arXiv subjects

Amare Abebe

Publications and source records attributed to Amare Abebe.

At least 19 recordsLinked to original sources

arXiv2026

Conformally Interacting Dark Energy with Early and Late-Time Measurements

The conformal interacting dark energy (CIDE) model is investigated by introducing a scalar field representing dark energy (DE) coupled to dark matter (DM) via a conformal transformation, thereby yielding a class of scalar-tensor theories. The interaction term ${Q}$, that indicts the flow of energy between the dark sectors is proportional to the trace of the energy momentum tensor of the DM fluid, $T^{\mathrm{DM}}_{\mu\nu}$, as ${Q}=\frac{C'(\phi)}{2C(\phi)}g^{\mu\nu}T^{\mathrm{DM}}_{\mu\nu}$, where $C(\phi)$ is the conformal function of a scalar potential (coupling) field. We assume the power-law parametrization $C(\phi)\propto (1+\phi)^m$, with $m$ a coupling parameter, and determine the direction and magnitude of the energy flow between the DM and DE components. The dynamical nature of DE is modeled by the two conformal interacting scenarios, CIDE and $w$CIDE, with $w$ the DE equation of state parameter. To test the viability of each model, we constrain them using a combination of early- and late-time cosmological data, namely: CMB measurements from the South Pole Telescope, Planck 2018, and the Atacama Cosmology Telescope (DR6) (\texttt{CMB SPA}); BAO data from the Dark Energy Survey (\texttt{DESI DR2 BAO}); and Supernova Type Ia distance compilations (\texttt{PantheonPlus, PantheonPlus + SH0ES, Union3}, and \texttt{DES Dovekie}). Parameter inference is performed with Monte Carlo Markov Chain (\texttt{MCMC}) simulations using \texttt{COBAYA} and a modified \texttt{CLASS}. Further statistical analysis using the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) is summarized to assess the viability of the model in comparison with the standard cosmological model, investigating the model's potential to alleviate the $H_0$ and $S_8$ tensions.

astro-ph.CO↗

arXiv2026

Constraint closure and gravitational-wave content of shear-free cosmologies in metric f(R) gravity

We derive the consistency conditions governing the propagating content of linear shear-free perturbations of Friedmann-Lema\^{\i}tre-Robertson-Walker cosmologies in metric $f(R)$ gravity. The divergence of the shear-free constraint is shown to be the total momentum-conservation equation and therefore does not imply geodesic flow. Its projected time derivative instead supplies a nontrivial integrability condition. Scalar, vector, and tensor sectors must then be tested separately. Shear-freeness removes the independent transverse-traceless electric-magnetic Weyl pair, so no ordinary $+$ or $\times$ tensor gravitational wave survives. The scalaron is not removed algebraically, but its four-variable harmonic system must remain in the time-dependent consistent subspace generated by the shear-free constraint and all of its time derivatives. For a geodesic shear-free congruence in the spatially flat expanding de Sitter patch, this excludes every nonzero fixed comoving scalar harmonic, including the healthy $R+\alpha R^2-2\Lambda$ model with $\alpha,\Lambda>0$. Vector modes obey a curvature-dependent global eigenvalue condition whose right-hand side is negative for positive-density matter with $f'>0$ and $1+w>0$; hence no nonzero vector harmonic survives on that branch. The familiar coasting $R^3$ example evades this sign obstruction only because it lies on an $f'<0$ branch. Thus tensor radiation is absent in the imposed shear-free sector, whereas scalar radiation is not excluded kinematically but remains a model- and background-dependent constraint-closure question.

gr-qc↗

arXiv2026

From Timbuktu to SKA: Who owns the Astronomy knowledge Africa produces?

