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arxiv: 2605.18934 · v1 · pith:4P4CUGUInew · submitted 2026-05-18 · 🌀 gr-qc

Scalar Field Reconstructions of Standard, Power Law and Logarithmic Holographic Dark Energy with a Gauss-Bonnet IR cut-off

Antonio Pasqua This is my paper

Pith reviewed 2026-05-20 09:20 UTC · model grok-4.3

classification 🌀 gr-qc
keywords holographic dark energyGauss-Bonnet invariantscalar field reconstructionequation of statedeceleration parameterentropy corrected HDEdark matter interaction
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The pith

Holographic dark energy with a Gauss-Bonnet infrared cutoff corresponds to tachyon, quintessence and other scalar field models

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

This paper examines standard, power-law, and logarithmic holographic dark energy by adopting an infrared cutoff given by the inverse fourth root of the Gauss-Bonnet invariant. It calculates the equation of state parameter, deceleration parameter, and the time evolution of the dark energy density fraction in flat and non-flat universes, with and without interactions between dark energy and dark matter. The central result is a set of explicit reconstructions that identify these holographic models with tachyon, k-essence, quintessence, generalized Chaplygin gas, Yang-Mills, and nonlinear electrodynamics scalar field models. A sympathetic reader would see this as a way to link the holographic principle directly to the dynamics generated by scalar fields. If the mappings are accurate, they allow the same cosmic expansion history to be described from either perspective.

Core claim

By taking the infrared cutoff to be L equal to the inverse fourth root of the Gauss-Bonnet invariant, the holographic dark energy density is defined and its equation of state, deceleration parameter and density evolution are derived for the standard, power law and logarithmic cases. These quantities are obtained both for flat and non-flat universes and for interacting and non-interacting dark sectors. In the dark-energy-dominated limit the asymptotic forms are given. Correspondences are then established by constructing the scalar field and potential for each of the listed models so that they reproduce the same energy density and pressure as the holographic models.

What carries the argument

The Gauss-Bonnet infrared cutoff L = G^{-1/4} that determines the holographic dark energy density and permits the scalar field reconstructions for multiple models.

Load-bearing premise

The choice of the infrared cutoff as the inverse fourth root of the Gauss-Bonnet invariant, which is adopted to enable the derivations without additional justification from observations or theory.

What would settle it

High-precision measurements of the dark energy equation of state parameter at low redshifts that fall outside the ranges obtained from the asymptotic analysis or the explicit expressions for any of the HDE models would disprove the claimed scalar field correspondences.

read the original abstract

In this paper, we investigate the Holographic Dark Energy (HDE) model and its entropy-corrected versions, namely the Power Law and Logarithmic entropy corrected HDE models, by considering the infrared cut-off $L=\mathcal{G}^{-1/4}$, where $\mathcal{G}$ is the Gauss-Bonnet invariant. We derived the Equation of State parameter $\omega_D$, the deceleration parameter $q$ and the evolutionary form of the fractional energy density of DE $\Omega_D'$ for flat and non-flat universes, with and without interaction between DE and Dark Matter. We also analyzed the asymptotic behavior in the DE dominated epoch. Furthermore, correspondences between the considered HDE models and several scalar field models, including tachyon, k-essence, quintessence, Generalized Chaplygin Gas, Yang-Mills, and Nonlinear Electrodynamics models, were established.

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. The manuscript investigates the standard, power-law, and logarithmic holographic dark energy (HDE) models using an infrared cutoff L = G^{-1/4}, where G is the Gauss-Bonnet invariant. It derives the equation of state ω_D, deceleration parameter q, and the evolution of the dark energy density parameter Ω_D' for both flat and non-flat universes, considering cases with and without interaction between dark energy and dark matter. Additionally, the paper analyzes the asymptotic behavior in the dark energy dominated epoch and establishes correspondences between these HDE models and several scalar field models, including tachyon, k-essence, quintessence, Generalized Chaplygin Gas, Yang-Mills, and Nonlinear Electrodynamics models.

