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arxiv: 2506.13446 · v2 · submitted 2025-06-16 · 🌀 gr-qc

Dark Energy Phenomenology in a f(R,Sigma,T) Gravity Framework: O_m(z) Parameterization Approach

N. Myrzakulov , Anirudh Pradhan , Anil Kumar Yadav , S. H. Shekh This is my paper

Pith reviewed 2026-05-19 09:37 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(R,Σ,T) gravityOm(z) parameterizationdark energyequation of statecosmic accelerationFRW metricenergy conditions
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The pith

A logarithmic Om(z) parameterization in f(R,Σ,T) gravity reconstructs a Hubble parameter that produces quintessence dark energy driving late-time acceleration.

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

This paper uses a logarithmic parameterization of the Om(z) diagnostic as a model-independent probe to reconstruct the Hubble parameter inside f(R,Σ,T) gravity. The authors adopt the specific form f(R,Σ,T) = R + Σ + 2π η T and solve the field equations in a flat FRW metric. They obtain an equation-of-state parameter that evolves dynamically yet remains strictly inside the quintessence interval without phantom crossing. The same reconstruction reproduces the observed shift from cosmic deceleration to acceleration. The work positions the model as a viable alternative to the cosmological constant while flagging a classical instability that requires further refinement.

Core claim

Within the f(R,Σ,T) = R + Σ + 2π η T framework, the logarithmic Om(z) parameterization yields a Hubble parameter whose derived equation-of-state parameter ω(z) satisfies −1 < ω < −1/3 at all times, approaches −1 in the far future, and never enters the phantom regime; the deceleration parameter q(z) changes sign at low redshift, confirming the transition to acceleration; and the weak energy condition holds throughout, furnishing a dynamically consistent description of accelerated expansion distinct from ΛCDM.

What carries the argument

The logarithmic parameterization of the Om(z) diagnostic, employed to reconstruct the Hubble parameter that enters the modified Friedmann equations of the f(R,Σ,T) theory.

Load-bearing premise

The specific logarithmic form chosen for Om(z) faithfully represents the true expansion history of the universe.

What would settle it

High-redshift observations that show the Om(z) diagnostic deviating substantially from the assumed logarithmic shape would invalidate the reconstructed Hubble parameter and the derived dark-energy properties.

Figures

Figures reproduced from arXiv: 2506.13446 by Anil Kumar Yadav, Anirudh Pradhan, N. Myrzakulov, S. H. Shekh.

Figure 1
Figure 1. Figure 1: depicts the two-dimensional confidence contours at 1σ and 2σ intervals of our model using the OHD dataset while [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The behavior of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The behavior of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The behavior of [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The behavior of [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The behavior of [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The behavior of [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: The behavior of [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
read the original abstract

This study investigates the cosmological implications of $f(R,\Sigma,T)$ gravity by reconstructing the Hubble parameter from a logarithmic parameterization of the $O_m(z)$ diagnostic. Our approach offers a model-independent way to probe the nature of dark energy and differentiate it from a cosmological constant. We derive the field equations for $f(R,\Sigma,T) = R + \Sigma + 2\pi\eta T$ within the homogeneous, isotropic, and spatially flat Friedmann-Robertson-Walker (FRW) metric. A comprehensive analysis of key physical parameters, including the equation of state (EoS) parameter $\omega(z)$, the $(\omega-\omega')$-plane, the squared sound speed $\vartheta^2$, and various energy conditions (Null, Dominant, Strong), is presented. Our findings reveal a dynamic EoS parameter that consistently remains within the quintessence regime ($-1 < \omega < -1/3$), approaching $\omega = -1$ in the far future, thereby avoiding phantom behavior and maintaining the weak energy condition. The model successfully reproduces the cosmic transition from deceleration to acceleration, as indicated by the deceleration parameter $q(z)$ crossing zero. While the model aligns well with observational data for cosmic expansion, the analysis of $\vartheta^2$ indicates classical instability, a point requiring further theoretical refinement. Overall, this work demonstrates the viability of $f(R,\Sigma,T)$ gravity as a framework capable of describing the universe's accelerated expansion, consistent with current cosmological observations, while offering a dynamic alternative to the $\Lambda$CDM model.

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 investigates dark energy phenomenology in f(R,Σ,T) gravity by reconstructing the Hubble parameter from a logarithmic parameterization of the Om(z) diagnostic. For the specific model f(R,Σ,T) = R + Σ + 2π η T in a flat FRW metric, it derives the modified Friedmann equations and analyzes the redshift-dependent equation-of-state ω(z), deceleration parameter q(z), squared sound speed ϑ², and energy conditions, concluding that ω(z) stays in the quintessence regime, approaches -1 at late times, q(z) crosses zero, the weak energy condition holds, and the model is consistent with observations but exhibits classical instability.

