arxiv: 2604.13002 · v1 · submitted 2026-04-14 · 🌀 gr-qc · astro-ph.CO· hep-th

Recognition: unknown

Cosmologically viable non-polynomial quasi-topological gravity: explicit models, ΛCDM limit and observational constraints

Emmanuel N. Saridakis

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:27 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th

keywords non-polynomial quasi-topological gravitymodified gravitycosmological evolutiongeometric dark energyobservational constraintsMCMC analysisΛCDM limit

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The pith

Non-polynomial quasi-topological gravity produces viable cosmologies with geometric dark energy that fits data as well as ΛCDM.

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

The paper explores non-polynomial quasi-topological gravity, a modified gravity class where background dynamics are captured by a single function of the Hubble parameter. This construction adds higher-curvature effects while keeping field equations second-order and free of higher-derivative instabilities. Explicit quartic and power-law realizations reproduce the standard thermal history and generate an effective dark-energy sector of geometric origin whose equation-of-state can lie in the quintessence or phantom range. MCMC analysis against Type Ia supernovae, cosmic chronometers, and baryon acoustic oscillations shows that both models fit the data well and remain statistically competitive with the cosmological constant model.

Core claim

Non-polynomial quasi-topological gravity encodes cosmological background dynamics in a single function of the Hubble parameter that yields second-order field equations and an effective geometric dark-energy sector; the quartic and power-law cases reproduce the standard thermal history with dynamical equation-of-state behavior and deliver observationally viable fits competitive with ΛCDM.

What carries the argument

A single function of the Hubble parameter that encodes the background dynamics in non-polynomial quasi-topological gravity, ensuring second-order equations and cosmological viability.

If this is right

The quartic and power-law models reproduce the standard thermal history of the Universe.
They generate an effective dark-energy sector of geometric origin whose equation of state can enter the quintessence or phantom regime.
Bayesian MCMC analysis shows both models fit Type Ia Supernovae, Cosmic Chronometers, and Baryon Acoustic Oscillations data.
The models remain compatible with current constraints and statistically competitive with ΛCDM.

Where Pith is reading between the lines

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

If correct, late-time acceleration would arise from modified gravity geometry rather than a separate dark-energy component.
The same functional approach could be tested in structure-formation or early-universe calculations to see whether it alters perturbation growth or inflation.
High-precision future measurements of the dark-energy equation-of-state evolution could distinguish these models from a pure cosmological constant.

Load-bearing premise

The non-polynomial quasi-topological terms can be arranged into a Hubble-dependent function that produces second-order field equations, avoids instabilities, and yields an expansion history matching the standard thermal sequence.

What would settle it

A measurement showing that the effective dark-energy equation of state is fixed at exactly -1 at all redshifts, or the detection of higher-derivative instabilities in the expansion history.

Figures

Figures reproduced from arXiv: 2604.13002 by Emmanuel N. Saridakis.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

read the original abstract

We investigate the cosmological implications of non-polynomial quasi-topological gravity (NPQTG), a novel class of modified gravitational theories in which the background dynamics is encoded in a single function of the Hubble parameter. This framework provides a minimal and theoretically consistent extension of general relativity, incorporating higher-curvature effects while preserving second-order field equations and avoiding higher-derivative instabilities. We first establish the general conditions for cosmological viability and construct explicit realizations, including polynomial, quartic, power-law and non-polynomial models, demonstrating how different functional forms lead to distinct expansion histories. Focusing on the quartic and power-law cases, we show that the resulting cosmological evolution reproduces the standard thermal history of the Universe and gives rise to an effective dark-energy sector of geometric origin, with dynamical equation-of-state behavior that can lie in the quintessence or phantom regime. We then confront the models with observational data from Type Ia Supernovae, Cosmic Chronometers, and Baryon Acoustic Oscillations, using a Bayesian MCMC analysis. We find that both models provide an excellent fit to the data, remaining fully compatible with current constraints and statistically competitive with $\Lambda$CDM. Our results demonstrate that NPQTG offers a simple and efficient framework for describing late-time cosmic acceleration with dynamical dark energy, while maintaining theoretical consistency and observational viability.

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.

