Bayesian analysis utilizing Pantheon supernovae, cosmic chronometer, and DESI BAO data reveals that the matter-geometry coupling parameter beta is weakly constrained and remains consistent with the LambdaCDM limit."

    HRDE density is defined in terms of the Hubble parameter (standard form rho_HRDE = 3c^2 (2H^2 + dot H)), a construction chosen to produce w_eff ~ -1 and late acceleration. Inserting this fluid, solving the modified Friedmann equations, and then Bayesian-tuning beta to data forces the demonstrated de Sitter approach and LambdaCDM consistency; the late-time result therefore reduces to the choice of HRDE input rather than an independent prediction from f(Q,L_m) = -Q + alpha Q^2 + 2L_m + beta Q L_m alone.

full rationale

The paper's central unification claim relies on distinct curvature regimes, but late-time de Sitter behavior is inserted via HRDE (whose density is defined from H and dot{H}) and then fitted with beta; this makes the late-time result partly by construction of the effective fluid input. Early-time Starobinsky-like inflation from the alpha Q^2 term is independent and geometric. The derivation chain therefore contains one instance of fitted input called prediction but retains independent content overall, yielding a moderate circularity score.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumed polynomial form of f(Q,L_m), the holographic cutoff for dark energy, and the validity of the RGUP metric deformation; none of these are derived from first principles within the paper.

free parameters (2)
  • alpha
    Coefficient of the quadratic non-metricity term, chosen to produce Starobinsky-like inflation.
  • beta
    Matter-geometry coupling strength, fitted to late-time data and only weakly constrained.
axioms (2)
  • domain assumption The background evolution is governed by the modified Friedmann equations derived from the f(Q,L_m) action.
    Standard assumption in modified gravity cosmology; invoked to obtain the Hubble evolution.
  • ad hoc to paper HRDE density is given by the holographic Ricci cutoff.
    Introduced as an effective fluid to drive late-time acceleration.

pith-pipeline@v0.9.0 · 5644 in / 1609 out tokens · 42908 ms · 2026-05-13T01:13:32.680188+00:00 · methodology

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Reference graph

Works this paper leans on

150 extracted references · 150 canonical work pages · 1 internal anchor

  1. [1]

    The general theory of relativity

    Albert Einstein. The general theory of relativity. InThe meaning of relativity, pages 54–75. Springer, 1922

    work page 1922

  2. [2]

    Tests of general relativity: A review.arXiv preprint arXiv:1705.04397, 2017

    Estelle Asmodelle. Tests of general relativity: A review.arXiv preprint arXiv:1705.04397, 2017

    work page arXiv 2017

  3. [3]

    The quest to validate general relativity.Teaching Einsteinian Physics in Schools: An Essential Guide for Teachers in Training and Practice, page 51, 2021

    David Blair and Magdalena Kersting. The quest to validate general relativity.Teaching Einsteinian Physics in Schools: An Essential Guide for Teachers in Training and Practice, page 51, 2021

    work page 2021

  4. [4]

    Testing general relativity with grav- itational waves: An overview.Universe, 7(12):497, 2021

    NV Krishnendu and Frank Ohme. Testing general relativity with grav- itational waves: An overview.Universe, 7(12):497, 2021

    work page 2021

  5. [5]

    Experimental tests of general relativity.Annual Review of Nuclear and Particle Science, 58(1):207–248, 2008

    Slava G Turyshev. Experimental tests of general relativity.Annual Review of Nuclear and Particle Science, 58(1):207–248, 2008

    work page 2008

  6. [6]

    Testing general relativity with the event horizon telescope.General Relativity and Gravitation, 51(10):137, 2019

    Dimitrios Psaltis. Testing general relativity with the event horizon telescope.General Relativity and Gravitation, 51(10):137, 2019

    work page 2019

  7. [7]

    A dynamical study of the friedmann equations.European Journal of Physics, 22(4):371, 2001

    Jean-Philippe Uzan and Roland Lehoucq. A dynamical study of the friedmann equations.European Journal of Physics, 22(4):371, 2001

    work page 2001

  8. [8]