Significance. The paper offers a detailed analysis by considering multiple variants of HDE (standard, power law, logarithmic) with interaction terms and both flat and non-flat geometries, along with explicit mappings to a range of scalar field models. This systematic approach is a strength if the underlying cutoff is accepted. The results could aid in comparing different dark energy descriptions, but the overall significance depends on addressing the motivation for the specific IR cutoff choice.

major comments (1)
  1. [Model definition / abstract] Model definition (as introduced in the abstract and setup): The infrared cutoff is taken to be L = G^{-1/4} where G is the Gauss-Bonnet invariant. This choice is introduced without independent observational or theoretical justification beyond enabling the subsequent derivations. Since all derived quantities (ω_D, q, Ω_D') and the scalar-field correspondences rest on this specific scale, the lack of motivation from the holographic bound, Gauss-Bonnet cosmology, or data makes the mappings algebraic identities rather than physically motivated reconstructions.
minor comments (2)
  1. [Notation] Ensure consistent notation for the Gauss-Bonnet invariant throughout (e.g., script G vs plain G).
  2. [References] Add citations to prior literature on Gauss-Bonnet invariants as IR cutoffs in holographic models to better situate the choice.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript. We address the major comment regarding the motivation for the infrared cutoff in detail below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: Model definition (as introduced in the abstract and setup): The infrared cutoff is taken to be L = G^{-1/4} where G is the Gauss-Bonnet invariant. This choice is introduced without independent observational or theoretical justification beyond enabling the subsequent derivations. Since all derived quantities (ω_D, q, Ω_D') and the scalar-field correspondences rest on this specific scale, the lack of motivation from the holographic bound, Gauss-Bonnet cosmology, or data makes the mappings algebraic identities rather than physically motivated reconstructions.

    Authors: We appreciate the referee's observation on the need for clearer motivation. The cutoff L = 𝒢^{-1/4} is selected because the Gauss-Bonnet invariant 𝒢 has dimensions of length^{-4}, yielding an infrared scale L with the correct dimensions required by the holographic principle (ρ_D ∝ L^{-2}). This extends standard HDE constructions to the context of Gauss-Bonnet gravity, where curvature invariants naturally define characteristic scales. We acknowledge, however, that the manuscript would benefit from an explicit discussion of this rationale. In the revised version we will add a dedicated paragraph in the introduction that derives the dimensional consistency, references prior literature on holographic models in modified gravity, and explains why this choice is physically motivated rather than ad hoc, thereby framing the subsequent derivations and scalar-field correspondences as arising from a motivated cutoff. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations follow from stated model assumptions

full rationale

The paper defines the HDE models using the explicit IR cut-off choice L = G^{-1/4} and derives ω_D, q, and Ω_D' directly from the resulting energy density ρ_D = 3c²M_p²/L². Scalar-field correspondences are then obtained by matching this ρ_D and p_D = ω_D ρ_D to the energy density and pressure expressions of tachyon, k-essence, quintessence, GCG, Yang-Mills, and NED Lagrangians. This is a standard reconstruction procedure that does not reduce any output quantity to an input by algebraic identity or self-definition. The cut-off selection is an input assumption of the model rather than a fitted parameter or self-referential definition, and no load-bearing step relies on unverified self-citation or imported uniqueness theorems. The chain remains self-contained against the paper's own equations.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is populated from the minimal assumptions stated there; full text would likely reveal additional fitted scales and interaction terms.

free parameters (1)
  • interaction coupling constant
    Mentioned for the interacting cases; value must be chosen to produce the reported evolutionary forms.
axioms (2)
  • domain assumption Universe is either flat or has small constant curvature
    Explicitly used to derive separate expressions for flat and non-flat cases.
  • ad hoc to paper Gauss-Bonnet invariant supplies a valid IR cutoff
    Introduced as L = G^{-1/4} without derivation from first principles or observational calibration.

pith-pipeline@v0.9.0 · 5681 in / 1344 out tokens · 48565 ms · 2026-05-20T09:20:21.435384+00:00 · methodology

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Reference graph

Works this paper leans on

170 extracted references · 170 canonical work pages · 5 internal anchors

  1. [1]

    Cosmological F ramework7

    work page

  2. [2]

    Correspondence with Scalar Field Models14

    work page

  3. [3]

    Tachyon Scalar Field Model 14

    work page

  4. [4]

    k-essence Scalar Field Model 20

    work page

  5. [5]

    Quintessence Scalar Field Model 22

    work page

  6. [6]

    Generalized Chaplygin Gas (GCG) Model 25

    work page

  7. [7]

    Yang-Mills (YM) Model 28

    work page

  8. [8]

    Non Linear Electro-Dynamics (NLED) Model 32

    work page

  9. [9]

    Conclusions 35 References 35 ∗Electronic address:toto.pasqua@gmail.com arXiv:2605.18934v1 [gr-qc] 18 May 2026 2

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  10. [10]

    INTRODUCTION Observational cosmology strongly indicates that the present Universe is undergoing a phase of accelerated expansion. This picture is supported by a wide variety of independent astrophysical observations, including Type Ia Supernovae (SNeIa) measurements [1, 2], anisotropies in the Cosmic Microwave Background (CMB) radiation detected by the Wi...

