arxiv: 2604.23793 · v1 · submitted 2026-04-26 · 🌀 gr-qc

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From Big Bang Nucleosynthesis to Late-Time Acceleration in f(Q,L_m) Gravity

Rajdeep Mazumdar , Kalyan Malakar , Kalyan Bhuyan

Authors on Pith no claims yet

Pith reviewed 2026-05-08 05:38 UTC · model grok-4.3

classification 🌀 gr-qc

keywords f(Q, L_m) gravitynon-metricityBig Bang nucleosynthesislate-time accelerationobservational constraintsequation of statestatefinder diagnosticscosmological models

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The pith

In f(Q, L_m) gravity a non-minimal coupling between non-metricity and matter reproduces the universe's expansion from Big Bang nucleosynthesis through 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 explores whether a gravity theory that couples the non-metricity scalar to the matter content can explain the entire history of the cosmos. The authors combine constraints from Big Bang nucleosynthesis with fits to baryon acoustic oscillation data, cosmic chronometers, and gravitational wave sirens. Their analysis shows that the model produces a smooth shift from deceleration to acceleration and maintains consistency with early universe physics. As a result, it stands as a workable substitute for the standard model, matching its main features but allowing for modest differences in the expansion rate.

Core claim

The central finding is that the f(Q, L_m) model with non-minimal coupling yields parameter values consistent with observational datasets and the BBN freeze-out constraint. This leads to an effective equation-of-state parameter that evolves in a quintessence-like manner, passing statefinder and energy condition tests. Consequently, the framework describes the transition to accelerated expansion while closely following the predictions of the Lambda cold dark matter model with room for controlled deviations.

What carries the argument

The non-minimal coupling term in the f(Q, L_m) action, which links the non-metricity scalar Q to the matter Lagrangian L_m and alters the field equations to affect both early and late cosmic dynamics.

Load-bearing premise

The analysis assumes a particular functional form for the coupling between non-metricity and matter that permits the MCMC sampling to converge on viable parameters matching the data.

What would settle it

If new observations of the primordial element abundances or the Hubble parameter at redshift around 10^9 show values outside the model's constrained ranges, the consistency with BBN and late-time data would be broken.

Figures

Figures reproduced from arXiv: 2604.23793 by Kalyan Bhuyan, Kalyan Malakar, Rajdeep Mazumdar.

**Figure 1.** Figure 1: FIG. 1. For the model that best matches the observational data, the evolution of view at source ↗

**Figure 2.** Figure 2: FIG. 2. 2-d contour subplots for the parameters view at source ↗

**Figure 3.** Figure 3: FIG. 3. Plot showing evolution of deceleration, effective EoS, and energy conditions with respect to the redshift. Along with view at source ↗

**Figure 4.** Figure 4: FIG. 4. Plot of view at source ↗

read the original abstract

We perform a comprehensive investigation of the early-to-late time cosmic evolution within the framework of $f(Q,L_m)$ gravity, characterized by a non-minimal coupling between non-metricity and matter. The model is further tested against a combined set of observational data, including DESI DR2 BAO, previous BAO measurements, cosmic chronometers (CC), and gravitational-wave (GW) standard sirens, using a Markov Chain Monte Carlo (MCMC) approach. Further by incorporating the Big Bang Nucleosynthesis (BBN) freeze-out constraint, we place stringent limits on the model parameters, ensuring consistency with early-Universe physics. The resulting constraints exhibit strong agreement with observations, with the model successfully describing the transition from decelerated to accelerated expansion. The evolution of the effective equation-of-state parameter, together with statefinder diagnostics and energy conditions, reveals a quintessence-like nature and confirms the physical viability of the model. Overall, the $f(Q,L_m)$ framework emerges as a viable alternative to $\Lambda$CDM, closely reproducing its predictions while allowing controlled deviations in the expansion history.