Africa has deep and diverse traditions of astronomical knowledge, ranging from archaeological astronomy, pharaonic stellar timekeeping, and manuscript astronomy in Timbuktu and the Sahel, to ecological seasonal astronomy in southern Africa and calendrical computation in the Ethiopian tradition. These multiple epistemic traditions form part of a long intellectual history that precedes and intersects with contemporary astronomy on the continent. In the context of this long-standing intellectual heritage, an important question arises regarding the contemporary circulation of African astronomical knowledge within the global scientific system. This study therefore examines where African astronomical knowledge is produced, validated, and circulated in modern scholarly communication. Using bibliometric data from the Web of Science Core Collection, our analysis investigates publication and citation patterns in the research area Astronomy and Astrophysics between 2000 and 2025, with particular attention to the publication venues of African scholars. The findings highlight a critical paradox: while African researchers are active contributors to global astronomical discovery, the intellectual capital generated through this work is largely stored, validated, and circulated through publication systems located outside the continent. This pattern reflects broader asymmetries within global scholarly communication, where dominant publishing infrastructures shape visibility, citation impact, and authority. By applying a decolonial lens to metrics such as citation impact and ownership, the paper calls for a critical reassessment of the academic practices that sustain epistemic coloniality. It concludes that achieving scientific equity requires a strategic shift in publication choices to build and fortify a sovereign African knowledge archive.

physics.soc-ph↗

arXiv2026

A No-Go Theorem for Curvature Neutrality in f(Q) Cosmology?

In the framework of $f(Q)$ gravity, we investigate whether spatial curvature can be made dynamically invisible in the cosmological background equations. We consider open spatial sections, $k<0$, on an explicitly specified homogeneous and isotropic symmetric-teleparallel connection branch. For $k\neq0$, the coincident gauge cannot be imposed simultaneously with the standard curved-FLRW coordinate form. Re-deriving the background equations from the minisuperspace action, we show that curvature enters through $x=H+\delta\sqrt{-k}/a$ and appears with inequivalent weights in the energy and pressure equations. For $f\in C^3((0,\infty))$, we prove a branch-specific no-go theorem: strict curvature independence for every scale factor and every $k<0$ requires $f=\mathrm{const}$, which contains no metric kinetic term. STEGR is not curvature-neutral, since its Friedmann equation retains the usual $3k/a^2$ contribution. A weaker cancellation, imposed only on backgrounds satisfying $\delta\sqrt{-k}/a=cH$, necessarily produces a coasting expansion and yields $f(Q)=A Q^{(c+2)/2}+B$, or $f(Q)=A\ln Q+B$ when $c=-2$. For the illustrative choice $c=-3$, the solution becomes $f=\alpha_1/\sqrt Q+\beta_1$. Under the conventional positive-coupling assumption $f_Q>0$, the required source violates the null energy condition. Moreover, adding positive radiation or pressureless matter forces a compensating negative-energy component at sufficiently early times. The weak branch is therefore neither curvature-neutral in an invariant sense nor a viable cosmological model. The principal result is the background-level obstruction itself. Perturbative stability and gravitational-wave propagation require a separate analysis including perturbations of the nontrivial affine connection and are not established in this work.

physics.gen-ph↗

arXiv2026

Dynamical dark energy in the Bianchi Type-V Universe with DESI DR2 BAO, SNIa compilation and RSD measurements

We investigate the cosmological implications of dynamical dark energy (DDE) models within an anisotropic, spatially homogeneous Bianchi Type-V spacetime framework using a $1+3$ covariant thermodynamics approach. By implementing both constant ($w$) and time-varying ($w_0, w_a$) parameterized equations of state, we evaluate the background expansion history and track linear matter perturbations via the quasi-static approximation. We confront these scenarios with the latest cosmological datasets, including the Dark Energy Spectroscopic Instrument (DESI) DR2 Baryon Acoustic Oscillations (BAO), the Union3 and Dark Energy Survey 5-year (DESY5) Type Ia Supernovae compilations, Cosmic Chronometers (CC), and Redshift-Space Distortion (RSD) measurements. Our joint statistical analyses reveal that the introduction of spatial anisotropy coupled with DDE efficiently accommodates recent late-time measurements and provides a viable mechanism to mitigate the persistent $H_0$ and $S_8$ cosmological tensions. Model selection metrics show that while Akaike criteria strongly support the extended Bianchi Type-V scenarios across most joint data combinations, Bayesian criteria continue to favor the simpler standard $\Lambda$CDM baseline due to its lower dimensionality. Finally, we establish tight constraints on the current matter density parameter $\Omega_{m,0}$, the shear parameter $\Omega_{\sigma,0}$, and the dark energy evolution parameters, confirming that anisotropic extensions remain viable and testable frameworks for modern precision cosmology.

