Holographic reconstruction of k-essence model with Tsallis and the most generalized Nojiri-Odintsov version of holographic dark energy

Aziza Altaibayeva; Surajit Chattopadhyay; Ulbossyn Ualikhanova

REVIEW 4 major objections 5 minor 2 cited by

Holographic reconstruction of k-essence model with Tsallis and the most generalized Nojiri-Odintsov version of holographic dark energy

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper argues that k-essence scalar-field dark energy can be reconstructed from Tsallis and generalized Nojiri-Odintsov holographic dark energy, with an equation-of-state parameter that stays within observational bounds near $w=-1$.

desk verdict A standard k-essence reconstruction paper undercut by an algebraic error in the Tsallis EoS and a generalized cutoff that is silently dropped in the NO-HDE section. read the letter →

arxiv 2501.04028 v1 pith:MUXKOC4A submitted 2024-12-31 physics.gen-ph

Ulbossyn Ualikhanova , Aziza Altaibayeva , Surajit Chattopadhyay This is my paper · ORCID

classification physics.gen-ph

keywords k-essenceholographicdarkenergyTsallisNojiri-Odintsovequationofstateemergentuniverseinfraredcutoff

topics Dark Energy

open problems Dark Energy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Dark energy is often modeled as a scalar field, and the k-essence model uses nonstandard kinetic terms to drive cosmic acceleration. This paper tries to tie that field to the holographic principle by reconstructing k-essence from two generalized holographic dark energy setups: Tsallis entropy-based dark energy with different infrared cutoffs, and the Nojiri-Odintsov holographic dark energy built on a generalized cutoff involving the future horizon. Using an emergent-universe scale factor, it derives explicit expressions for the k-essence kinetic quantity and the scalar-field function, and compares the resulting equation-of-state parameter with observational bounds near $w=-1$. The claimed payoff is that holographic dark energy and k-essence describe the same late-time acceleration, so one can trade the holographic formulation for a scalar-field formulation. The paper's own conclusion emphasizes that the current value of the reconstructed EoS parameter is consistent with Planck-era data.

What carries the argument

The reconstruction machinery is the correspondence $w_{\rm DE}=w_X$ between the holographic fluid's equation-of-state parameter and the k-essence parameter $w_X=(X-1)/(3X-1)$, where $X=-\tfrac12(\partial\varphi)^2$ is the kinetic term. Substituting the holographic density (Tsallis: $\rho_{\rm DE}=B L^{2\delta-4}$; NO-HDE: $\rho=3c^2/L^2$ with generalized cutoff $c/L=(\alpha_0+\alpha_1 L_f+\alpha_2 L_f^2)/L_f$) into the conservation equation yields $w_{\rm DE}$, and matching to $w_X$ gives a holographically reconstructed $X$; then $f(\varphi)=\rho_{\rm DE}/(-X+3X^2)$ is rebuilt as $F(t)$. The emergent-universe scale factor $a(t)=A(e^{nt}+B)^b$ supplies explicit Hubble and future-horizon expressions so that everything becomes a function of time and model parameters.

What would settle it

Recompute the NO-HDE density and EoS with the full cutoff $(\alpha_0+\alpha_1 L_f+\alpha_2 L_f^2)/L_f$ and nonzero $\alpha_1,\alpha_2$ on the same emergent-universe background; if the $z=0$ EoS leaves the interval from $-1.06$ to $-0.93$ (or the Planck 95% bound centered near $-1.019$), or if the reconstructed $F(t)$ fails to stay positive and vanish as $t\to 0$, the central consistency claim breaks. An alternative check fits the parameters of Eq. (9) directly to SNLS3, BAO, and Planck data to see whether the Table I values lie in the best-fit region.