    work page

  11. [14]

    non-flat interacting Universe. In Section 3, we establish a correspondence between our models and some scalar fields model, in particular the Tachyon, the k-essence, the Quintessence, the Generalized Chaplygin Gas (GCG), the Yang-Mills (YM) and the Nonlinear Electrodynamics (NLED) fields. Finally, in Section 4 we write the Conclusions

    work page

  12. [15]

    COSMOLOGICAL FRAMEWORK We construct our cosmological model on the foundation of a non-flat Friedmann-Lemaˆ ıtre- Robertson-Walker (FLRW) geometry. The background spacetime is characterized by the following invariant line element: ds2 =−dt 2 +a 2(t) dr2 1−kr 2 +r 2 dθ2 + sin2 θdφ2 ,(20) 8 Probing the gravitational sector via the Einstein field equations yi...

    work page

  13. [16]

    Such correspondences are particularly valuable because these specific formulations act as effective field representations of a more fundamental, microscopic Dark Energy theory

    CORRESPONDENCE WITH SCALAR FIELD MODELS We now establish an explicit correspondence between the DE models we studied and several well- known scalar fields models, in particular the Tachyon, the k-essence, the Quintessence, the Gener- alized Chaplygin Gas (GCG), the Yang-Mills (YM) and the Nonlinear Electrodynamics (NLED) fields. Such correspondences are p...

    work page

  14. [17]

    T achyon Scalar Field Model We start with the first scalar field model considered in this paper, the tachyon. In recent years, tachyon fields have attracted considerable attention in the context of early-Universe inflation and late-time cosmic acceleration, as they can also provide a viable candidate for DE [115– 118]. In string theory, the tachyon is int...

    work page

  15. [18]

    k-essence Scalar Field Model A class of scalar field theories in which the kinetic contribution enters the Lagrangian in a non- standard (non-canonical) way is commonly referred to as k-essence. This framework was originally inspired by the Born–Infeld action arising in string theory and has been extensively employed to account for the observed late-time ...

    work page

  16. [19]

    The action describing this system is given by [12]: S= Z d4x√−g −1 2 gµν∂µϕ∂νϕ−V(ϕ) .(139) 23 By performing a variation of the action in Eq

    Quintessence Scalar Field Model In the quintessence framework, the late-time acceleration of the universe is accounted for by a minimally coupled, spatially homogeneous scalar fieldϕ(t) governed by an appropriate potential V(ϕ). The action describing this system is given by [12]: S= Z d4x√−g −1 2 gµν∂µϕ∂νϕ−V(ϕ) .(139) 23 By performing a variation of the a...

    work page

  17. [20]

    Generalized Chaplygin Gas (GCG) Model Next, we focus on the Generalized Chaplygin Gas (GCG) framework. Initially, Kamenshchiket al.[126] introduced the standard Chaplygin Gas (CG) model, a homogeneous scenario characterized by a single fluid governed by the equation of state (EoS)p=− A0 ρ , wherepandρrepresent the fluid pressure and energy density, whileA...

    work page 1904

  18. [21]

    In recent years, the YM field has been widely investigated as a compelling candidate to explain the nature of DE [136–139]

    Y ang-Mills (YM) Model We now turn our attention to the Yang-Mills (YM) framework. In recent years, the YM field has been widely investigated as a compelling candidate to explain the nature of DE [136–139]. Two primary arguments motivate the choice of a YM field over standard scalar field prototypes. First, its physical foundations are more rigorously gro...

    work page

  19. [22]

    In recent years, non-linear extensions of Maxwell’s electromagnetic 33 theory have attracted significant interest as a novel approach to avoid primordial cosmic singu- larities

    Non Linear Electro-Dynamics (NLED) Model We now turn our attention to the final framework chosen for this study: the Non-Linear Electro- Dynamics (NLED) model. In recent years, non-linear extensions of Maxwell’s electromagnetic 33 theory have attracted significant interest as a novel approach to avoid primordial cosmic singu- larities. Indeed, exact solut...

    work page

  20. [23]

    The HDE scenario represents an important approach to understanding the nature of DE within the context of quantum gravity

    CONCLUSIONS In this paper, we considered the Holographic Dark Energy HDE model along with the Power Law and the Logarithmic entropy-corrected versions of the HDE model with IR cut-off equivalent toL=G −1/4, whereGindicates the Gauss-Bonnet invariant. The HDE scenario represents an important approach to understanding the nature of DE within the context of ...