    ¨Uber die kr¨ ummung des raumes.Zeitschrift f¨ ur Physik, 10(1):377–386, 1922

    Alexander Friedman. ¨Uber die kr¨ ummung des raumes.Zeitschrift f¨ ur Physik, 10(1):377–386, 1922. 35

    work page 1922

  9. [9]

    Georges Lemaˆ ıtre. A homogeneous universe of constant mass and in- creasing radius accounting for the radial velocity of extra-galactic neb- ulae.Monthly Notices of the Royal Astronomical Society, Vol. 91, p. 483-490, 91:483–490, 1931

    work page 1931

  10. [10]

    Kinematics and world-structure.Astrophys- ical Journal, vol

    Howard Percy Robertson. Kinematics and world-structure.Astrophys- ical Journal, vol. 82, p. 284, 82:284, 1935

    work page 1935

  11. [11]

    On milne’s theory of world-structure.Pro- ceedings of the London Mathematical Society, 2(1):90–127, 1937

    Arthur Geoffrey Walker. On milne’s theory of world-structure.Pro- ceedings of the London Mathematical Society, 2(1):90–127, 1937

    work page 1937

  12. [12]

    Testing general relativity: Progress, problems, and prospects.General Relativity and Gravitation, 3(1):135–148, 1972

    Irwin I Shapiro. Testing general relativity: Progress, problems, and prospects.General Relativity and Gravitation, 3(1):135–148, 1972

    work page 1972

  13. [13]

    The problem of n bodies in general relativity theory.Proceedings of the Royal Society of London

    Arthur Stanley Eddington and Gordon Leonard Clark. The problem of n bodies in general relativity theory.Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 166(927): 465–475, 1938

    work page 1938

  14. [14]

    Problems on the frontiers between general relativity and differential geometry.Reviews of Modern Physics, 34(4): 873, 1962

    John Archibald Wheeler. Problems on the frontiers between general relativity and differential geometry.Reviews of Modern Physics, 34(4): 873, 1962

    work page 1962

  15. [15]

    Inflationary universe: A possible solution to the horizon and flatness problems.Physical Review D, 23(2):347, 1981

    Alan H Guth. Inflationary universe: A possible solution to the horizon and flatness problems.Physical Review D, 23(2):347, 1981

    work page 1981

  16. [16]

    A new inflationary universe scenario: a possible so- lution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems.Physics Letters B, 108(6):389–393, 1982

    Andrei D Linde. A new inflationary universe scenario: a possible so- lution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems.Physics Letters B, 108(6):389–393, 1982

    work page 1982

  17. [17]

    Cosmology for grand unified theories with radiatively induced symmetry breaking.Physical Review Letters, 48(17):1220, 1982

    Andreas Albrecht and Paul J Steinhardt. Cosmology for grand unified theories with radiatively induced symmetry breaking.Physical Review Letters, 48(17):1220, 1982

    work page 1982

  18. [18]

    Dynamics of phase transition in the new in- flationary universe scenario and generation of perturbations.Physics Letters B, 117(3-4):175–178, 1982

    Alexei A Starobinsky. Dynamics of phase transition in the new in- flationary universe scenario and generation of perturbations.Physics Letters B, 117(3-4):175–178, 1982

    work page 1982

  19. [19]

    A thousand problems in cosmology: Horizons.arXiv preprint arXiv:1310.6329, 2013

    Yu L Bolotin and IV Tanatarov. A thousand problems in cosmology: Horizons.arXiv preprint arXiv:1310.6329, 2013. 36

    work page arXiv 2013

  20. [20]

    Is there a flatness problem in classical cosmology? Monthly Notices of the Royal Astronomical Society, 421(1):561–569, 2012

    Phillip Helbig. Is there a flatness problem in classical cosmology? Monthly Notices of the Royal Astronomical Society, 421(1):561–569, 2012

    work page 2012

  21. [21]

    Results from the high-z su- pernova search team.Physics Reports, 307(1-4):31–44, 1998

    Alexei V Filippenko and Adam G Riess. Results from the high-z su- pernova search team.Physics Reports, 307(1-4):31–44, 1998

    work page 1998

  22. [22]