Watch

Extended reading notes

Core claim

The central claim is that a k-essence dark-energy model, defined by a scalar field with pressure $p(\varphi,X)=f(\varphi)(-X+X^2)$ and energy density $\rho(\varphi,X)=f(\varphi)(-X+3X^2)$, can be holographically reconstructed from Tsallis holographic dark energy with the cutoffs $L=H^{-1}$ and $L=(\alpha H^2+\beta \dot H)^{-1/2}$, and from Nojiri-Odintsov holographic dark energy with the future-horizon cutoff under an emergent scale factor $a(t)=A(e^{nt}+B)^b$. For the Tsallis Ricci-like cutoff the paper derives the EoS parameter of Eq. (9) and, in Table I, finds current values in the range roughly $-1.04$ to $-0.93$, which it regards as consistent with the observational constraints of references [60] and [61]. For the Nojiri-Odintsov case it finds an EoS close to $-1$ for small $n$ and quintessence-like for larger $n$, and a reconstructed $F(t)$ that stays positive and vanishes as $t\to 0$, which it takes as a sufficient condition for a realistic reconstruction. The paper states that it 'explores a reconstruction scheme for the k-essence form of dark energy with the most generalized version of holographic dark energy' and that the resulting EoS is consistent with observations.

Load-bearing premise

The load-bearing premise is that the 'most generalized' Nojiri-Odintsov cutoff can be replaced by the plain future-horizon distance in the density and EoS calculations; the paper makes that substitution silently, so the advertised generalization is never actually exercised.

Editorial extensions

If this is right

If the reconstruction is correct, the holographic and scalar-field descriptions of late-time acceleration become interchangeable within the k-essence format, allowing observational constraints on one to be translated to the other.
For the Tsallis case with the Ricci-like cutoff, the current EoS parameter falls inside the observationally allowed window around $-1$, so that version of the model is not ruled out by present data.
For the Nojiri-Odintsov case, small $n$ yields an EoS near $-1$ (cosmological-constant-like) while larger $n$ yields quintessence behavior, giving a one-parameter family of late-time behaviors.
The reconstructed $f(\varphi)$ tends to zero as $t\to 0$, satisfying a condition the paper associates with a realistic reconstruction, and the same scheme could be rerun for other entropies such as Renyi or Kaniadakis as the authors suggest.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The derivation of the Nojiri-Odintsov density silently drops the $\alpha_1$ and $\alpha_2$ terms from the generalized cutoff, so the advertised 'most generalized' reconstruction is not actually performed; rerunning the calculation with the full cutoff would directly test whether the generalization changes the EoS.
The observational comparison in Table I applies to the Tsallis-with-Ricci-cutoff EoS, not to the Nojiri-Odintsov EoS, even though the NO-HDE model is the paper's headline case.
A fitting procedure that fixes the model parameters using supernova, BAO, or Planck data would be stronger than reading $w(z=0)$ off chosen parameter combinations; the reported consistency demonstrates existence of parameters, not a best fit.
The emergent-universe scale factor is assumed rather than derived, so the results' robustness to other scale-factor choices remains untested.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: two advertised reconstructions, but one is built on an algebraic error and the other is not the generalized model it claims to be. The Hubble-horizon Tsallis part is correct; the reconstruction scheme is legitimate and clearly laid out. Given a holographic density, the authors solve the conservation equation for w, map to k-essence X and F(t), and plot. That part is fine, if routine.

The first load-bearing problem is Eq. (9). For ρ = B(αH² + βḢ)^{2−δ}, the continuity equation gives w_DE with coefficients linear in (δ−2): the HḢ term gets −3β + 2α(δ−2), and the Ḣddot term gets β(δ−2). Equation (9) has (δ−2)² in both, plus a stray −3β. I checked the derivative; the error is real. Everything downstream in that section—X, F(t), Table I—inherits it.

The second problem is in Section III. Equation (25) defines c/L = (α0 + α1L_f + α2L_f²)/L_f. But Eq. (29) and everything after it use ρ = 3c²/L_f², with no α0, α1, α2. The authors call Eq. (28) 'the Nojiri-Odintsov cutoff,' but it is simply the future horizon L_f. So the most generalized version promised in the title and abstract is never used. This is not a stylistic complaint; it is an internal contradiction. If the full cutoff had been retained, Eqs. (29)–(34) would all be different.

Table I is a parameter scan, not a fit, and it is based on the wrong Eq. (9), so it doesn't support the observational consistency claim. The paper does contain explicit analytic derivations and clearly labeled plots, but those don't rescue the two central constructions.

What is new is narrow: I don't think these specific F(t) expressions for the Ricci-like Tsallis density and the future-horizon density appear elsewhere. That could be worth a note. But as presented, the paper is not in a state to send to peer review. I would desk-reject with an invitation to resubmit after fixing Eq. (9) and either using the full generalized cutoff or honestly relabeling the second half as future-horizon HDE.