Significance. If the logarithmic Om(z) choice is shown to be robust, the work provides a concrete example of how f(R,Σ,T) gravity can accommodate a dynamic dark-energy equation of state in the quintessence window without phantom crossing while reproducing the observed deceleration-to-acceleration transition. The explicit reconstruction from Om(z) and the reporting of both positive dynamical features and the instability constitute a useful addition to the modified-gravity literature.

major comments (2)
  1. Reconstruction section: The central claims that ω(z) remains in −1 < ω < −1/3, approaches −1, and that q(z) crosses zero all follow directly from inserting the Hubble parameter reconstructed from the assumed logarithmic Om(z) form into the modified Friedmann equations; no robustness tests against alternative Om(z) parameterizations (linear, CPL-style, etc.) or direct likelihood comparison with supernova/BAO data are reported, rendering the quintessence-regime and transition conclusions dependent on this specific functional choice.
  2. Stability analysis: The abstract states that ϑ² indicates classical instability, yet the manuscript provides no quantitative assessment of how this instability affects the viability of the reported energy-condition satisfaction or the late-time approach to ω = −1; this is a load-bearing caveat for the overall phenomenological conclusions.
minor comments (2)
  1. Clarify the physical motivation and field content of the Σ term introduced in the action.
  2. Specify the exact functional form and fitting procedure used for the logarithmic Om(z) parameterization, including any priors or data sets employed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate the revisions incorporated into the updated manuscript.

read point-by-point responses

  1. Referee: Reconstruction section: The central claims that ω(z) remains in −1 < ω < −1/3, approaches −1, and that q(z) crosses zero all follow directly from inserting the Hubble parameter reconstructed from the assumed logarithmic Om(z) form into the modified Friedmann equations; no robustness tests against alternative Om(z) parameterizations (linear, CPL-style, etc.) or direct likelihood comparison with supernova/BAO data are reported, rendering the quintessence-regime and transition conclusions dependent on this specific functional choice.

    Authors: We agree that the reported quintessence behavior and deceleration-to-acceleration transition are obtained for the specific logarithmic Om(z) parameterization adopted in the reconstruction. This functional form was chosen because it yields a simple analytic Hubble parameter that naturally produces −1 < ω(z) < −1/3 without phantom crossing while satisfying the observed late-time acceleration. In the revised manuscript we have added a dedicated paragraph in the reconstruction section that motivates the logarithmic choice by reference to its consistency with recent Om(z) reconstructions from observational data and briefly contrasts it with linear and CPL forms. We also explicitly state the model dependence of the conclusions. A full statistical comparison with supernova and BAO datasets lies outside the scope of the present phenomenological study and is noted as a worthwhile extension. revision: partial

  2. Referee: Stability analysis: The abstract states that ϑ² indicates classical instability, yet the manuscript provides no quantitative assessment of how this instability affects the viability of the reported energy-condition satisfaction or the late-time approach to ω = −1; this is a load-bearing caveat for the overall phenomenological conclusions.

    Authors: The referee correctly notes that the original text reports ϑ² < 0 but does not quantify its consequences for the other observables. In the revised version we have expanded the stability subsection to include a qualitative discussion: the negative sound-speed squared appears mainly at higher redshifts, while the weak energy condition remains satisfied and ω(z) approaches −1 at late times when the universe is accelerating. We emphasize that this classical instability signals the need for further theoretical work (e.g., on perturbation growth) but does not invalidate the background-level results presented. A fully quantitative stability analysis is flagged as future work. revision: yes

Circularity Check

0 steps flagged

Reconstruction via explicit Om(z) parameterization is a standard phenomenological method with no reduction to inputs by construction

full rationale

The paper explicitly adopts a logarithmic parameterization of the Om(z) diagnostic as its starting assumption to reconstruct H(z), then substitutes the resulting expansion history into the modified Friedmann equations of the chosen f(R,Σ,T) model. This produces derived quantities such as ω(z) and q(z) that are conditional on the input parameterization, but the method is presented as reconstruction rather than an independent first-principles derivation. No step equates a claimed prediction or result to its own fitted parameters by construction, nor does any load-bearing premise reduce to a self-citation or self-definition. The analysis remains self-contained as a model-specific exploration under a stated ansatz, consistent with common cosmological reconstruction techniques.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on a chosen functional form for f, a specific parameterization of Om(z), and standard cosmological assumptions; these introduce free parameters and domain assumptions that are not independently verified in the abstract.

free parameters (2)
  • η
    Coupling constant appearing in the linear f(R,Σ,T) = R + Σ + 2π η T form; its value is required to close the field equations.
  • logarithmic Om(z) parameters
    Coefficients in the assumed logarithmic parameterization of Om(z) that are adjusted to match expansion data.
axioms (1)
  • domain assumption Homogeneous, isotropic, spatially flat FRW metric
    Invoked to derive the field equations for the modified gravity theory.
invented entities (1)
  • Σ term in f(R,Σ,T) no independent evidence
    purpose: Additional geometric or matter-coupling degree of freedom in the modified gravity action
    Introduced as part of the f(R,Σ,T) framework without independent falsifiable prediction outside the model.

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