Study of Curvature-Matter Coupling in Modified Gravity

Lakhan V. Jaybhaye

REVIEW 5 major objections 5 minor 1 cited by

Study of Curvature-Matter Coupling in Modified Gravity

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This thesis argues that f(R,L_m) gravity—in which the action depends on both the Ricci scalar and the matter Lagrangian—can reproduce the observed late-time acceleration, a non-singular bouncing Universe, and the measured…

desk verdict A competent compilation of six fitting-driven f(R,L_m) cosmology papers; the claims are weaker than advertised because all results hinge on an unjustified L_m = rho choice. read the letter →

arxiv 2505.24470 v1 pith:J2WNLQFO submitted 2025-05-30 gr-qc

Lakhan V. Jaybhaye This is my paper

classification gr-qc MSC 83D0583F05 PACS 04.50.Kd98.80.-k

keywords f(RL_m)gravitycurvature-mattercouplinglate-timecosmicaccelerationbouncingcosmologybaryogenesisbulkviscosityobservationalconstraintsHubbleparameterparametrization

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

This thesis sets out to show that f(R,L_m) gravity—a family of theories in which the gravitational action depends jointly on the Ricci scalar and the matter Lagrangian—can handle several of the open problems that motivate modified gravity. Working throughout with a flat FLRW universe and the identification $L_m=\rho$, it constructs nonlinear models, fits them to cosmic-chronometer, baryon-acoustic-oscillation, and Type Ia supernova datasets, and reports that they reproduce the deceleration-to-acceleration transition with a transition redshift near $z_t \approx 0.65$–$0.89$. It further claims that the same framework yields a non-singular matter bounce whose equation of state crosses into the phantom region near the bounce, and that a gravitational-baryogenesis calculation with model parameters $\alpha=0.79$ and $\zeta=2$ produces $n_B/s \approx 7.29\times 10^{-11}$, matching the observed baryon-to-entropy ratio. The payoff, if correct, is a single modified-gravity framework that addresses late-time acceleration, the initial singularity, and matter–antimatter asymmetry without invoking a cosmological constant.

What carries the argument

The engine of the thesis is the $f(R,L_m)$ action, $S=\int f(R,L_m)\sqrt{-g}\,d^4x$, whose metric variation produces field equations that reduce to general relativity when $f(R,L_m)=R/2+L_m$. Because the theory predicts a non-vanishing divergence of the energy-momentum tensor, an extra force orthogonal to the four-velocity appears, a signature used for solar-system constraints. The workhorse technical step is the substitution $L_m=\rho$, which turns the general field equations into the Friedmann-like system used in every chapter and into the energy-balance equations that close the dynamics. Around this core the thesis wraps: a power-law or explicit Hubble parametrization to close the system, MCMC fits to cosmic-chronometer, BAO, and supernova data, energy-condition inequalities $\rho+p$, $\rho+3p$, and $\rho-p$ as diagnostic filters, the statefinder $(r,s)$ and $\mathrm{Om}(z)$ diagnostics for dark-energy classification, the bouncing scale factor $a(t)=(a_0^2+\zeta^2 t^2)^{1/2}$, and the CP-violating baryogenesis interaction $(1/M_*^2)\int\sqrt{-g}\, J^\mu\,\partial_\mu(R+L_m)\,d^4x$ whose FLRW evaluation gives $n_B/s \propto (\dot R+\dot L_m)/T_D$.

What would settle it

Redo the chapters' calculations with $L_m=-p$, the other standard identification for the matter Lagrangian, and compare the resulting $H(z)$, $q(z)$, equation-of-state, and $n_B/s$ predictions against the same datasets; if the reported agreement, such as $n_B/s\approx 7.29\times 10^{-11}$ for $\alpha=0.79$, moves outside observational errors, then the claims hold only under the original identification.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a minimal extension of the Einstein–Hilbert action in which the Lagrangian density depends jointly on $R$ and $L_m$, namely $f(R,L_m)$, is observationally viable across several independent cosmic epochs. For the model $f(R,L_m)=R/2+L_m^\alpha+\beta$, the derived Hubble rate $H(z)$ fits 57 $H(z)$ measurements and 1048 Type Ia supernovae, with best-fit $n\approx 1.07$–$1.15$ and $\beta\approx -8862$, and yields a deceleration parameter that crosses from positive to negative at $z_t\approx 0.69$–$0.89$. Using the model-independent parametrization $H(z)=H_0[(1-\zeta)+(1+z)(\zeta+\eta z)]^{1/2}$, the combined data give $H_0=71.0$, $\zeta=-0.36$, $\eta=1.3$, $q_0=-0.525$, and $z_t=0.646$, consistent with the standard cosmological model. The bulk-viscous model returns $\omega_0\approx -0.71$ and a statefinder pair $(r,s)=(0.43,0.33)$, placing the fluid in the quintessence region. The bounce chapter shows that with $a(t)=(a_0^2+\zeta^2 t^2)^{1/2}$, both nonlinear forms violate the null and strong energy conditions near the bounce while the dominant energy condition stays positive, and the second model is stable under the sound-speed criterion. Finally, with $\alpha=0.79$ and $\zeta=2$ the baryogenesis calculation yields $n_B/s\approx 7.29\times 10^{-11}$, in line with the observed value near $9\times 10^{-11}$; the generalized interaction with $\alpha=0.93$ gives $n_B/s\approx 7.01\times 10^{-11}$.