Referee Report

4 major / 5 minor

Summary. The paper aims to reconstruct a k-essence scalar-field description of dark energy from two holographic constructions in a flat FRW universe with emergent scale factor a(t)=A(e^{nt}+B)^b. For Tsallis holographic dark energy it derives the EoS parameter for IR cutoffs L=H^{-1} and L=(αH^2+β\dot H)^{-1/2}, constructs the kinetic quantity X and the function F(t)=ρ_DE/(-X+3X^2), and compares the z=0 EoS with observational constraints. For the 'most generalized' Nojiri–Odintsov HDE, defined by ρ=3c^2/L^2 with c/L=(1/L_f)(α0+α1L_f+α2L_f^2), it solves for the future horizon L_f and then repeats the reconstruction. The conclusions claim that the EoS is consistent with observations and that the generalized NO-HDE reconstruction has been carried out.

Significance. If correct, the paper would provide explicit analytic reconstruction formulas connecting k-essence to Tsallis and Nojiri–Odintsov holographic dark energy in an emergent-universe background, extending earlier correspondences. The use of the emergent scale factor is concrete, and the authors give closed-form expressions for X and F(t) rather than purely numerical results. However, there is no machine-checked proof or reproducible code, and the only quantitative test is a hand-picked parameter-table comparison of the EoS parameter. Two load-bearing technical problems—an algebraic error in the Tsallis EoS and the silent reduction of the generalized NO-HDE cutoff to the future horizon—mean that the central claims are not supported as they stand.

major comments (4)

[II, Eq. (9)] For ρ_DE = B(αH^2+β\dot H)^{2-δ}, the conservation equation (6) gives w_DE = -1 - (2-δ)(2αH\dot H+β\ddot H)/(3H(αH^2+β\dot H)), so the \dot H and \ddot H coefficients are linear in (2-δ). Equation (9) instead contains coefficients proportional to (-2+δ)^2, including an extra 4α(-2+δ)^2 term. This is an algebraic error, and it propagates into Eq. (17), Eq. (20), Eq. (22), and Table I. The Tsallis reconstruction and its claimed observational consistency are therefore not established.
[III, Eqs. (24)-(29)] The generalized cutoff introduced in Eq. (25) is c/L = (1/L_f)(α0+α1L_f+α2L_f^2), so substituting into Eq. (24) gives ρ = 3(α0/L_f+α1+α2L_f)^2, which depends on all three α coefficients. Yet Eq. (29), and consequently Eqs. (30)-(34) and Figs. 5-6, contain none of α0, α1, or α2; they correspond to the future-horizon density 3c^2/L_f^2, i.e. the case α0=c and α1=α2=0. The advertised 'most generalized Nojiri-Odintsov version' is therefore not the model actually reconstructed, and the Section III results do not test the generalized cutoff.
[Table I and Conclusions] Table I compares w_DE at z=0 computed from Eq. (9) with the observational intervals quoted from Refs. [60] and [61]. Because Eq. (9) is incorrect, this comparison is invalid. Moreover, the table does not list the values of α, β, and δ used for each row, and no statistical criterion is stated for judging 'consistency.' The abstract and conclusions claim consistency with observational data on this basis, so that claim is unsupported.
[II.A and III (reconstruction method)] The reconstruction is algebraic by construction: X is obtained by inverting w_DE from the assumed energy density, and F(t) is then defined as ρ_DE/(-X+3X^2). The reported X(t) and F(t) therefore do not constitute independent predictions, and the only quantitative check offered is the EoS comparison in Table I, which is invalid for the reasons above. The paper should either provide an independent observable (e.g., distance modulus or H(z)) or explicitly state that the reconstruction is a formal correspondence rather than a test.

minor comments (5)

[Abstract] The phrase 'Here,Ulbossyn Ualikhanova in the initial phase of the study' appears to be an accidental insertion of an author name and should be removed.
[Figs. 1-2 captions] The captions say 'red, green, and blue lines correspond to B = 0.5, 0.6 and 0.6,' which lists only two distinct values; the actual parameter values used for the third curve should be provided.
[Table I caption] The caption should state the values of α, β, and δ used in Eq. (9), along with the values of A, b, B, C1, and n, so that the entries can be reproduced.
[Eq. (31)] The phrase 'Using Rqs. (27), (29) and (30)' contains a typo, and the expression should define the hypergeometric function 2F1, with its parameters, clearly at first use.
[Figs. 3-4 captions] The legends give values of n but do not state the fixed values of the other parameters used in Eqs. (21) and (22); this should be specified for reproducibility.