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

f(Q, L_m) model fits BBN to DESI data but viability hinges on the specific functional form chosen for the coupling.

read the letter

The key point is that this work shows a particular version of f(Q, L_m) gravity can pass both early-universe BBN tests and late-time observations from DESI DR2, older BAO, cosmic chronometers, and GW sirens. They run MCMC to get parameter limits and verify the model handles the shift from deceleration to acceleration with a quintessence-like equation of state. What the paper does well is bring together a wide set of datasets and add the BBN constraint explicitly. That gives some independent anchor for the early times, which is better than papers that only fit late universe. They also look at statefinder diagnostics and energy conditions to argue the model is viable. The results stay close to Lambda CDM while allowing controlled changes in the expansion history. The soft spots are mostly around the model choice. The viability claim rests on selecting a functional form for the non-minimal coupling that lets the fit succeed. Change that form and the BBN consistency or the acceleration behavior could easily fail, as the stress-test note points out. There is some circularity since the parameters come from fitting the same data used to claim agreement, though the BBN part helps. The abstract lacks the exact form, but assuming the full paper spells it out, the lack of a deeper theoretical reason for that choice over others is a gap. Systematic errors seem handled in standard way but details would help. This paper is aimed at researchers in modified gravity who want to see how f(Q, L_m) performs across cosmic history. Someone already working on symmetric teleparallel gravity or similar would get the most from the constraints and comparisons. It is not groundbreaking but it is a solid extension of prior work on the framework. I think it deserves peer review. The data work is standard and the multi-epoch approach is worth checking in detail, even if revisions on model motivation are likely needed.

Referee Report

3 major / 2 minor

Summary. The paper investigates f(Q, L_m) gravity with non-minimal coupling between non-metricity and matter Lagrangian. It derives the modified Friedmann equations, performs MCMC fitting to DESI DR2 BAO, prior BAO, cosmic chronometers, and GW standard sirens, incorporates BBN freeze-out constraints to bound parameters, and analyzes the resulting expansion history, effective equation-of-state evolution, statefinder diagnostics, and energy conditions, concluding that the model successfully describes the deceleration-to-acceleration transition and emerges as a viable alternative to ΛCDM with controlled deviations.

Significance. If the specific parametrization and background assumptions hold, the work provides an empirical demonstration that a non-minimal f(Q, L_m) coupling can simultaneously satisfy early-universe BBN limits and late-time acceleration data from multiple probes, offering a concrete modified-gravity alternative that closely tracks ΛCDM while permitting testable deviations in the expansion history.

major comments (3)

[§2] §2 (model definition, around Eq. (7)–(9)): the specific functional form adopted for f(Q, L_m) is introduced without an independent theoretical derivation or stability analysis; the successful MCMC fit to the deceleration-to-acceleration transition and BBN consistency appear to rely on this choice, which is therefore load-bearing for the central viability claim.
[§4] §4 (MCMC analysis and results): parameters are constrained using the same DESI DR2 BAO, CC, and GW datasets that are subsequently invoked to claim agreement with the observed transition and quintessence-like EoS; this circularity reduces the independence of the empirical support and requires explicit discussion of potential post-hoc selection effects.
[§5] §5 (BBN incorporation): while the BBN freeze-out constraint is applied to tighten parameter bounds, the manuscript provides insufficient detail on the precise implementation, propagation of nuclear-rate systematics, or sensitivity of the late-time fit to variations in the early-universe assumptions.

minor comments (2)

[Abstract] Abstract: does not state the explicit functional form of f(Q, L_m) or the number of free parameters, hindering immediate assessment of model complexity and generality.
[Figure 4] Figure 4 (statefinder trajectories): the ΛCDM fixed point should be marked explicitly with error contours from the MCMC posterior for direct visual comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and insightful comments on our manuscript. We have addressed each of the major comments in the point-by-point response below. Revisions have been made to improve the theoretical motivation, clarify the analysis procedure, and expand the BBN section. We believe these changes enhance the clarity and robustness of our conclusions regarding the viability of the f(Q, L_m) gravity model as an alternative to ΛCDM.

read point-by-point responses

Referee: [§2] §2 (model definition, around Eq. (7)–(9)): the specific functional form adopted for f(Q, L_m) is introduced without an independent theoretical derivation or stability analysis; the successful MCMC fit to the deceleration-to-acceleration transition and BBN consistency appear to rely on this choice, which is therefore load-bearing for the central viability claim.

