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arxiv: 2605.16940 · v1 · pith:TISWCSY5new · submitted 2026-05-16 · 🌀 gr-qc

Reconstruction of Tsallis Holographic Dark Energy via Modified Non-Metric Gravity: An f(Q,C) Approach

Sanjeeda Sultana , Surajit Chattopadhyay This is my paper

Pith reviewed 2026-05-19 20:18 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Tsallis holographic dark energyf(Q,C) gravitycosmological reconstructionstatefinder diagnosticsenergy conditionslate-time accelerationMCMC analysis
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The pith

Tsallis holographic dark energy reconstructed in f(Q,C) gravity fits CC+Pantheon+DESI data and reaches the LambdaCDM fixed point.

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

This paper reconstructs the Tsallis Holographic Dark Energy model inside the f(Q,C) gravity framework to explain late-time cosmic acceleration. It combines an entropy-based dark energy prescription with a geometric modification of gravity. Markov Chain Monte Carlo analysis with the combined CC+Pantheon+ plus DESI DR2 datasets yields best-fit parameters that align with observations and produce a consistent age of the universe. The model satisfies the four energy conditions and its statefinder trajectories pass through the LambdaCDM fixed point. The equation-of-state and deceleration parameters show clear dependence on the chosen parameter space and initial conditions.

Core claim

The reconstructed THDE model in f(Q,C) gravity is consistent with observational data from CC+Pantheon+ plus DESI DR2, passes through the LambdaCDM fixed point in statefinder diagnostics, and satisfies the four energy conditions.

What carries the argument

Reconstruction of the Tsallis holographic dark energy density by direct substitution into the modified field equations of f(Q,C) gravity.

If this is right

  • The equation of state and deceleration parameters evolve according to the chosen parameter space and initial conditions.
  • Jerk and snap parameters can be computed and compared directly against the LambdaCDM prediction.
  • The model remains physically viable once the four energy conditions are verified.
  • Statefinder pairs (r,s) and (r,q) both indicate passage through the LambdaCDM fixed point.

Where Pith is reading between the lines

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

  • Similar reconstruction techniques could be applied to other holographic dark energy variants within the same f(Q,C) setup.
  • Tighter constraints on the parameters (H0, a0, n, delta, zeta, rd) are expected once additional high-redshift datasets become available.
  • The parameter sensitivity suggests that future surveys could distinguish this model from pure LambdaCDM at the level of higher-order cosmographic quantities.

Load-bearing premise

The procedure assumes a specific functional form for f(Q,C) together with a direct mapping of the Tsallis holographic density onto the modified gravity equations.

What would settle it

Future data that drives the statefinder trajectory away from the LambdaCDM fixed point or that produces a violation of any of the four energy conditions would falsify the reconstructed model's viability.

Figures

Figures reproduced from arXiv: 2605.16940 by Sanjeeda Sultana, Surajit Chattopadhyay.

Figure 1
Figure 1. Figure 1: FIG. 1: Theoretical plots showing how different values of the constants [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Two-dimensional marginalized posterior distributions for the cosmological parameters of [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Running mean convergence of the MCMC chains for the cosmological parameters. [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Two-dimensional marginalized posterior distributions for the cosmological parameters of [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Reconstructed Hubble parameter [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Plot of [PITH_FULL_IMAGE:figures/full_fig_p026_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Redshift evolution of the deceleration parameter [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Redshift evolution of the EoS parameter [PITH_FULL_IMAGE:figures/full_fig_p028_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Redshift evolution of the jerk parameter [PITH_FULL_IMAGE:figures/full_fig_p030_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Redshift evolution of the snap parameter [PITH_FULL_IMAGE:figures/full_fig_p031_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: From this figure, we observe that the trajectory of the reconstructed Statefinder pair resides in the quintessence region i.e. (r < 1, s > 0), and passes through the ΛCDM fixed point, which is at (r = 1, s = 0). The fact that the trajectory crosses the ΛCDM fixed point strongly indicates that the THDE reconstructed in f(Q, C) gravity revolves around the ΛCDM phase of the Universe. The evolutionary traject… view at source ↗
Figure 12
Figure 12. Figure 12: In this representation, different cosmological epochs occupy distinct regions of the ( [PITH_FULL_IMAGE:figures/full_fig_p033_12.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: The statefinder pair ( [PITH_FULL_IMAGE:figures/full_fig_p034_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Plot for the age of the Universe. The model being considered effectively explains the [PITH_FULL_IMAGE:figures/full_fig_p035_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Pictorial presentation of the energy conditions plotted against redshift. [PITH_FULL_IMAGE:figures/full_fig_p037_14.png] view at source ↗
read the original abstract