    work page

  21. [24]

    flat non-interacting Universe,

    work page

  22. [25]

    non-flat non-interacting Universe,

    work page

  23. [26]

    flat interacting Universe,

    work page

  24. [27]

    Furthermore, we investigated the corresponding limiting behavior in the Dark Energy dominated epoch of the Universe

    non-flat interacting Universe. Furthermore, we investigated the corresponding limiting behavior in the Dark Energy dominated epoch of the Universe. Furthermore, we constructed correspondences between the HDE models considered in this work and several scalar field descriptions of DE, namely the tachyon, k-essence, quintessence, General- ized Chaplygin Gas ...

    work page

  25. [28]

    J.517, 565 (1999)

    Perlmutter, S., et al., Astrophys. J.517, 565 (1999)

    work page 1999

  26. [29]

    Astrophys.447, 31 (2006)

    Astier, P., et al., Astron. Astrophys.447, 31 (2006)

    work page 2006

  27. [30]

    L., et al., Astrophys

    Bennett, C. L., et al., Astrophys. J. Suppl.148, 1 (2003)

    work page 2003

  28. [31]

    N., et al., Astrophys

    Spergel, D. N., et al., Astrophys. J. Suppl.148, 175 (2003)

    work page 2003

  29. [32]

    Tegmark, M., et al., Phys. Rev. D69, 103501 (2004). 36

    work page 2004

  30. [33]

    J.128, 502 (2004)

    Abazajian, K., et al., Astron. J.128, 502 (2004)

    work page 2004

  31. [34]

    J.129, 1755 (2005)

    Abazajian, K., et al., Astron. J.129, 1755 (2005)

    work page 2005

  32. [35]

    W., et al., Mon

    Allen, S. W., et al., Mon. Not. Roy. Astron. Soc.353, 457 (2004)

    work page 2004

  33. [36]

    V., et al., Astrophys

    Peiris, H. V., et al., Astrophys. J. Suppl.148, 213 (2003)

    work page 2003

  34. [37]

    Rept.380, 235 (2003)

    Padmanabhan, T., Phys. Rept.380, 235 (2003)

    work page 2003

  35. [38]

    Peebles, P. J. E., & Ratra, B., Rev. Mod. Phys.75, 559 (2003)

    work page 2003

  36. [39]

    J., Sami, M., & Tsujikawa, S., Int

    Copeland, E. J., Sami, M., & Tsujikawa, S., Int. J. Mod. Phys. D15, 1753 (2006)

    work page 2006

  37. [40]

    Weinberg, S., Rev. Mod. Phys.61, 1 (1989)

    work page 1989

  38. [41]

    Wetterich, C., Nucl. Phys. B302, 668 (1988)

    work page 1988

  39. [42]

    Ratra, B., & Peebles, P. J. E., Phys. Rev. D37, 3406 (1988)

    work page 1988

  40. [43]

    Chiba, T., Okamura, T., & Yamaguchi, M., Phys. Rev. D62, 023511 (2000)

    work page 2000

  41. [44]

    F., & Steinhardt, P

    Armendariz-Picon, C., Mukhanov, V. F., & Steinhardt, P. J., Phys. Rev. Lett.85, 4490 (2000)

    work page 2000

  42. [45]

    F., & Steinhardt, P

    Armendariz-Picon, C., Mukhanov, V. F., & Steinhardt, P. J., Phys. Rev. D63, 103510 (2001)

    work page 2001

  43. [46]

    R., Phys

    Caldwell, R. R., Phys. Lett. B545, 23 (2002)

    work page 2002

  44. [47]

    D., Phys

    Nojiri, S., & Odintsov, S. D., Phys. Lett. B562, 147 (2003)

    work page 2003

  45. [48]

    D., Phys

    Nojiri, S., & Odintsov, S. D., Phys. Rev. D68, 123512 (2003)

    work page 2003

  46. [49]

    Sen, A., JHEP0204, 048 (2002)

    work page 2002

  47. [50]

    Padmanabhan, T., Phys. Rev. D66, 021301 (2002)

    work page 2002

  48. [51]

    R., Phys

    Padmanabhan, T., & Choudhury, T. R., Phys. Rev. D66, 081301 (2002)

    work page 2002

  49. [52]

    Gasperini, M., Piazza, F., & Veneziano, G., Phys. Rev. D65, 023508 (2002)

    work page 2002

  50. [53]

    Piazza, F., & Veneziano, G., JCAP0407, 007 (2004)

    work page 2004

  51. [54]