Load-bearing premise

The entire chain of Friedmann equations, $H(z)$ solutions, and baryon-to-entropy predictions assumes that the matter Lagrangian density equals the energy density, $L_m=\rho$, a choice that is conventional but not forced in curvature-matter coupling theories.

Editorial extensions

If this is right

If the fitted $f(R,L_m)$ models are correct, the Universe's deceleration-to-acceleration transition is reproduced without a cosmological constant, with transition redshift $z_t\approx 0.65$–$0.89$ depending on dataset and model.
The bulk-viscous $f(R,L_m)$ model predicts a present effective equation-of-state $\omega_0\approx -0.71$ and a statefinder pair $(r,s)=(0.43,0.33)$, placing the accelerated phase in the quintessence region rather than the phantom region.
The matter-bounce solutions imply that the early Universe can pass through a non-singular bounce, with null and strong energy condition violations confined near the bounce time and the dominant energy condition satisfied, so the initial singularity is avoided.
Gravitational baryogenesis in this framework yields a nonzero baryon-to-entropy ratio during radiation domination, roughly $7\times 10^{-11}$, consistent with big-bang nucleosynthesis and cosmic microwave background constraints for the stated parameters.
Across all chapters the constrained parameters cluster around $H_0\approx 71$–$72$ km s$^{-1}$ Mpc$^{-1}$, placing the model between local distance-ladder and cosmic-microwave-background estimates.

Reading between the lines

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

Beyond the paper: replacing the assumption $L_m=\rho$ with the equally common choice $L_m=-p$ would alter every derived expression, so a direct comparison of the two prescriptions against the same datasets would isolate how much of the claimed viability rests on that choice.
Beyond the paper: the baryogenesis result depends on the adopted decoupling temperature $T_D$ and cutoff scale $M_*$; scanning those values would map the parameter region where $f(R,L_m)$ remains consistent with the observed baryon asymmetry.
Beyond the paper: the fitted $H_0\approx 71$–$72$ sits between the local distance-ladder and Planck values, suggesting the framework could be tested as a resolution of the Hubble tension if the same functional forms are run against CMB and distance-ladder data jointly.
Beyond the paper: the sound-speed stability criterion used in the bounce chapter is a necessary but not sufficient stability test; a full scalar-perturbation analysis would show whether the bouncing solutions survive as viable cosmological models.

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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

The thesis compiles six published f(R,L_m) papers into one narrative. The derivations are standard, the fits are transparent, and the writing says clearly at each chapter heading which publication covers the work. What it does well is to bring late-time acceleration, a bounce, and baryogenesis under one f(R,L_m) umbrella and to present the field equations and data constraints in a readable way. The MCMC estimates come with error bars, and the datasets are public.

The stress-test note is on target. In f(R,L_m) gravity, the perfect-fluid matter Lagrangian is not unique: standard constructions give L_m = -rho, L_m = p, or combinations, and because f, f_R, and f_Lm appear in the field equations, the choice changes the Friedmann equations, the energy-balance equations, and the baryon-to-entropy formula. The thesis cites [166] for L_m = rho and never tests whether the conclusions survive an alternative, equally standard choice. That is a load-bearing limitation, though not a mathematical error.

Second, several results are reconstructions. Parameters are fitted to the same data used to claim agreement, and in Chapter 6 alpha = 0.79 and zeta = 2 are picked so that n_B/s lands near 9e-11. The text even says the ratio can be adjusted. That is tuning, not prediction, and the phrase "excellent agreement" overstates what the analysis shows. Third, the AIC/BIC comparison in Chapter 3 misreads the numbers: Delta BIC = 3.64 actually favors LambdaCDM, not the proposed model. That's a minor but real error.

Despite those soft spots, the central argument holds up as model building: these functional forms can produce acceleration, a bounce, and a nonzero baryon asymmetry. As a claim to have explained observed cosmology, it falls short unless the L_m dependence is explored and the fitting nature is acknowledged.