    Measurements ofωand λfrom 42 high-redshift supernovae.The Astrophysical Journal, 517(2): 565, 1999

    Saul Perlmutter, Goldhaber Aldering, Gerson Goldhaber, Richard A Knop, Peter Nugent, Patricia G Castro, Susana Deustua, Sebastien Fabbro, Ariel Goobar, Donald E Groom, et al. Measurements ofωand λfrom 42 high-redshift supernovae.The Astrophysical Journal, 517(2): 565, 1999

    work page 1999

  23. [23]

    The case forλcdm.arXiv preprint astro-ph/9703161, 1997

    Michael S Turner. The case forλcdm.arXiv preprint astro-ph/9703161, 1997

    work page arXiv 1997

  24. [24]

    Everyone wants something better thanλcdm.arXiv preprint arXiv:2510.05483, 2025

    Michael S Turner. Everyone wants something better thanλcdm.arXiv preprint arXiv:2510.05483, 2025

    work page arXiv 2025

  25. [25]

    Modified theories of gravity: Why, how and what?General Relativity and Gravitation, 54 (5):44, 2022

    S Shankaranarayanan and Joseph P Johnson. Modified theories of gravity: Why, how and what?General Relativity and Gravitation, 54 (5):44, 2022

    work page 2022

  26. [26]

    Cosmology without singularity and nonlinear gravita- tional lagrangians.General Relativity and Gravitation, 14(5):453–469, 1982

    Richard Kerner. Cosmology without singularity and nonlinear gravita- tional lagrangians.General Relativity and Gravitation, 14(5):453–469, 1982

    work page 1982

  27. [27]

    Cosmography of f (r) gravity.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 78(6):063504, 2008

    Salvatore Capozziello, VF Cardone, and V Salzano. Cosmography of f (r) gravity.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 78(6):063504, 2008

    work page 2008

  28. [28]

    f (r) theories of gravity.Re- views of Modern Physics, 82(1):451–497, 2010

    Thomas P Sotiriou and Valerio Faraoni. f (r) theories of gravity.Re- views of Modern Physics, 82(1):451–497, 2010

    work page 2010

  29. [29]

    The dark matter problem from f (r) gravity viewpoint.Annalen der Physik, 524(9-10): 545–578, 2012

    Salvatore Capozziello and Mariafelicia De Laurentis. The dark matter problem from f (r) gravity viewpoint.Annalen der Physik, 524(9-10): 545–578, 2012

    work page 2012

  30. [30]

    Modified gravity description of neutron star in the f (r) framework.Axioms, 12 (3):234, 2023

    Samprity Das, Irina Radinschi, and Surajit Chattopadhyay. Modified gravity description of neutron star in the f (r) framework.Axioms, 12 (3):234, 2023. 37

    work page 2023

  31. [31]

    Disappearing cosmological constant in f (r) grav- ity.JETP letters, 86(3):157–163, 2007

    Alexei A Starobinsky. Disappearing cosmological constant in f (r) grav- ity.JETP letters, 86(3):157–163, 2007

    work page 2007

  32. [32]

    f (r) gravity without a cosmological constant.Physical Review D—Particles, Fields, Gravi- tation, and Cosmology, 74(8):087501, 2006

    Alvaro De la Cruz-Dombriz and Antonio Dobado. f (r) gravity without a cosmological constant.Physical Review D—Particles, Fields, Gravi- tation, and Cosmology, 74(8):087501, 2006

    work page 2006

  33. [33]

    Stable worm- holes in the background of an exponential f (r) gravity.Universe, 6(4): 48, 2020

    Ghulam Mustafa, Ibrar Hussain, and M Farasat Shamir. Stable worm- holes in the background of an exponential f (r) gravity.Universe, 6(4): 48, 2020

    work page 2020

  34. [34]

    Energy condi- tions in f (r) gravity.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 76(8):083513, 2007

    J Santos, JS Alcaniz, MJ Reboucas, and FC Carvalho. Energy condi- tions in f (r) gravity.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 76(8):083513, 2007

    work page 2007

  35. [35]