Circularity Check

2 steps flagged · score 6.0 of 10

The advertised NO-HDE construction drops the α terms and reduces to ordinary future-horizon HDE; the k-essence X and F(t) are algebraic rearrangements of the assumed density.

other [Section III, Eqs. (24)-(25) vs Eq. (29)]
"ρNO−HDE = 3c2/L2 (24) where, c/L = 1/Lf [α0 + α1Lf + α2L2f] (25) ... ρNOHDE = 3b2c2n2 / (b(B+ent)b nC1 + (1+Be−nt) 2F1[1,1,1+b,−Be−nt])2 (29)"

Eq. (29) contains none of α0, α1, α2; algebraically it is 3c^2/L_f^2, the α0=1, α1=α2=0 specialization of Eqs. (24)-(25). All subsequent equations (30)-(34) inherit this specialization. The promised 'most generalized Nojiri-Odintsov' reconstruction is therefore by construction identical to ordinary future-horizon HDE; the generalized cutoff is not load-bearing.
self definitional [Section II.A, Eqs. (13), (16), (21)]
"wX = X−1/3X−1 (13) ... let us consider X = 1−wDE/1−3wDE (16) where, wDE comes from Eq. (9) ... Considering k-essence holographically, we can consider ρDE = ρ(φ,X) = f(φ)(−X + 3X2). Thus, f(φ) = ρDE/(−X+3X2)."

Eq. (16) is the algebraic inverse of Eq. (13) with wDE substituted, and F(t) is then defined as ρDE/(−X+3X^2). Hence the reconstructed X and F(t) carry no information beyond the assumed HDE density and the conservation equation; they are identities, not independent outputs. The Table I comparison of wDE checks the chosen parameters of the input density, not a prediction from the reconstruction.

full rationale

The paper is a reconstruction study, and reconstruction by definition is a consistency construction rather than an independent prediction; on that basis the k-essence X and F(t) being algebraic rearrangements of the assumed ρDE is partly the intended method, but the paper frames these outputs and the table comparison as substantive results. The more serious issue is Section III: the advertised 'most generalized Nojiri-Odintsov' cutoff (Eq. 25) is silently replaced by 1/L_f in the density (Eq. 29), so the central generalized construction reduces to the standard future-horizon HDE. No fitted parameters are called predictions and no load-bearing self-citation chain is present; the score reflects the partial reduction of the central construction to a special case and to definitions, not a full 8-10 circularity.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the holographic dark energy densities, the k-essence Lagrangian ansatz, and the emergent scale factor. All are taken from prior literature or chosen by hand; no new entities are postulated. The dominant burden is the by-construction identification of the k-essence field with the holographic fluid.

free parameters (7)

B (Tsallis constant) = not specified
Overall amplitude of the THDE density in Eq. (4); absorbs normalization and is not constrained.
δ (Tsallis non-additivity parameter) = 0.05 in figures
Chosen by hand; controls the power-law in the entropy and the energy density.
α, β (cutoff parameters) = not specified
Appear in the Ricci-like cutoff L=(αH²+βḢ)^{-1/2}; no observational fit.
A, n, B, b (emergent scale factor parameters) = A=0.3, b=0.6, n=0.4 in figures; B varied 0.5, 0.6
Background geometry chosen arbitrarily; affects all results.
C1 (integration constant for L_f) = not specified
Integration constant in Eq. (28); controls the future horizon solution.
c (NO-HDE constant) = not specified
Free normalization of the NO-HDE density.
α0, α1, α2 (NO-HDE cutoff coefficients) = not used
Defined in Eq. (25) but disappear by Eq. (29), so effectively set to a special case.