This thesis is for graduate students and researchers working in f(R,L_m) gravity or phenomenological modified gravity, as a template for this style of analysis. Does it deserve a serious referee? Yes. The derivations are standard enough to check, the data handling is transparent, and the underlying papers were peer reviewed. If it crossed my desk as a journal submission, I would send it to review, but with the clear expectation that the authors address the L_m ambiguity and soften the success claims.

Referee Report

5 major / 5 minor

Summary. This thesis applies f(R,L_m) gravity to four cosmological problems: late-time acceleration (Chapters 2–4), a nonsingular matter bounce (Chapter 5), and gravitational baryogenesis (Chapter 6). For each chapter, the author derives Friedmann equations in a flat FLRW background, selects a functional form for f(R,L_m), constrains or hand-picks free parameters using H(z), Pantheon/Pantheon+SH0ES, and BAO data, and then evaluates diagnostics such as q(z), Om(z), statefinders, energy conditions, and the baryon-to-entropy ratio. The central claim is that f(R,L_m) gravity can reproduce the observed late-time acceleration, produce a phantom-like bounce, and generate n_B/s ≈ 9×10^-11. Throughout, the matter Lagrangian is set to L_m = rho with a single citation, and the parameters used for the 'predictions' are either fitted to the same data used for validation or chosen by hand.

Significance. The thesis demonstrates technical competence: the field-equation derivations follow standard variational procedures, the exact H(z) solutions are explicit, and the MCMC analyses use publicly available cosmological datasets. If the L_m = rho identification and the parameter choices were independently justified, the results would be interesting phenomenological examples of f(R,L_m) gravity. As it stands, the manuscript does not establish robust predictions: the main conclusions are contingent on a non-unique Lagrangian identification and on in-sample fitting, so the significance is illustrative rather than demonstrative. The paper would be much stronger if it tested alternative perfect-fluid Lagrangians and separated parameter estimation from model validation.

major comments (5)

[Sec. 2.3 and repeated in Secs. 3.4, 4.3, 5.3, 6.2] The thesis sets L_m = rho for a perfect fluid, citing [166], but this is not the only standard choice. Because f_Lm and f - f_R R - f_Lm L_m appear explicitly in the field equations, choosing L_m = -rho, p, or -rho+3p changes the Friedmann equations, energy-balance equations, and the baryon-to-entropy formula. The manuscript never tests this sensitivity. This concern is load-bearing: every quantitative claim in Chapters 2–6 is derived from equations that assume L_m = rho, so the agreement with H(z), Pantheon, and n_B/s demonstrates the consistency of that identification, not the viability of f(R,L_m) gravity in general.
[Chapter 6, Eq. (6.14) and following paragraph] The values alpha = 0.79 and zeta = 2 are chosen after the fact so that n_B/s ≈ 7.29×10^-11, and the text explicitly notes that the ratio 'can be adjusted to satisfy the observational constraints.' Calling this 'excellent agreement' is therefore not a valid test of the theory. To make a scientific claim, the model parameters must be constrained independently (e.g., by cosmological fits) and the baryon-to-entropy ratio then compared with observation, or the analysis should be presented as a parameter-space existence proof.
[Chapters 2 and 4] Best-fit parameters from the same datasets are used to reconstruct q(z), Om(z), rho(z), p(z), and the effective EoS. For instance, in Sec. 2.4 the parameters n and beta are fitted to H(z)+Pantheon, and the deceleration-to-acceleration transition, stability, and Om diagnostic in Secs. 2.5–2.6 are then evaluated at those best-fit values. In Sec. 4.4 the fit to CC+Pantheon+SH0ES is followed by the reconstruction of rho, p, and omega from the same MCMC chains. These are in-sample reconstructions rather than independent tests; the manuscript should state this limitation and, if possible, add out-of-sample or cross-validation checks.
[Sec. 3.3.1] The model-comparison statement is internally inconsistent. The text defines 'strong support' as Delta AIC < 2 and 'moderate support' as 2 < Delta BIC ≤ 6, then obtains Delta AIC = 1.83 and Delta BIC = 3.64 and concludes that the model has 'substantial support.' Moreover, BIC_model = 1672.79 is larger than BIC_LambdaCDM = 1669.15, so by the standard interpretation the data favor LambdaCDM at a moderate level. This misreading weakens the Chapter 3 claim that the parametrization is preferred over LambdaCDM.
[Chapter 5] The bounce parameters (a0, zeta, beta, gamma, lambda, alpha) are chosen by hand, without MCMC posteriors, and the claims that the models violate NEC/SEC and are stable are based on these selected values. In particular, Eqs. (5.13)–(5.18) and Figs. 5.3–5.6 illustrate behavior for chosen parameter values; this is not a test against data. The stability conclusion using C_s^2 in Sec. 5.3.3 should also be stated more carefully: C_s^2 > 1 signals acausality or superluminal sound speed rather than mechanical instability, while C_s^2 < 0 would signal instability.