    Confronting rainbow- deformed f (r) gravity with the act data.Physics Letters B, page 139909, 2025

    Sergei D Odintsov and Vasilis K Oikonomou. Confronting rainbow- deformed f (r) gravity with the act data.Physics Letters B, page 139909, 2025

    work page 2025

  36. [36]

    Power-law f (r) gravity as deformations to starobinsky inflation in view of act.Physics Letters B, page 139907, 2025

    Sergei D Odintsov and Vasilis K Oikonomou. Power-law f (r) gravity as deformations to starobinsky inflation in view of act.Physics Letters B, page 139907, 2025

    work page 2025

  37. [37]

    Translation of einstein’s at- tempt of a unified field theory with teleparallelism, 2005

    Alexander Unzicker and Timothy Case. Translation of einstein’s at- tempt of a unified field theory with teleparallelism, 2005. URL https://arxiv.org/abs/physics/0503046

    work page arXiv 2005

  38. [38]

    Cosmography in f (t) gravity.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 84(4):043527, 2011

    Salvatore Capozziello, VF Cardone, H Farajollahi, and A Ravanpak. Cosmography in f (t) gravity.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 84(4):043527, 2011

    work page 2011

  39. [39]

    Accelerating universe from f (t) gravity.The European Physical Journal C, 71(9):1752, 2011

    Ratbay Myrzakulov. Accelerating universe from f (t) gravity.The European Physical Journal C, 71(9):1752, 2011

    work page 2011

  40. [40]

    f (t) teleparallel gravity and cosmology.Reports on Progress in Physics, 79(10):106901, 2016

    Yi-Fu Cai, Salvatore Capozziello, Mariafelicia De Laurentis, and Em- manuel N Saridakis. f (t) teleparallel gravity and cosmology.Reports on Progress in Physics, 79(10):106901, 2016

    work page 2016

  41. [41]

    Cosmolog- ical solutions of f (t) gravity.Physical Review D, 94(2):023525, 2016

    Andronikos Paliathanasis, John D Barrow, and PGL Leach. Cosmolog- ical solutions of f (t) gravity.Physical Review D, 94(2):023525, 2016. 38

    work page 2016

  42. [42]

    Degrees of freedom of f (t) gravity.Journal of High Energy Physics, 2011(7):1–15, 2011

    Miao Li, Rong-Xin Miao, and Yan-Gang Miao. Degrees of freedom of f (t) gravity.Journal of High Energy Physics, 2011(7):1–15, 2011

    work page 2011

  43. [43]

    Large-scale struc- ture in f (t) gravity.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 83(10):104017, 2011

    Baojiu Li, Thomas P Sotiriou, and John D Barrow. Large-scale struc- ture in f (t) gravity.Physical Review D—Particles, Fields, Gravitation, and Cosmology, 83(10):104017, 2011

    work page 2011

  44. [44]

    The covariant formulation of f (t) gravity.Classical and Quantum Gravity, 33(11):115009, 2016

    Martin Krˇ sˇ s´ ak and Emmanuel N Saridakis. The covariant formulation of f (t) gravity.Classical and Quantum Gravity, 33(11):115009, 2016

    work page 2016

  45. [45]

    Dy- namical stability analysis of accelerating f (t) gravity models.The European Physical Journal C, 82(5):448, 2022

    LK Duchaniya, Santosh V Lohakare, B Mishra, and SK Tripathy. Dy- namical stability analysis of accelerating f (t) gravity models.The European Physical Journal C, 82(5):448, 2022

    work page 2022

  46. [46]

    J. M. Nester and H-J Yo. Symmetric teleparallel general relativity,

    work page

  47. [47]

    URLhttps://arxiv.org/abs/gr-qc/9809049

    work page internal anchor Pith review arXiv

  48. [48]

    f (Q, Lm) gravity , and its cosmological implications,

    Ayush Hazarika, Simran Arora, PK Sahoo, and Tiberiu Harko. f(q, l m) gravity, and its cosmological implications.arXiv preprint arXiv:2407.00989, 2024

    work page arXiv 2024

  49. [49]