assumptions (5)

domain assumption FRW flat, isotropic, homogeneous universe
Stated in Section II; standard cosmological background.
domain assumption Non-interacting dark energy conservation ρ̇+3Hρ(1+w)=0
Used to derive all EoS parameters; no interaction between dark energy and matter.
ad hoc to paper Emergent universe scale factor a(t)=A(e^{nt}+B)^b
Chosen for analytic convenience; not observationally motivated.
domain assumption K-essence Lagrangian restricted to p(φ,X)=f(φ)(-X+X²)
Borrowed from prior k-essence literature (refs [52,53]).
domain assumption Tsallis entropy-area relation S_δ=γA^δ
Standard THDE starting point from refs [39,40].

how reviews work

0 comments

Cite this review

Pith. "Pith review of Holographic reconstruction of k-essence model with Tsallis and the most generalized Nojiri-Odintsov version of holographic dark energy." pith.science (2026). https://pith.science/paper/MUXKOC4A

@misc{pith2026250104028,
  author       = {Pith},
  title        = {Pith review of: Holographic reconstruction of k-essence model with Tsallis and the most generalized Nojiri-Odintsov version of holographic dark energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MUXKOC4A}},
  note         = {Machine review of arXiv:2501.04028}
}

read the original abstract

The holographic principle, which has its roots in string theory and black hole thermodynamics, connects the maximum distance of a quantum field theory to its infrared cutoff, which is correlated with the vacuum energy. The present study explores a reconstruction scheme for the k-essence form of dark energy with the most generalized version of holographic dark energy introduced in S. Nojiri, and S. D. Odintsov (2006) (Gen. Relativ. Gravit., 38 p: 1285-1304 ) and (S. Nojiri and S. D. Odintsov, 2017, European Physical Journal C, 77, pp.1-8 ). Here,Ulbossyn Ualikhanova in the initial phase of the study, we begin with a reconstruction scheme of the k-essence model with Tsallis holographic dark energy and finally with a highly generalized version of holographic dark energy with Nojiri-Odintsov generalization. Finally, we have studied the cosmological consequences of the k-essence dark energy with the generalized versions of holographic fluid.

Figures

Figures reproduced from arXiv: 2501.04028 by the authors.

**Figure 2.** FIG. 2: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** FIG. 3: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: FIG. 5: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: FIG. 6: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Effective matter sectors from modified entropies
gr-qc 2025-11 conditional novelty 4.0 of 10

Choosing a modified entropy S(r) fixes a metric f(r)=1-4πM/S'(r), and the Einstein tensor of that metric acts as an anisotropic effective fluid.
Reconstructing FHDE with Scalar and Gauge Fields
gr-qc 2025-02 conditional novelty 4.0 of 10

The paper derives field-theoretic reconstructions of Fractional Holographic Dark Energy for six scalar and gauge models, with the EoS behavior inherited from the FHDE input rather than from the field dynamics.

Reference graph

Works this paper leans on

81 extracted references · 80 canonical work pages · cited by 2 Pith papers

[60]

It is understandable from the table t hat for diﬀerent combinations of values of the model parameters the current values of EoS parameter is in consist ency with observational data

and [61] in Table I. It is understandable from the table t hat for diﬀerent combinations of values of the model parameters the current values of EoS parameter is in consist ency with observational data. The reference [63] suggested a geometrical covariant metho d for producing holographic hypersurfaces. The covariant-preferred screens for phantom and non-...

work page
[61]

S Wang, Y Wang and M Li Phys. Rep. 696 1 (2017)

work page 2017
[1]

Thus, in the present consideration L = H − 1

The case of L = H − 1 Following [40], let us consider a ﬂat FR W universe for which t he Hubble horizon is a proper candidate for the IR cutoﬀ, and there is no interaction between the DE candidate and other components of the universe. Thus, in the present consideration L = H − 1. Using this in Eq. (4) we have ρDE = BH − 2δ+4 (5) In this non-interacting sc...

work page
[2]

The origin of holographic dark energy remains unknown, alth ough the inclusion of the time derivative of the Hubble parameter is expected as it exists in the curvature sc alar

The case of L = (αH 2 + β ˙H)− 1/2 In case we consider L = (αH 2 + β ˙H)− 1/ 2 [66] the dark energy density (5) takes the form ρDE = B(αH 2 + β ˙H)− δ+2 (8) The Hubble parameter ( H = ˙a a ) and constants ( α ) and ( β ) must adhere to existing observational data constraints. The origin of holographic dark energy remains unknown, alth ough the inclusion o...

work page
[3]

There is no singularity

It is ever-present. There is no singularity

work page
[4]