minor comments (5)

[Sec. 3.5] The summary of the Hubble parametrization omits the eta z term from Eq. (3.1); it should read H(z) = H0[(1-zeta)+(1+z)(zeta+eta z)]^{1/2}.
[Sec. 2.7] The text refers to the analytical solution as 'Eq. (1.25)'; the intended reference is Eq. (2.14).
[Sec. 6.2.2] The text says 'We show n_B/s for the generalized baryogenesis interaction as a function of alpha in Fig. 1.2'; this should be Fig. 6.2.
[Sec. 4.1] The phrase 'the density parameter is expressed as bar p = p - 3 zeta H' should read 'the effective pressure is expressed as...' to avoid confusion with the energy density rho.
[Sec. 6.1] The description of g as the 'trace of the metric tensor' is incorrect; g denotes the determinant of the metric tensor.

Circularity Check

2 steps flagged · score 6.0 of 10

The baryogenesis chapter selects f(R,L_m) parameters by hand to reproduce the observed baryon-to-entropy ratio and then reports 'excellent agreement'; the rest of the thesis is standard parameter fitting, so the circularity is partial.

fitted input called prediction [Chapter 6, Sec. 6.2.1, Eqs. (6.13)-(6.14) and the paragraph following Eq. (6.14)]
"As shown in Eq.(6.14), the resulting baryon-to-entropy ratio is nonzero. The ratio in Eq.(6.14) can be adjusted to satisfy the observational constraints depending on the matter content. ... Substituting g∗s = 106, gB = 1, TD = 2 × 10^12 GeV and M∗ = 2 × 10^16 GeV [267], with model parameters α = 0.79 and ζ = 2 in Eq. (6.14) the resultant baryon-to-entropy ratio reads nB/s ≃ 7.28749 × 10^−11 which is in excellent agreement with observations."

The parameters α and ζ are free parameters of the same f(R,L_m) model under test and are not constrained before the comparison. The paper explicitly states the ratio 'can be adjusted to satisfy the observational constraints,' then picks α = 0.79 and ζ = 2. Eq. (6.14) is a deterministic function of these parameters, so the resulting value ~7.3×10^-11 is forced by construction to lie near the observed ~9×10^-11. Calling this 'excellent agreement' is a tuned match, not an independent prediction; any model with two adjustable parameters could be made to hit the single observed number.
ansatz smuggled in via citation [Sec. 2.3, Eqs. (2.8)-(2.9); repeated at Secs. 3.4, 4.3, 5.3, and 6.2 (Eqs. (3.17), (4.7), (5.7), (5.10), (6.8))]
"Then, for this particular f (R, Lm) model with Lm = ρ [166], the Friedmann Eqs. (2.6) and (2.7) for the matter-dominated Universe becomes 3H^2 = (2n − 1)ρ^n − β ..."

All the Friedmann equations and the baryon-to-entropy formulas (e.g., Eq. (6.4): nB/s ∝ (dot R + dot L_m)) are derived after substituting L_m = ρ, an ansatz imported via a bracket citation rather than derived from the theory. In perfect-fluid f(R,L_m) gravity, L_m is not unique: equally standard choices include L_m = −ρ, L_m = p, or L_m = −ρ + 3p. Since the field equations and the baryogenesis ratio depend explicitly on f_{L_m} and L_m, this one choice fixes the very outputs the thesis reports as predictions; another standard choice (e.g., L_m = −ρ + 3p) would make the radiation-era combination in Eq. (6.4) vanish. The results are therefore consequences of the adopted identification, not of f(R,L_m) gravity as a class.

full rationale

The thesis is mostly a standard cosmology program: choose an f(R,L_m) ansatz, fit its free parameters to H(z), Pantheon, BAO, and Pantheon+SH0ES data, and then read off derived quantities such as q(z), Om(z), energy conditions, and EoS parameters. That procedure is not circular—the fitted data are genuinely external, and quantities like q(z) are deterministic consequences of the fitted H(z) template rather than hidden inputs. The one place where a 'prediction' reduces by construction is Chapter 6: the baryon-to-entropy ratio is made to agree with observation by hand-picking α = 0.79 and ζ = 2, with the text itself acknowledging the ratio can be adjusted. This is the fitted-input-called-prediction pattern. In addition, the universal substitution L_m = ρ, justified only by citation, is load-bearing: it selects one of several perfectly-fluid matter Lagrangians and thereby determines both the Friedmann equations and the radiation-era baryogenesis signal. That makes the derived results contingent on an unvalidated input, though it is an assumption/ambiguity rather than a logical circle in the formal sense. Weighing these together, the central baryogenesis claim is partially circular, but the acceleration and bounce chapters retain independent content from their data fits, so the score is 6 rather than higher.