    Myrzakulov, Alnadhief H.A

    Y. Myrzakulov, Alnadhief H.A. Alfedeel, M. Koussour, S. Muminov, E.I. Hassan, and J. Rayimbaev. Modified cosmology in f(q,lm) grav- ity.Physics Letters B, 866:139506, 2025. ISSN 0370-2693. doi: https://doi.org/10.1016/j.physletb.2025.139506. URLhttps://www. sciencedirect.com/science/article/pii/S0370269325002679

    work page doi:10.1016/j.physletb.2025.139506 2025

  50. [50]

    Koussour, O

    Kairat Myrzakulov, M. Koussour, O. Donmez, A. Cilli, E. G¨ udekli, and J. Rayimbaev. Observational analysis of late-time acceleration in f(q,lm) gravity.Journal of High Energy Astrophysics, 44:164–171,

    work page

  51. [51]

    doi: https://doi.org/10.1016/j.jheap.2024

    ISSN 2214-4048. doi: https://doi.org/10.1016/j.jheap.2024. 09.014. URLhttps://www.sciencedirect.com/science/article/ pii/S221440482400096X

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

  52. [52]

    Donmez, M

    Yerlan Myrzakulov, O. Donmez, M. Koussour, D. Alizhanov, S. Bekchanov, and J. Rayimbaev. Late-time cosmology in f(q,lm) gravity: Analytical solutions and observational fits.Physics of the Dark Universe, 46:101614, 2024. ISSN 2212-6864. doi: https://doi. org/10.1016/j.dark.2024.101614. URLhttps://www.sciencedirect. com/science/article/pii/S2212686424001961. 39

    work page doi:10.1016/j.dark.2024.101614 2024

  53. [53]

    V. A. Kshirsagar, S. A. Kadam, and Vishwajeet S. Goswami. Cos- mological dynamics of hyperbolic evolution models inf(q, l m) gravity,

    work page

  54. [54]

    URLhttps://arxiv.org/abs/2601.22780

    work page arXiv

  55. [55]

    Sharif, S

    Waseem Ahmad, Tayyab Naseer, M. Sharif, S. Rehman, and Ozod- bek Rahimov. Role of minimal geometric deformation in construct- ing stellar models in f(q, lm) theory: Stability analysis under kohler- chao-tikekar spacetime.International Journal of Geometric Methods in Modern Physics, 0(ja):null, 0. doi: 10.1142/S0219887826501604. URL https://doi.org/10.1142...

    work page doi:10.1142/s0219887826501604

  56. [56]

    Myrzakulov, O

    Y. Myrzakulov, O. Donmez, M. Koussour, S. Muminov, I.Y. Davle- tov, and J. Rayimbaev. Constraining f(q,lm) gravity with bulk viscos- ity.Physics of the Dark Universe, 48:101829, 2025. ISSN 2212-6864. doi: https://doi.org/10.1016/j.dark.2025.101829. URLhttps://www. sciencedirect.com/science/article/pii/S221268642500024X

    work page doi:10.1016/j.dark.2025.101829 2025

  57. [57]

    A novel approach to baryo- genesis in f (q, lm) gravity and its cosmological implications.Nuclear Physics B, 1012:116834, 2025

    Amit Samaddar and S Surendra Singh. A novel approach to baryo- genesis in f (q, lm) gravity and its cosmological implications.Nuclear Physics B, 1012:116834, 2025

    work page 2025

  58. [58]

    Firouzjaee, and Ali Tiz- fahm

    Maryam Shiravand, Saeed Fakhry, Javad T. Firouzjaee, and Ali Tiz- fahm. Cosmological inflation inf(q,L m) gravity, 2025. URLhttps: //arxiv.org/abs/2511.09031

    work page arXiv 2025

  59. [59]

    Surendra Singh

    Amit Samaddar and S. Surendra Singh. Observational signatures of scalar field dynamics in modifiedf(q, l m) gravity, 2025. URLhttps: //arxiv.org/abs/2507.08897

    work page arXiv 2025

  60. [60]