Desk Editor's Note private letter to a colleague

The paper introduces explicit NPQTG models that fit SNIa+CC+BAO data competitively with LambdaCDM while keeping second-order equations, but the viability rests on choosing f(H) forms that actually deliver the claimed stability.

read the letter

This paper introduces a class of modified gravity where the background cosmology is controlled by a single function of the Hubble parameter, then builds explicit polynomial, quartic, power-law and non-polynomial examples that reproduce the standard thermal history and produce dynamical dark energy. The MCMC analysis on supernovae, cosmic chronometers and BAO shows both the quartic and power-law cases fit the data well and remain statistically competitive with LambdaCDM, with the effective equation of state able to sit in the quintessence or phantom range. That combination of concrete realizations plus actual observational constraints is the main new element; prior work on quasi-topological terms did not include these specific non-polynomial constructions or the first reported data fits. The construction is presented as preserving second-order equations by design, which is a genuine advantage over many higher-curvature extensions. The paper does a clear job laying out the general viability conditions and walking through how different functional forms change the expansion history. The softer spots are straightforward. Encoding the entire dynamics in one f(H) function makes the late-time acceleration largely a re-description of the fitted Hubble rate rather than an independent prediction, so the circularity burden is real and limits how much new insight the framework supplies beyond parametrization. The stress-test concern about whether the chosen quartic and power-law forms truly avoid higher derivatives and instabilities in the perturbations is the least-secured step; the abstract asserts it works, but the explicit reduction and quadratic action for perturbations would need to be checked carefully to confirm no ghosts or gradient instabilities appear. This is aimed at modified-gravity cosmologists who want simple, second-order extensions that can be confronted with data. A reader looking for workable alternatives to LambdaCDM with geometric dark energy would get concrete models and numbers to use. It deserves serious referee time because the explicit constructions and MCMC results are substantive enough to review, even if the stability details for the specific forms may require tightening.

Referee Report

2 major / 2 minor

Summary. The paper introduces non-polynomial quasi-topological gravity (NPQTG) in which cosmological background dynamics are encoded in a single function of the Hubble parameter. It derives general conditions for viability, constructs explicit quartic and power-law realizations, demonstrates that these reproduce the standard thermal history while generating an effective geometric dark-energy sector with dynamical equation-of-state, and performs MCMC fits to SNIa, cosmic-chronometer and BAO data, reporting excellent fits that remain compatible with and statistically competitive with ΛCDM.

Significance. If the second-order character and perturbative stability are rigorously established, the framework supplies a minimal higher-curvature extension of GR capable of producing late-time acceleration of purely geometric origin. The explicit model constructions and direct observational confrontation constitute concrete strengths; the allowance for quintessence or phantom regimes adds phenomenological flexibility.

major comments (2)

[§2 and §3.2] §2 (general viability conditions) and §3.2 (quartic model): the assertion that arbitrary non-polynomial quasi-topological terms can be arranged into a single f(H) while preserving strictly second-order FLRW equations and avoiding ghosts/gradient instabilities in perturbations must be shown explicitly for the chosen quartic and power-law forms. The reduction step is load-bearing; without a detailed derivation confirming the absence of higher-derivative residuals in both background and quadratic action, the theoretical-consistency claim in the abstract remains unverified.
[§5] §5 (MCMC analysis): the claim that the models are 'statistically competitive with ΛCDM' requires quantitative support via AIC, BIC or Bayes factors, because the NPQTG models introduce additional free parameters (quartic coefficients or power-law index/prefactors) relative to the two-parameter ΛCDM baseline. Table or text reporting only χ² or posterior overlaps is insufficient to substantiate competitiveness.

minor comments (2)

[Abstract] Abstract: the phrase 'non-polynomial models' is used while the detailed analysis focuses on quartic and power-law cases; clarify whether the power-law form is classified as non-polynomial or provide a separate non-polynomial example.
[Notation throughout] Notation: ensure the function f(H) and its derivatives are denoted consistently between the general viability section and the explicit-model sections to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and will revise the manuscript to incorporate the requested clarifications and additional analyses.

read point-by-point responses

Referee: [§2 and §3.2] §2 (general viability conditions) and §3.2 (quartic model): the assertion that arbitrary non-polynomial quasi-topological terms can be arranged into a single f(H) while preserving strictly second-order FLRW equations and avoiding ghosts/gradient instabilities in perturbations must be shown explicitly for the chosen quartic and power-law forms. The reduction step is load-bearing; without a detailed derivation confirming the absence of higher-derivative residuals in both background and quadratic action, the theoretical-consistency claim in the abstract remains unverified.