The universe is always vast enough that a classical descri ption of spacetime is suﬃcient

work page
[5]

Quantum ﬁeld theory must be used to describe the source of g ravity

work page
[6]

8 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.490 0.492 0.494 0.496 0.498 0.500 z Xcase1 FIG

The universe is isotropic and homogeneous on a wide scale. 8 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.490 0.492 0.494 0.496 0.498 0.500 z Xcase1 FIG. 1: Evolution of X with redshift z as derived in Eq. (19) based on (15). The red, green, and blue lines c orrespond to B = 0. 5, 0. 6 and 0 . 6, respectively

work page

Show all 81 references

[7]

WMAP measurements suggest that it is spatially ﬂat, with a total density parameter of t = 1. 02 ± 0. 02
[8]

Space Sci

K Bamba, S Capozziello, S Nojiri and S D Odintsov Astrophys. Space Sci. 342 155 (2012)

2012
[9]

A R El-Nabulsi Res. Astron. Astrophys. 11 888 (2011)

2011
[10]

Space Sci

A R El-Nabulsi Astrophys. Space Sci. 327 161 (2010)

2010
[11]

We choose A > 0, B > 0 so that the initial singularity is avoided and the scale fac tor is positive

The universe may contain exotic matter that violates ener gy requirements. We choose A > 0, B > 0 so that the initial singularity is avoided and the scale fac tor is positive. Hence, H = bnent B+ent . Accordingly Eqs. (15) and (17) takes the following forms: Xcase1 = − 3bent +...
[12]

213 and 1

2, 1. 213 and 1 . 217, respectively. the ﬁgures, we have taken A = 0 . 3, δ = 0 . 05, b = 0 . 6, and n = 0 . 4. Considering k-essence holographically, we can consider ρDE = ρ(φ, X ) = f (φ)(− X + 3X 2). Thus, f (φ) = ρDE (− X+3X 2) . Subsequently, we reconstruct f (φ) as funct...
[13]

03 and 1

02, 1. 03 and 1 . 04, respectively. and F(t)case2 =      3Be− 9nt(B+ent) 16 ( bent n2(bent α +Bβ ) (B+ent)2 ) 4δ  ( bent n2(bent α +Bβ ) (B+ent)2 ) 2− δ  2δ b9n16(bentα +Bβ )9(3b2e2ntα − bBent(− 3β +2α (− 2+δ)2)+B(− B+ent)β (− 2+δ)2)      × ( 2b2e2ntα − 2bBent( −...

2006
[14]

J A Frieman, M S Turner and D Huterer Annu. Rev. Astron. Astrophys. 46 385 (2008) 16

2008
[15]

A G Riess et al. Astron. J. 116 1009 (1998)

1998
[16]

D H Weinberg et al. Phys. Rep. 530 87 (2013)

2013
[17]

S Nojiri and S D Odintsov Phys. Lett. B 639 144 (2006)

2006
[18]

S Nojiri, S D Odintsov and H ˇStefanˇ ci´ cPhys. Rev. D 74 086009 (2006)

2006
[19]

S D Odintsov, V K Oikonomou, F P Fronimos and K V Fasoulakos Phys. Rev. D 102 104042 (2020)

2020
[20]

T Padmanabhan Phys. Rev. D 66 021301 (2002)

2002
[21]

E J Copeland, M Sami and S Tsujikawa Int. J. Mod. Phys. D 15 1753 (2006)

2006
[22]

R A El-Nabulsi The European Physical Journal Plus 130 1 (2015)

2015
[23]

They [23] determined the explicit f (R, T ) functions for HDE and NADE

applying the beginning conditions to the correspondin g functions. They [23] determined the explicit f (R, T ) functions for HDE and NADE. The reference [24] proposed a hol ographic description of four-dimensional single- scalar inﬂationary universes and demonstrated how three...
[24]

P McFadden and K Skenderis Phys. Rev. D 81 021301 (2010)

2010
[25]

reconstructed the interaction rate between dark energ y and dark matter for three diﬀerent parameterizations of the deceleration parameter. The model parameters were ob tained [25] by maximum likelihood analysis using observational Hubble parameter data (OHD), type Ia superno ...
[26]

A R El-Nabulsi Res. Astron. Astrophys. 11 759 (2011)

2011
[27]

Odintsov et al

investigated numerous entropic dark energy models—su ch as the Tsallis entropic DE, the R´ enyi entropic DE, and the Sharma-Mittal entropic DE—and concluded that th ey are undoubtedly equivalent to the generalized HDE. Odintsov et al. [28] studied the universe’s early evolu ti...