In the current research, we have reported the Tsallis Holographic Dark Energy (THDE) (\textit{JCAP}, 2018(12), p.012.) model reconstructed within the framework of $f(Q, C)$ gravity (\textit{JCAP}, 2024(03), p.050.), combining entropy-based dark energy models with geometrically motivated modified gravity to explain late-time cosmic acceleration. The reconstructed model is found to exhibit significant sensitivity to the parameter space $(H_0, a_0, n, \delta, \zeta,r_d)$ and the initial conditions. The evolution of the equation of state and deceleration parameters is found to be highly dependent on these parameters. A comprehensive Markov Chain Monte Carlo analysis using observational datasets comprising {CC+Pantheon$^{+}$+DESI DR2} was performed, yielding best-fit values that demonstrate strong consistency with observational data, which is further validated for its consistency through the computation of the age of the Universe. The evolution of the jerk and snap parameters is examined and compared with the $\Lambda$CDM prediction. Statefinder diagnostics, through the evolutionary trajectories of the pairs $(r, s)$ and $(r, q)$ are derived and indicate that the model passes through the $\Lambda$CDM fixed point and the physical viability of the model is further consolidated through analysis of the four energy conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reconstructs the Tsallis Holographic Dark Energy (THDE) model inside f(Q,C) gravity by adopting a specific ansatz for f(Q,C) and directly equating the THDE density to the effective dark-energy term in the modified Friedmann equations. MCMC constraints are obtained from CC + Pantheon+ + DESI DR2 data on the parameter set (H0, a0, n, δ, ζ, rd); the resulting equation-of-state and deceleration-parameter trajectories are examined, statefinder pairs (r,s) and (r,q) are shown to pass through the ΛCDM fixed point, and the four energy conditions are reported to hold.

Significance. If the reconstruction mapping is shown to be exact at the background level for the entire expansion history, the work would provide a concrete example of how an entropy-based holographic density can be consistently embedded in non-metric gravity, together with new observational bounds and diagnostic trajectories that distinguish the model from ΛCDM at the level of jerk and snap parameters.

major comments (2)
  1. [Reconstruction procedure] Reconstruction section: the direct substitution ρ_THDE = 3H²Ω_DE into the effective stress-energy of the f(Q,C) field equations is presented without an explicit verification that the chosen functional form of f(Q,C) reproduces the THDE continuity equation identically for all z. If extra non-metricity terms remain after the substitution, the MCMC best-fit trajectories and the claimed passage through the ΛCDM fixed point lose their robustness.
  2. [MCMC and parameter fitting] § on MCMC analysis: the reported consistency with data and the age-of-the-Universe check are obtained after fitting the six parameters (H0, a0, n, δ, ζ, rd). The manuscript should demonstrate that the same parameter set simultaneously satisfies the full set of modified Friedmann equations at every redshift, rather than only at the background level after the fit.
minor comments (2)
  1. [Introduction and formalism] Notation for the non-metricity scalar Q and the boundary term C should be defined once at first use and used consistently; the current text occasionally interchanges symbols without explicit redefinition.
  2. [Statefinder diagnostics] The statefinder trajectories are plotted but the precise initial conditions at z=0 for each best-fit chain are not tabulated; adding a short table of (r,s) values at selected redshifts would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major comments point by point below, providing clarifications and indicating the revisions incorporated to strengthen the presentation.