    C., Luty, M

    Arkani-Hamed, N., Cheng, H. C., Luty, M. A., & Mukohyama, S., JHEP0405, 074 (2004)

    work page 2004

  52. [55]

    D., Phys

    Elizalde, E., Nojiri, S., & Odintsov, S. D., Phys. Rev. D70, 043539 (2004)

    work page 2004

  53. [56]

    D., & Tsujikawa, S., Phys

    Nojiri, S., Odintsov, S. D., & Tsujikawa, S., Phys. Rev. D71, 063004 (2005)

    work page 2005

  54. [57]

    Anisimov, A., Babichev, E., & Vikman, A., JCAP0506, 006 (2005)

    work page 2005

  55. [58]

    Y., Moschella, U., & Pasquier, V., Phys

    Kamenshchik, A. Y., Moschella, U., & Pasquier, V., Phys. Lett. B511, 265 (2001)

    work page 2001

  56. [59]

    R., Phys

    Setare, M. R., Phys. Lett. B654, 1 (2007)

    work page 2007

  57. [60]

    R., & Gabadadze, G., Phys

    Deffayet, C., Dvali, G. R., & Gabadadze, G., Phys. Rev. D65, 044023 (2002)

    work page 2002

  58. [61]

    Sahni, V., & Shtanov, Y., JCAP0311, 014 (2003)

    work page 2003

  59. [62]

    G., Kaplan, D

    Cohen, A. G., Kaplan, D. B., & Nelson, A. E., Phys. Rev. Lett.82, 4971 (1999)

    work page 1999

  60. [63]

    Horava, P., & Minic, D., Phys. Rev. Lett.85, 1610 (2000)

    work page 2000

  61. [64]

    R., Phys

    Setare, M. R., Phys. Lett. B644, 99 (2007)

    work page 2007

  62. [65]

    R., Phys

    Setare, M. R., Phys. Lett. B653, 145 (2007)

    work page 2007

  63. [66]

    R., Phys

    Setare, M. R., Phys. Lett. B642, 1 (2006)

    work page 2006

  64. [67]

    R., Phys

    Setare, M. R., Phys. Lett. B648, 329 (2007)

    work page 2007

  65. [68]

    R., JCAP0701, 023 (2007)

    Setare, M. R., JCAP0701, 023 (2007)

    work page 2007

  66. [69]

    Setare, M. R., Eur. Phys. J. C52, 689 (2007). 37

    work page 2007

  67. [70]

    G., Phys

    Cai, R. G., Phys. Lett. B657, 228 (2007)

    work page 2007

  68. [71]

    G., Phys

    Wei, H., & Cai, R. G., Phys. Lett. B660, 113 (2008)

    work page 2008

  69. [72]

    D., Wang, S., & Wang, Y., Commun

    Li, M., Li, X. D., Wang, S., & Wang, Y., Commun. Theor. Phys.56, 525 (2011)

    work page 2011

  70. [73]

    ’t Hooft, G., gr-qc/9310026; Susskind, L., J. Math. Phys.36, 6377 (1995)

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  71. [74]

    Fischler, W., & Susskind, L., hep-th/9806039

    work page internal anchor Pith review Pith/arXiv arXiv

  72. [75]

    G., & Li, M., JCAP0408, 013 (2004)

    Huang, Q. G., & Li, M., JCAP0408, 013 (2004)

    work page 2004

  73. [76]

    Hsu, S. D. H., Phys. Lett. B594, 13 (2004)

    work page 2004

  74. [77]

    G., & Abdalla, E., Phys

    Wang, B., Gong, Y. G., & Abdalla, E., Phys. Lett. B624, 141 (2005)

    work page 2005

  75. [78]

    Guberina, B., Horvat, R., & Stefancic, H., Phys. Rev. D72, 025011 (2005)

    work page 2005

  76. [79]

    Guberina, B., Horvat, R., & Nikolic, P., Phys. Lett. B636, 80 (2006)

    work page 2006

  77. [80]

    G., Phys

    Gong, Y. G., Phys. Rev. D70, 064029 (2004)

    work page 2004

  78. [81]

    N., & Setare, M

    Jamil, M., Saridakis, E. N., & Setare, M. R., Phys. Lett. B679, 172 (2009)

    work page 2009

  79. [83]

    Sheykhi, A., & Jamil, M., Gen. Rel. Grav.43, 2661 (2011)

    work page 2011

  80. [84]

    Sheykhi, A., & Jamil, M., Phys. Lett. B694, 284 (2011)

    work page 2011

Showing first 80 references.