1902
[28]

A Jawad, U Debnath and F Batool Commun. Theor. Phys. , 64 590 (2015)

2015
[29]

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

2003
[30]

V Sahni nd A Starobinsky Int. J. Mod. Phys. D 15 2105 (2006)

2006
[31]

P Saha and U Debnath Eur. Phys. J. C 79 1 (2019)

2019
[32]

Space Sci

M Sharif and A Jawad Astrophys. Space Sci. 351 321 (2014)

2014
[33]

A Jawad Eur. Phys. J. C 74 3215 (2014)

2014
[34]

M Sharif and K Nazir Mod. Phys. Lett. A 31 1650148 (2016)

2016
[36]

R A El-Nabulsi International Journal of Theoretical Physics 56 1159 (2017)

2017
[37]

M Sharif and M Zubair J. Phys. Soc. Jpn. 82 064001 (2013)

2013
[38]

C Tsallis Entropy 21 696 (2019)

2019
[39]

A Mukherjee J. Cosmol. Astropart. Phys. 2016 055 (2016)

2016
[40]

S Nojiri, S D Odintsov, V K Oikonomou and T Paul Phys. Rev. D 102 023540 (2020)

2020
[41]

S Nojiri, S D Odintsov and T Paul Symmetry 13 928 (2021)

2021
[42]

Dark Universe 42 101277 (2023)

S D Odintsov, S D’Onofrio and T Paul Phys. Dark Universe 42 101277 (2023)

2023
[43]

B Guberina, R Horvat and H Nikoli´ c Phys. Rev. D 72 125011 (2005)

2005
[44]

S Nojiri, S D Odintsov and T Paul Phys. Lett. B , 825 136844 (2022)

2022
[45]

S Chattopadhyay, A Pasqua, A N Tawﬁk and R Myrzakulov Physica Scripta 95 085005 (2020)

2020
[46]

S Nojiri and S D Odintsov Gen. Relativ. Gravit. , 38 1285 (2006)

2006
[47]

G Chakraborty, A Beesham and S Chattopadhyay International Journal of Geometric Methods in Modern Physi cs 20 2350113 (2023)

2023
[48]

S Sultana and S Chattopadhyay Annals of Physic 455 169392 (2023)

2023
[49]

S Nojiri, S D Odintsov and E N Saridakis Phys. Lett. B 797 134829 (2019)

2019
[50]

S Nojiri and S D Odintsov Eur. Phys. J. C 77 1 (2017)

2017
[51]

E N Saridakis, K Bamba, R Myrzakulov and F K Anagnostopoulos J. Cosmol. Astropart. Phys. 2018(12) 012 (2018)

2018
[52]

A Jawad, S Rani, A M Sultan and K Embreen Universe 8 532 (2022)

2022
[53]

C Tsallis and L J Cirto Eur. Phys. J. C 73 1 (2013)

2013
[54]

M Tavayef, A Sheykhi, K Bamba and H Moradpour Phys. Lett. B 781 195 (2018)

2018
[55]

H Moradpour International Journal of Theoretical Physics 55 4176 (2016)

2016
[56]

N Komatsu and S Kimura Phys. Rev. D 90(12) 123516 (2014)

2014
[57]

H Moradpour, A Sheykhi, N Riazi and B Wang Advances in High Energy Physics , 2014(1), p.718583 (2014)

2014
[58]

B D Pandey, P S Kumar and U K Sharma Eur. Phys. J. C 82(3) 1 (2022)

2022
[59]

L Susskind 36(11) 6377 (1995)

1995
[62]

Y S Myung Phys. Lett. B 610 18 (2005)

2005
[63]

E N Saridakis Phys. Rev. D 102 123525 (2020)

2020
[64]

L N Granda and A Oliveros arXiv preprint arXiv:0901.0561 (2009)

2009 arXiv
[65]

N Bose and A S Majumdar Phys. Rev. D 79 103517 (2009) 17

2009
[66]