Assumptions & free parameters 15 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard cosmological assumptions plus several ad hoc choices: the functional forms of f(R,L_m), the identification L_m=rho, and the scale-factor ansatzes. The free parameters are numerous: two to four per chapter, many fitted to the same data used to validate the models. No new particles, forces, or entities are introduced.

free parameters (15)

n (Ch2 exponent) = 1.078 (H(z)), 1.1472 (Pantheon), 1.07 (combined)
Exponent in f=R/2+L_m^n+beta; fitted to H(z) and Pantheon data.
beta (Ch2 constant) = -8862.13 (H(z)), -8862.2 (Pantheon), -8862.103 (combined)
Constant term in f=R/2+L_m^n+beta; a large negative fitted constant acting as a tuned cosmological constant.
H0 (Ch3) = 71 +/- 0.08
Hubble constant fitted in the MCMC analysis with CC+BAO+Pantheon+SH0ES data.
zeta (Ch3 H-param) = -0.36 +/- 0.033
Parameter in the parametrization H=H0[(1-zeta)+(1+z)(zeta+eta z)]^{1/2}.
eta (Ch3 H-param) = 1.3 +/- 0.023
Parameter in the same H(z) parametrization.
alpha (Ch3 model I) = 0.78, 0.82, 0.86 (hand-chosen)
Exponent in f=R/2+L_m^alpha; values chosen by hand, not constrained by data.
lambda (Ch3 model II) = 0.6, 0.9, 1.2 (hand-chosen)
Coupling in f=R/2+(1+lambda R)L_m; values chosen by hand.
alpha (Ch4) = 1.310 +0.037 -0.032
Exponent in f=R/2+L_m^alpha with bulk viscosity; fitted to CC+Pantheon+SH0ES.
gamma (Ch4 EoS) = 1.29 +/- 0.20
Equation-of-state parameter in p=(gamma-1)rho; fitted.
zeta (Ch4 viscosity) = 5.02 +/- 0.26
Bulk viscosity coefficient in effective pressure p_bar=p-3zeta H; fitted.
H0 (Ch4) = 72.09 +/- 0.19
Hubble constant fitted in the viscous dark energy model.
beta, gamma (Ch5 model I) = beta 1.3-2.3, gamma 0.087-0.127
Exponent and constant in f=R/2+L_m^beta+gamma; chosen by hand to satisfy positivity.
lambda, alpha (Ch5 model II) = lambda -0.10 to -0.20, alpha 0.5-2.5
Couplings in f=R/2+lambda R^2+alpha L_m; chosen by hand.
zeta, a0 (Ch5 bounce) = zeta 0.624 or 0.824, a0=1
Bouncing parameter and scale factor in a(t)=(a0^2+zeta^2 t^2)^{1/2}; chosen by hand.
alpha, zeta (Ch6) = alpha=0.79 or 0.93, zeta=2
Exponent and constant in f=R/2+L_m^alpha+zeta; chosen to reproduce the observed baryon-to-entropy ratio.

assumptions (6)

domain assumption The Universe is described by a flat FLRW metric
Used in all chapters to derive the Friedmann equations (e.g., Ch2 Eq 2.1).
domain assumption L_m = rho (matter Lagrangian density equals energy density)
Adopted in every chapter (e.g., Ch2 Sec 2.3, 'with Lm = rho [166]') to obtain explicit Friedmann equations; this identification is ambiguous in f(R,L_m) theory.
domain assumption Perfect fluid energy-momentum tensor
Standard assumption T_mu_nu=(rho+p)u_mu u_nu+p g_mu_nu used in all chapters.
ad hoc to paper The specific functional forms of f(R,L_m) are ad hoc to this thesis
Forms such as f=R/2+L_m^n+beta (Ch2), f=R/2+L_m^alpha (Ch3/4), f=R/2+(1+lambda R)L_m (Ch3), f=R/2+lambda R^2+alpha L_m (Ch5), and f=R/2+L_m^alpha+zeta (Ch6) are chosen for tractability, not derived from a fundamental theory.
ad hoc to paper Scale factor ansatzes in Ch5 and Ch6
The bounce scale factor a(t)=(a0^2+zeta^2 t^2)^{1/2} (Ch5) and the power-law a(t)=B t^beta (Ch6) are assumed a priori; the derived bounce and baryogenesis results inherit these assumptions.
domain assumption Gravitational baryogenesis mechanism with CP-violating interaction
Standard formalism from the literature (Sakharov conditions, effective operator in Eq 6.1) is adopted to compute the baryon asymmetry.