Authors: The specific functional form for f(Q, L_m) is a phenomenological choice designed to introduce non-minimal coupling between non-metricity and the matter Lagrangian in a simple, analytically manageable way. It builds upon existing models in the modified gravity literature. We will revise the manuscript to include additional theoretical motivation for this choice and a discussion of the stability of the Friedmann equations derived from it. A full linear perturbation analysis is left for future work, as the current focus is on background cosmology and observational constraints. revision: partial
Referee: [§4] §4 (MCMC analysis and results): parameters are constrained using the same DESI DR2 BAO, CC, and GW datasets that are subsequently invoked to claim agreement with the observed transition and quintessence-like EoS; this circularity reduces the independence of the empirical support and requires explicit discussion of potential post-hoc selection effects.

Authors: We disagree that this constitutes problematic circularity. The MCMC analysis constrains the model parameters using the observational datasets, after which we analyze the implications for the expansion history and effective EoS using those best-fit values. This is the standard approach for testing modified gravity models. The deceleration-to-acceleration transition emerges from the dynamics of the constrained model. In the revision, we will add a paragraph explicitly discussing the independence of the model selection from the data fitting and addressing potential selection effects. revision: partial
Referee: [§5] §5 (BBN incorporation): while the BBN freeze-out constraint is applied to tighten parameter bounds, the manuscript provides insufficient detail on the precise implementation, propagation of nuclear-rate systematics, or sensitivity of the late-time fit to variations in the early-universe assumptions.

Authors: We thank the referee for pointing this out. The revised manuscript will include a more detailed description of the BBN freeze-out implementation, including the specific formulas employed, how nuclear rate uncertainties are considered (by adopting conservative bounds from the literature), and a sensitivity test demonstrating that the late-time constraints remain robust under reasonable variations in early-universe parameters. revision: yes

Circularity Check

1 steps flagged

MCMC fit to BAO/CC/GW/BBN data presented as successful description of transition and viability as ΛCDM alternative

specific steps

fitted input called prediction [Abstract]
"The model is further tested against a combined set of observational data, including DESI DR2 BAO, previous BAO measurements, cosmic chronometers (CC), and gravitational-wave (GW) standard sirens, using a Markov Chain Monte Carlo (MCMC) approach. Further by incorporating the Big Bang Nucleosynthesis (BBN) freeze-out constraint, we place stringent limits on the model parameters... The resulting constraints exhibit strong agreement with observations, with the model successfully describing the transition from decelerated to accelerated expansion. ... Overall, the f(Q,L_m) framework emerges as a vi"

Model parameters are obtained by MCMC fitting to the identical observational datasets (DESI DR2 BAO, CC, GW sirens, BBN) against which agreement and viability are then claimed. The 'strong agreement', 'successful description' of the transition, and emergence as 'viable alternative' are therefore direct consequences of the fit converging within the chosen functional form, not independent theoretical predictions.

full rationale

The paper derives modified Friedmann equations from a chosen f(Q, L_m) ansatz, then constrains its free parameters via MCMC on the same late-time and BBN datasets used to assert agreement and physical viability. The resulting 'strong agreement', 'successful description' of deceleration-to-acceleration transition, quintessence-like EoS, and status as viable alternative are outputs of the fit rather than independent predictions. BBN supplies an external early-universe anchor but does not alter the fact that late-time success is statistically forced by construction of the fit. This is a clear instance of fitted input called prediction; the theoretical framework itself is not circular.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on a specific (unspecified in abstract) functional form for f(Q, L_m), standard FLRW cosmology, and parameters fitted to data rather than derived from first principles.

free parameters (1)

f(Q, L_m) model parameters
Determined via MCMC fitting to BAO, CC, GW, and BBN data

axioms (2)

domain assumption The universe follows the FLRW metric with homogeneous isotropic expansion
Invoked for all cosmological evolution calculations from BBN to late time
domain assumption Non-metricity Q is non-minimally coupled to the matter Lagrangian L_m
Core definition of the f(Q, L_m) theory used throughout

pith-pipeline@v0.9.0 · 5502 in / 1474 out tokens · 73013 ms · 2026-05-08T05:38:53.081009+00:00 · methodology

discussion (0)

Reference graph

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