    A model of holographic dark energy.Physics Let- ters B, 603(1):1–5, 2004

    Miao Li. A model of holographic dark energy.Physics Let- ters B, 603(1):1–5, 2004. ISSN 0370-2693. doi: https://doi.org/ 10.1016/j.physletb.2004.10.014. URLhttps://www.sciencedirect. com/science/article/pii/S0370269304014388

    work page doi:10.1016/j.physletb.2004.10.014 2004

  61. [61]

    Holo- graphic dark energy model from ricci scalar curvature.Phys

    Changjun Gao, Fengquan Wu, Xuelei Chen, and You-Gen Shen. Holo- graphic dark energy model from ricci scalar curvature.Phys. Rev. D, 79:043511, Feb 2009. doi: 10.1103/PhysRevD.79.043511. URL https://link.aps.org/doi/10.1103/PhysRevD.79.043511. 40

    work page doi:10.1103/physrevd.79.043511 2009

  62. [62]

    A re- construction of modified holographic ricci dark energy in f(r, t) grav- ity.Canadian Journal of Physics, 91(8):632–638, 2013

    Antonio Pasqua, Surajit Chattopadhyay, and Iuliia Khomenko. A re- construction of modified holographic ricci dark energy in f(r, t) grav- ity.Canadian Journal of Physics, 91(8):632–638, 2013. doi: 10.1139/ cjp-2013-0016. URLhttps://doi.org/10.1139/cjp-2013-0016

    work page doi:10.1139/cjp-2013-0016 2013

  63. [63]

    Generalized holographic and ricci dark energy: Cos- mological diagnostics and scalar field realizations, 2025

    Antonio Pasqua. Generalized holographic and ricci dark energy: Cos- mological diagnostics and scalar field realizations, 2025. URLhttps: //arxiv.org/abs/2509.19386

    work page arXiv 2025

  64. [64]

    Holographic ricci dark energy: Current observational con- straints, quintom feature, and the reconstruction of scalar-field dark en- ergy.Phys

    Xin Zhang. Holographic ricci dark energy: Current observational con- straints, quintom feature, and the reconstruction of scalar-field dark en- ergy.Phys. Rev. D, 79:103509, May 2009. doi: 10.1103/PhysRevD.79. 103509. URLhttps://link.aps.org/doi/10.1103/PhysRevD.79. 103509

    work page doi:10.1103/physrevd.79 2009

  65. [65]

    Baryogenesis and possible insights into the hub- ble tension from f(t) gravity with holographic ricci dark en- ergy.Modern Physics Letters A, 40(37):2550181, 2025

    Gargee Chakraborty, Surajit Chattopadhyay, Nishi Gupta, and Harpreet Kaur. Baryogenesis and possible insights into the hub- ble tension from f(t) gravity with holographic ricci dark en- ergy.Modern Physics Letters A, 40(37):2550181, 2025. doi: 10.1142/S0217732325501810. URLhttps://doi.org/10.1142/ S0217732325501810

    work page doi:10.1142/s0217732325501810 2025

  66. [66]

    M., Crawford, T

    Imanol Albarran and Mariam Bouhmadi-L´ opez. Quantisation of the holographic ricci dark energy model.Journal of Cosmology and As- troparticle Physics, 2015(08):051, aug 2015. doi: 10.1088/1475-7516/ 2015/08/051. URLhttps://doi.org/10.1088/1475-7516/2015/08/ 051

    work page doi:10.1088/1475-7516/ 2015

  67. [67]

    Anisotropic modified holographic ricci dark energy cosmological model with hybrid expansion law

    Kanika Das and Tazmin Sultana. Anisotropic modified holographic ricci dark energy cosmological model with hybrid expansion law. Astrophysics and Space Science, 360(1):4, 2015. doi: 10.1007/ s10509-015-2517-y

    work page 2015

  68. [68]

    Chokyi and Surajit Chattopadhyay

    Khandro K. Chokyi and Surajit Chattopadhyay. A truncated scale factor to realize cosmological bounce under the purview of modified gravity.Astronomische Nachrichten, 344(7):e220119, 2023. doi: https: //doi.org/10.1002/asna.20220119. URLhttps://onlinelibrary. wiley.com/doi/abs/10.1002/asna.20220119. 41

    work page doi:10.1002/asna.20220119 2023

  69. [69]