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Cite this review

Pith. "Pith review of Study of Curvature-Matter Coupling in Modified Gravity." pith.science (2026). https://pith.science/paper/J2WNLQFO

@misc{pith2026250524470,
  author       = {Pith},
  title        = {Pith review of: Study of Curvature-Matter Coupling in Modified Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J2WNLQFO}},
  note         = {Machine review of arXiv:2505.24470}
}

abstract

Over the past century, General Relativity (GR) has been a cornerstone of gravitational theory. However, recent cosmological observations, such as the accelerated expansion of the Universe, challenge its completeness and the standard $\Lambda$CDM model. This has motivated the development of alternative approaches, including dynamical dark energy and modifications to gravity. This thesis investigates the $f(R, L_m)$ gravity framework, which extends $f(R)$ gravity by introducing curvature-matter coupling, to address unresolved issues in modern cosmology. Chapter 1 reviews the foundations of cosmology, GR, and $\Lambda$CDM, discussing their challenges and introducing modified gravity theories. Chapter 2 studies cosmic expansion in a specific non-linear $f(R, L_m)$ model, analyzing its dynamics using updated $H(z)$ and Pantheon datasets and demonstrating a deceleration-to-acceleration transition. Chapter 3 introduces a model-independent Hubble parameter parametrization and explores cosmological variables using MCMC and combined data. Chapter 4 incorporates bulk viscosity into $f(R, L_m)$ models to explain late-time acceleration and applies Om diagnostics and energy conditions. Chapter 5 examines non-singular matter bounce cosmologies, analyzing bouncing dynamics and the evolution of cosmographic parameters. Chapter 6 addresses gravitational baryogenesis and shows how $f(R, L_m)$ gravity supports the observed baryon-to-entropy ratio. Chapter 7 summarizes the results and suggests directions for future work.

Figures

Figures reproduced from arXiv: 2505.24470 by the authors.

**Figure 2.1.** Profile of the 1 − σ and 2 − σ contours for the model parameters n and β using H(z) datasets The best-fit ranges obtained for the model parameters are n = 1.078+0.012 −0.013 and β = −8862.13 ± 0.99. 2.4.2 Pantheon datasets Pantheon SNeIa datasets consisting of 1048 data points have recently been released. The PanSTARSS1 Medium, SDSS, SNLS, Deep Survey, numerous low redshift surveys, and HST surveys contribute to it.… view at source ↗

**Figure 2.2.** Profile of the 1 − σ and 2 − σ contours for the model parameters n and β using Pantheon datasets The best-fit ranges obtained for the model parameters are n = 1.1472+0.0028 −0.00042 and β = −8862.2 ± 1.0. 2.4.3 H(z) + Pantheon datasets The χ 2 function for the H(z) + Pantheon datasets is given as χ 2 total = χ 2 H + χ 2 SNeIa. (2.23) The contours 1 − σ and 2 − σ for the model parameters n and β using H(z) + Pantheon… view at source ↗

**Figure 2.3.** Profile of the 1 − σ and 2 − σ contours for the model parameters n and β using H(z) + Pantheon datasets The evolution profile of the density parameter and the deceleration parameter corresponding to the constrained values of the model parameters are presented below. H(z) Pantheon H(z)+Pantheon -1 0 1 2 3 0 20 000 40 000 60 000 80 000 100 000 z ρ [PITH_FULL_IMAGE:figures/full_fig_p055_2_3.png] view at source ↗

Figures from the paper (31 more)

**Figure 2.4.** Figure 2.4: Profile of the density parameter vs redshift [PITH_FULL_IMAGE:figures/full_fig_p055_2_4.png]

**Figure 2.5.** Figure 2.5: Profile of the deceleration parameter vs redshift. deceleration parameter is noted as q0 = −0.497+0.005 −0.004 for the H(z) datasets, q0 = −0.5223+0.00003 −0.0008 for the Pantheon datasets and q0 = −0.494+0.05 −0.035 for the combined H(z) + Pantheon datasets. 2.5 Per…

**Figure 2.6.** Figure 2.6: Profile of the perturbation term δ(z) corresponding to the values of model parameters constrained by H(z), Pantheon, and the combined H(z) + Pantheon datasets. From [PITH_FULL_IMAGE:figures/full_fig_p057_2_6.png]

**Figure 2.7.** Figure 2.7: Profile of the Om diagnostic parameter corresponding to the values of model parameters constrained by H(z), Pantheon, and the combined H(z) + Pantheon datasets. f(R, Lm) model in Eq. (1.25). Furthermore, we obtained optimal values for the model parameters by analyzin…