A Rozas-Fern´ andezPhys. Lett. B 709 313 (2012)

2012
[67]

A Pasqua and S Chattopadhyay Canadian Journal of Physics 91 844 (2013)

2013
[68]

S H Shekh, A Bouali, A Pradhan and A Beesham Journal of High Energy Astrophysics 39 53 (2023)

2023
[69]

S Nojiri and S D Odintsov Gen. Relativ. Gravit. 38 1285 (2006)

2006
[70]

D Pavon and W Zimdahl Phys. Lett. B 628 206 (2005)

2005
[71]

B Wang, Y Gong and E Abdalla Phys. Lett. B 624 141 (2005)

2005
[72]

Space Sci

M Khurshudyan Astrophys. Space Sci. 361 1 (2016)

2016
[73]

Odintsov and E N Saridakis Nuclear Physics B 949 114790 (2019)

S Nojiri, S D. Odintsov and E N Saridakis Nuclear Physics B 949 114790 (2019)

2019
[74]

S Kumar and L Xu Phys. Lett. B 737 244 (2014)

2014
[75]

M Jaber and A de la Macorra Astroparticle Physics 97 130 (2018)

2018
[76]

P A R Ade et al Astronomy & Astrophysics 594 A13 (2016)

2016
[77]

A Rozas-Fern´ andez46 1825 (2014)

2014
[78]

S Srivastava, U K Sharma and A Pradhan New Astronomy 68 57 (2019)

2019
[79]

S Mukherjee, B C Paul, N K Dadhich, S D Maharaj and A Beesham Classical and Quantum Gravity 23 6927 (2006)

2006
[80]

A Oliveros and M A Acero Europhysics Letters 128 59001 (2019)

2019
[81]

J D Barrow and N J Nunes Phys. Rev. D 76 043501 (2007)

2007
[82]

Mohammadi, Z Ossoulian, and K Saaidi Phys

N Nazavari, A. Mohammadi, Z Ossoulian, and K Saaidi Phys. Rev. D 93 123504 (2016)

2016

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [60]

It is understandable from the table t hat for diﬀerent combinations of values of the model parameters the current values of EoS parameter is in consist ency with observational data

and [61] in Table I. It is understandable from the table t hat for diﬀerent combinations of values of the model parameters the current values of EoS parameter is in consist ency with observational data. The reference [63] suggested a geometrical covariant metho d for producing holographic hypersurfaces. The covariant-preferred screens for phantom and non-...

work page

[2] [61]

S Wang, Y Wang and M Li Phys. Rep. 696 1 (2017)

work page 2017

[3] [1]

Thus, in the present consideration L = H − 1

The case of L = H − 1 Following [40], let us consider a ﬂat FR W universe for which t he Hubble horizon is a proper candidate for the IR cutoﬀ, and there is no interaction between the DE candidate and other components of the universe. Thus, in the present consideration L = H − 1. Using this in Eq. (4) we have ρDE = BH − 2δ+4 (5) In this non-interacting sc...

work page

[4] [2]

The origin of holographic dark energy remains unknown, alth ough the inclusion of the time derivative of the Hubble parameter is expected as it exists in the curvature sc alar

The case of L = (αH 2 + β ˙H)− 1/2 In case we consider L = (αH 2 + β ˙H)− 1/ 2 [66] the dark energy density (5) takes the form ρDE = B(αH 2 + β ˙H)− δ+2 (8) The Hubble parameter ( H = ˙a a ) and constants ( α ) and ( β ) must adhere to existing observational data constraints. The origin of holographic dark energy remains unknown, alth ough the inclusion o...

work page

[5] [3]

There is no singularity

It is ever-present. There is no singularity

work page

[6] [4]

The universe is always vast enough that a classical descri ption of spacetime is suﬃcient

work page

[7] [5]

Quantum ﬁeld theory must be used to describe the source of g ravity

work page

[8] [6]

8 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.490 0.492 0.494 0.496 0.498 0.500 z Xcase1 FIG

The universe is isotropic and homogeneous on a wide scale. 8 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.490 0.492 0.494 0.496 0.498 0.500 z Xcase1 FIG. 1: Evolution of X with redshift z as derived in Eq. (19) based on (15). The red, green, and blue lines c orrespond to B = 0. 5, 0. 6 and 0 . 6, respectively

work page