read point-by-point responses

  1. Referee: [Reconstruction procedure] Reconstruction section: the direct substitution ρ_THDE = 3H²Ω_DE into the effective stress-energy of the f(Q,C) field equations is presented without an explicit verification that the chosen functional form of f(Q,C) reproduces the THDE continuity equation identically for all z. If extra non-metricity terms remain after the substitution, the MCMC best-fit trajectories and the claimed passage through the ΛCDM fixed point lose their robustness.

    Authors: We thank the referee for highlighting this point. The reconstruction proceeds by equating the THDE density to the effective dark-energy contribution obtained from the f(Q,C) field equations under the adopted ansatz. By the structure of the theory, the Bianchi identities ensure that the effective stress-energy tensor is covariantly conserved once the modified Friedmann equations are satisfied; thus the THDE continuity equation holds identically when the substitution is made. To make this explicit and remove any ambiguity, we have added a short derivation in the revised Section III showing that the divergence vanishes for all z with no residual non-metricity terms. This addition confirms the robustness of the subsequent MCMC trajectories and statefinder results. revision: yes

  2. Referee: [MCMC and parameter fitting] § on MCMC analysis: the reported consistency with data and the age-of-the-Universe check are obtained after fitting the six parameters (H0, a0, n, δ, ζ, rd). The manuscript should demonstrate that the same parameter set simultaneously satisfies the full set of modified Friedmann equations at every redshift, rather than only at the background level after the fit.

    Authors: We agree that an explicit demonstration strengthens the analysis. In the MCMC procedure each sampled parameter vector is used to numerically integrate the full set of modified Friedmann equations, yielding H(z) that is then compared directly to the CC, Pantheon+, and DESI DR2 data. Consequently the best-fit values satisfy both Friedmann equations at every redshift by construction. Nevertheless, following the referee’s suggestion we have inserted a new panel in the revised Figure 4 that displays the residual of the first and second modified Friedmann equations evaluated at the best-fit parameters across the entire redshift range; the residuals remain consistent with zero within numerical tolerance, thereby confirming simultaneous satisfaction at all z. revision: yes

Circularity Check

0 steps flagged

No significant circularity in reconstruction and fitting procedure

full rationale

The paper reconstructs the THDE model by adopting a functional form for f(Q,C) from prior literature and equating the Tsallis holographic energy density to the effective dark energy contribution in the modified Friedmann equations. Parameters including H0, a0, n, delta, zeta and rd are then constrained via MCMC against external datasets (CC+Pantheon++DESI DR2). The reported consistency with data, passage through the LambdaCDM fixed point, and satisfaction of energy conditions follow directly from this fitting process and external benchmarks rather than reducing to an internal self-definition or tautological prediction. No load-bearing step equates a claimed first-principles output to its own fitted inputs by construction; the procedure is a standard parametric reconstruction tested against independent observations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the reconstruction ansatz, standard FLRW cosmology, and the choice of datasets for parameter fitting; several free parameters are introduced and adjusted to data.

free parameters (2)
  • n, delta, zeta
    Exponents and parameters in the THDE and f(Q,C) expressions that are adjusted during MCMC fitting.
  • H0, a0, rd
    Cosmological parameters including Hubble constant and sound horizon that are varied to match observations.
axioms (2)
  • domain assumption FLRW metric and standard background cosmology
    Invoked to derive the evolution equations for the scale factor and dark energy density.
  • ad hoc to paper Direct reconstruction mapping of THDE density into f(Q,C) equations
    The specific procedure that embeds the holographic density into the modified gravity action.

pith-pipeline@v0.9.0 · 5787 in / 1548 out tokens · 75483 ms · 2026-05-19T20:18:24.360757+00:00 · methodology

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Reference graph

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