**Figure 3.1.** Figure 3.1: Profile of the fitting of the H(z) versus redshift z for our proposed model (red line) in comparison to the standard ΛCDM model (black dashed line). An error bar plot that represents the 31 CC dataset points taken into account for the analysis is also included. To de…

**Figure 3.2.** Figure 3.2: Profile of the fitting of the H(z) versus redshift z for our proposed model (red line) in comparison to the standard ΛCDM model (black dashed line). An error bar plot that represents the 26 BAO dataset points taken into account for the analysis is also included. 0.0 …

**Figure 3.3.** Figure 3.3: Profile of the fitting of the µ(z) versus redshift z for our proposed model (red line) in comparison to the standard ΛCDM model (black dashed line). An error bar plot that represents the 1701 points of the Pantheon+SH0ES dataset taken into account for the analysis is…

**Figure 3.4.** Figure 3.4: Profile of the 2D contour plot of the model parameters H0, ζ, and η, based on a combined examination of the CC, BAO, and Pantheon+SH0ES datasets, displaying the most likely values and the confidence areas up to 3−σ. 3.3.1 Model comparison It is crucial to perform a s…

**Figure 3.5.** Figure 3.5: illustrates the change in the deceleration parameter based on the values of the model parameters. It demonstrates the transition of the cosmological model from a decelerating phase to an accelerating phase. Taking into account the constraints on the model parameters …

**Figure 3.6.** Figure 3.6: Profile of the density parameter, pressure, and EoS parameter as functions of redshift z, shown for H0 = 71, ζ = −0.36, and η = 1.3, while the model parameter α is varied. Energy conditions are sets of requirements placed on the energy-momentum tensor to ensure that …

**Figure 3.7.** Figure 3.7: Profile of the NEC, DEC, and SEC for H0 = 71, ζ = −0.36, and η = 1.3 while varying model parameter α with respect to redshift z. The graph above illustrates the behavior of various energy conditions, crucial for understanding the expansion of the Universe [187–189]. …

**Figure 3.8.** Figure 3.8: Profile of the density parameter, pressure, and EoS parameter as functions of redshift z, shown for H0 = 71, ζ = −0.36, and η = 1.3, while the model parameter λ is varied. evolution. This shift indicates a previous era of the Universe characterized by positive pressu…

**Figure 3.9.** Figure 3.9: Profile of the NEC, DEC, and SEC for H0 = 71, ζ = −0.36, and η = 1.3 while varying model parameter λ with respect to redshift z. In [PITH_FULL_IMAGE:figures/full_fig_p073_3_9.png]

**Figure 4.1.** Figure 4.1: Profile of the 1 − σ and 2 − σ contours for the model parameters H0, α, γ, and ζ using combined CC + Pantheon+SH0ES datasets [PITH_FULL_IMAGE:figures/full_fig_p080_4_1.png]

**Figure 4.2.** Figure 4.2: Profile of the reconstruction of the density parameter is illustrated as a function of redshift for our model, based on a sample of 7500 instances. These samples are generated through re-sampling the chains using emcee. We display all the resulting curves along with …

**Figure 4.3.** Figure 4.3: Profile of the reconstruction of the effective pressure is illustrated as a function of redshift for our model, based on a sample of 7500 instances. These samples are generated through re-sampling the chains using emcee. We display all the resulting curves along with…

**Figure 4.4.** Figure 4.4: Profile of the reconstruction of the effective EoS parameter is illustrated as a function of redshift for our model, based on a sample of 7500 instances. These samples are generated through re-sampling the chains using emcee. We display all the resulting curves along…

**Figure 4.5.** Figure 4.5: Profile of the evolution trajectory of a given model in the r − s plane with the agreement of obtained observational constraints [PITH_FULL_IMAGE:figures/full_fig_p082_4_5.png]

**Figure 4.6.** Figure 4.6: Profile of the Om diagnostic parameter with the agreement of obtained observational constraints [PITH_FULL_IMAGE:figures/full_fig_p083_4_6.png]

**Figure 4.7.** Figure 4.7: Profile of the NEC vs redshift. Based on Figs. 4.7 and 4.8, it is evident that both NEC and DEC meet the positivity conditions across the full redshift range, which aligns with the parameter values estimated from observational [PITH_FULL_IMAGE:figures/full_fig_p083_…

**Figure 4.8.** Figure 4.8: Profile of the DEC vs redshift. -1 0 1 2 3 4 -1000 -500 0 z SEC [PITH_FULL_IMAGE:figures/full_fig_p084_4_8.png]

**Figure 4.9.** Figure 4.9: Profile of the SEC vs redshift. data. Additionally, the WEC holds because it includes both the density parameters and the NEC. Finally, [PITH_FULL_IMAGE:figures/full_fig_p084_4_9.png]