    C. P. Singh and Ajay Kumar. Holographic ricci dark energy with con- stant bulk viscosity in f(r,t) gravity.Gravitation and Cosmology, 25 (1):58–68, 2019. doi: 10.1134/S0202289319010109

    work page doi:10.1134/s0202289319010109 2019

  70. [70]

    Chokyi and Surajit Chattopadhyay

    Khandro K. Chokyi and Surajit Chattopadhyay. Cosmological models within f(t, b) gravity in a holographic framework.Particles, 7(3):856– 878, 2024. ISSN 2571-712X. doi: 10.3390/particles7030051. URL https://www.mdpi.com/2571-712X/7/3/51

    work page doi:10.3390/particles7030051 2024

  71. [71]

    String theory, supersymmetry, unification, and all that.Reviews of Modern Physics, 71(2):S112, 1999

    John H Schwarz and Nathan Seiberg. String theory, supersymmetry, unification, and all that.Reviews of Modern Physics, 71(2):S112, 1999

    work page 1999

  72. [72]

    On the interpretation of minimal length in string theories.Modern Physics Letters A, 4(16), 1989

    Tamiaki Yoneya. On the interpretation of minimal length in string theories.Modern Physics Letters A, 4(16), 1989

    work page 1989

  73. [73]

    Baryogenesis without grand unification

    D. Amati, M. Ciafaloni, and G. Veneziano. Can spacetime be probed below the string size?Physics Letters B, 216(1): 41–47, 1989. ISSN 0370-2693. doi: https://doi.org/10.1016/ 0370-2693(89)91366-X. URLhttps://www.sciencedirect.com/ science/article/pii/037026938991366X

    work page arXiv 1989

  74. [74]

    Gross and Paul F

    David J. Gross and Paul F. Mende. String theory beyond the planck scale.Nuclear Physics B, 303(3):407–454, 1988. ISSN 0550-3213. doi: https://doi.org/10.1016/0550-3213(88)90390-2. URLhttps://www. sciencedirect.com/science/article/pii/0550321388903902

    work page doi:10.1016/0550-3213(88)90390-2 1988

  75. [75]

    Veneziano

    G. Veneziano. A stringy nature needs just two constants.Europhysics Letters, 2(3):199, aug 1986. doi: 10.1209/0295-5075/2/3/006. URL https://doi.org/10.1209/0295-5075/2/3/006

    work page doi:10.1209/0295-5075/2/3/006 1986

  76. [76]

    Black-hole thermodynamics.Physics Today, 33 (1):24–31, 1980

    Jacob D Bekenstein. Black-hole thermodynamics.Physics Today, 33 (1):24–31, 1980

    work page 1980

  77. [77]

    Doubly Special Relativity

    Giovanni Amelino-Camelia. Doubly special relativity.arXiv preprint gr-qc/0207049, 2002

    work page Pith review arXiv 2002

  78. [78]

    Kowalski-Glikman.Introduction to Doubly Special Relativity, pages 131–159

    J. Kowalski-Glikman.Introduction to Doubly Special Relativity, pages 131–159. Springer Berlin Heidelberg, Berlin, Heidelberg, 2005. ISBN 978-3-540-31527-8. doi: 10.1007/11377306 5. URLhttps://doi.org/ 10.1007/11377306_5. 42

    work page doi:10.1007/11377306 2005

  79. [79]

    Doubly-special relativity: first results and key open problems.International Journal of Modern Physics D, 11 (10):1643–1669, 2002

    Giovanni Amelino-Camelia. Doubly-special relativity: first results and key open problems.International Journal of Modern Physics D, 11 (10):1643–1669, 2002

    work page 2002

  80. [80]

    Heisenberg’s uncer- tainty principle.Physics reports, 452(6):155–176, 2007

    Paul Busch, Teiko Heinonen, and Pekka Lahti. Heisenberg’s uncer- tainty principle.Physics reports, 452(6):155–176, 2007

    work page 2007

Showing first 80 references.