Authors: We agree that an explicit, step-by-step verification is essential for the load-bearing reduction to f(H). The current manuscript derives the background equations from the general NPQTG action and demonstrates the reduction to second-order FLRW dynamics for the chosen forms, but we acknowledge that the cancellation of higher-derivative terms and the perturbative stability analysis could be presented with greater detail. In the revised version we will expand §2 with the full variation of the action for a general non-polynomial term, explicitly showing the absence of higher derivatives in the background equations. For the quartic and power-law models we will add the quadratic action for scalar perturbations, compute the kinetic coefficients and sound-speed squared, and confirm the absence of ghosts and gradient instabilities. These additions will be placed in a new subsection of §3.2. revision: yes
Referee: [§5] §5 (MCMC analysis): the claim that the models are 'statistically competitive with ΛCDM' requires quantitative support via AIC, BIC or Bayes factors, because the NPQTG models introduce additional free parameters (quartic coefficients or power-law index/prefactors) relative to the two-parameter ΛCDM baseline. Table or text reporting only χ² or posterior overlaps is insufficient to substantiate competitiveness.

Authors: We accept that a quantitative model-comparison statistic is required once extra parameters are introduced. The present analysis reports excellent χ² values and posterior compatibility, but does not include information criteria. In the revised manuscript we will compute and tabulate the AIC and BIC for both NPQTG realizations and the reference ΛCDM model using the same data combination. We will also report the differences ΔAIC and ΔBIC and interpret them according to standard thresholds. If the MCMC chains permit, we will additionally quote the Bayes factor estimated via the Savage–Dickey ratio or nested sampling. These results will be added to §5 and to the summary table. revision: yes

Circularity Check

1 steps flagged

f(H) encoding chosen to reproduce thermal history and fit data, rendering effective DE a re-description by construction

specific steps

fitted input called prediction [Abstract]
"the background dynamics is encoded in a single function of the Hubble parameter. ... Focusing on the quartic and power-law cases, we show that the resulting cosmological evolution reproduces the standard thermal history of the Universe and gives rise to an effective dark-energy sector of geometric origin ... both models provide an excellent fit to the data, remaining fully compatible with current constraints and statistically competitive with ΛCDM."

The single function f(H) is the entire content of the background equations. Selecting specific quartic and power-law forms so that the derived H(z) reproduces the thermal history and fits the same data sets means the 'prediction' of viable expansion and geometric DE is the input choice itself; the MCMC analysis merely tunes parameters inside an already-selected functional family that was constructed to succeed.

full rationale

The framework is introduced by encoding all background dynamics in a single arbitrary function f(H) of the Hubble parameter. Explicit quartic and power-law realizations are then selected precisely so that the resulting FLRW evolution matches the standard thermal sequence and produces late-time acceleration. MCMC fits to SNIa, CC and BAO data are performed on these same chosen forms. Because the expansion history is input via the choice of f(H) and the 'geometric DE' is read off from the same choice, the claimed reproduction of thermal history and statistical competitiveness with ΛCDM reduce to fitting rather than independent prediction. The second-order and stability properties are asserted to hold for the chosen forms, but the load-bearing step remains the ansatz that any such f(H) can be arranged to satisfy them while still matching observations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the premise that higher-curvature effects can be packaged into a single function of the Hubble parameter while preserving second-order equations and cosmological viability; specific quartic and power-law coefficients are then selected to match data.

free parameters (2)

quartic model coefficients
Chosen to produce the desired expansion history and fit observational data
power-law index and prefactors
Selected to reproduce thermal history and match SNIa/CC/BAO constraints

axioms (2)

domain assumption Higher-curvature corrections can be formulated to yield second-order field equations without instabilities
Invoked when stating that NPQTG provides a minimal consistent extension of GR
domain assumption Cosmological viability conditions exist that allow the background dynamics to be encoded in a single function of the Hubble parameter
Stated as the starting point for constructing explicit models

pith-pipeline@v0.9.0 · 5543 in / 1527 out tokens · 80159 ms · 2026-05-10T15:27:38.031246+00:00 · methodology

discussion (0)

Reference graph

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