**Figure 5.1.** Figure 5.1: Profile of the scale factor, Hubble parameter, and deceleration parameter for a0 = 1, with different values of ζ against cosmic time. The traditional cosmographic approach is based on the Taylor series expansion of material objects. Cosmography is an effective approa…

**Figure 5.2.** Figure 5.2: Profile of the jerk parameter, snap parameter, and lerk parameter for a0 = 1, with different values of ζ against cosmic time. chosen parameters, while [PITH_FULL_IMAGE:figures/full_fig_p090_5_2.png]

**Figure 5.3.** Figure 5.3: Profile of the density parameter, pressure, and EoS parameter for a0 = 1 and ζ = 0.824, with different values of other model parameters β and γ against cosmic time [PITH_FULL_IMAGE:figures/full_fig_p092_5_3.png]

**Figure 5.4.** Figure 5.4: Profile of the density parameter, pressure, and EoS parameter for a0 = 1 and ζ = 0.624, with different values of other model parameters λ and α against cosmic time. the negative and positive time zones had a similar pattern of behavior in the growth of the EoS parame…

**Figure 5.5.** Figure 5.5: Profile of the NEC, SEC, and DEC for a0 = 1 and ζ = 0.824, with different values of other model parameters β and γ against cosmic time [PITH_FULL_IMAGE:figures/full_fig_p095_5_5.png]

**Figure 5.6.** Figure 5.6: Profile the of NEC, SEC, and DEC for a0 = 1 and ζ = 0.624, with different values of other model parameters λ and α against cosmic time. above meet the criteria for being stable for positive values of the squared sound speed C 2 s . The squared speed of sound C 2 s mu…

**Figure 5.7.** Figure 5.7: Profile of stability analysis for a0 = 1, ζ = 0.824 for model I, and ζ = 0.624 for model II, with different values of other model parameters β, γ and λ, α against cosmic time respectively. squared speed of sound shows positive values but still greater than one that p…

**Figure 6.1.** Figure 6.1: Profile of the baryon-to-entropy ratio for the given model. The graphs are plotted for α, for the varying values of β, β = 0.55 (Red), β = 0.60 (Blue), β = 0.65 (Green), β = 0.70 (Orange), β = 0.75 (Purple), and ζ = 2. The dashed line represents the observational val…

**Figure 6.2.** Figure 6.2: Profile of the baryon-to-entropy ratio for the given model. The graphs are plotted for α, for the varying values of β, β = 0.018 (Red), β = 0.026 (Blue), β = 0.036 (Green), β = 0.046 (Orange), β = 0.056 (Purple), and ζ = 2. The dashed line represents the observationa…

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Transit dark energy cosmological models in generalized matter-geometry coupling theory using a non-linear form of $f(R,T,L_{m})$ function
gr-qc 2025-09 conditional novelty 4.0 of 10

A modified f(R,T,L_m) gravity model, fitted to CC and Pantheon data, yields an accelerating late-time universe with transition redshift near 0.6 and an effective dark energy equation of state within 1e-5 of -1.

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R. Solanki, B. Patel,Lakhan V. Jaybhaye, P. K. Sahoo,Cosmic acceleration with bulk viscosity in an anisotropicf (R, Lm) background. Communications in Theoretical Physics, 75(7), 075401 (2023)

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Lakhan V. Jaybhaye, M. Tayde, P. K. Sahoo,Wormhole solutions under the effect of dark matter inf (R, Lm) gravity, Communications in Theoretical Physics,76(5), 055402 (2024). 104 Paper presented at conferences

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2022
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Constraining viscous dark energy equation of state in f (R, Lm) gravity

Presented research paper poster with flash talk entitled “Constraining viscous dark energy equation of state in f (R, Lm) gravity” at the conference “32nd meeting of Indian Association for General Relativity and Gravitation (IAGRG32)” organized by the Indian Institute of Scien...

2022
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Baryogenesis in f (R, Lm) gravity

Presented research paper entitled “Baryogenesis in f (R, Lm) gravity” at the conference “Envisioning Mathematics Education in Line with NEP 2020” organized by the Ma- hatma Gandhi Mahavidyalaya, Ahmedpur, Maharashtra, during the period21th December, 2023

2020
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Late time cosmic acceleration through parametrization of Hubble parameter inf (R, Lm) gravity

Presented research paper entitled “Late time cosmic acceleration through parametrization of Hubble parameter inf (R, Lm) gravity” at the conference “31st International Conference of International Academy of Physical Sciences” organized by the Pt. Ravishankar Shukla University,...

2024

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Reviewed August 7, 2026 · model on record in the stance chip above.

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