physics.gen-ph↗

arXiv2026

Rotating traversable wormholes and particle dynamics in $f(R,T)$ gravity

Traversable wormholes are among the most interesting solutions of gravitational theories, but within General Relativity they generally require exotic matter violating the null energy condition. Modified gravity theories with matter-geometry coupling provide a promising framework in which wormhole geometries may instead be supported by effective gravitational contributions. Motivated by this possibility, we investigate rotating traversable wormholes in $f(R,T)$ gravity, where $R$ is the scalar curvature and $T$ is the trace of the energy-momentum tensor, within the slow-rotation approximation. We construct stationary and axisymmetric wormhole solutions supported by an anisotropic fluid and show that the obtained geometries are regular, asymptotically flat, horizonless, and satisfy the flare-out condition at the throat. A central result is that the matter sector satisfies both the null and strong energy conditions, indicating that traversable rotating wormholes can be supported without exotic matter. We further analyze particle motion, frame dragging, and non-geodesic effects arising from matter-geometry coupling, together with shadow deformation and gravitational lensing signatures induced by rotation. A preliminary stability analysis based on sound-speed conditions indicates the physical viability of the solutions. These results demonstrate that rotating wormholes in $f(R,T)$ gravity constitute physically consistent compact configurations with potentially observable astrophysical signatures.

gr-qc↗

arXiv2026

Effective Constrained Scalar--Gauss--Bonnet Inflation Motivated by $f(R,\mathcal{G})$ Gravity

We develop an effective framework for inflation in a constrained scalar--Gauss--Bonnet theory motivated by a restricted sector of $f(R,\mathcal{G})$ gravity. Using unified parametrizations of the Hubble expansion rate and the Gauss--Bonnet coupling function within a generalized slow-roll formalism, we derive analytical expressions for the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, and study their dependence on the model parameters. We show that the Hubble parametrization mainly controls the scalar sector through the slow-roll parameter $\epsilon_1$, while the Gauss--Bonnet-induced contribution $\epsilon_4$ can significantly affect the scalar tilt and strongly suppress primordial tensor modes, naturally leading to very small values of $r$. A representative benchmark solution yields $n_s \simeq 0.958$ and $r \simeq 2.7 \times 10^{-4}$, marginally compatible with current Planck, ACT, and BICEP/Keck constraints. We further investigate the scalar perturbation structure of the exactly constrained theory, where the Lagrange-multiplier constraint forces the lapse perturbation to vanish and, together with the gravitational momentum constraint, implies $\dot{\mathcal{R}}=0$, eliminating the propagating scalar degree of freedom at linear order. This exact result clarifies that the generalized slow-roll treatment should be interpreted as an effective softly constrained description. We also discuss perturbative stability conditions, including the positivity of the relevant kinetic coefficients and propagation speeds. Our results demonstrate that the effective constrained scalar--Gauss--Bonnet framework provides a flexible and observationally viable description of inflation while clarifying the distinction between the exact constrained limit and its effective slow-roll realization.

physics.gen-ph↗

arXiv2026

Alleviating the Hubble Tension Using $Λ$sCDM Model: A Coupled Dark Energy - Dark Matter Interaction

The considerable difference between early and late universe measurements of the Hubble constant, called the Hubble tension, poses a potential challenge to the standard $Λ$CDM cosmological model. We examine an interacting dark matter-dark energy model, $Λ_s$CDM, characterized by a gauge-invariant coupling $Q = ξHρ_{\mathrm{de}}$ and an effective pressure dynamically induced within the dark matter fluid. Using the CLASS Boltzmann code modified in this work, we analyze both the background and perturbation observables and compute an extensive Markov Chain Monte Carlo analysis with the latest cosmological datasets, including observational Hubble parameter data, Planck 2018 CMB compressed likelihood, BAO (from DESI DR2), Pantheon+ Type Ia supernovae, and redshift-space distortion measurements. The model predicts $H_0 = 71.8_{-0.3}^{+0.4}\mathrm{kms^{-1}Mpc^{-1}}$, reducing the tension with the SH0ES local measurement from about $5σ$ in $Λ$CDM to $1.2σ$ in $Λ_s$CDM. In contrast to the early dark energy model, the resolution emerges from late-time modification of the expansion history induced by the energy transfer from dark matter to dark energy. Moreover, the model suppresses late-time structure growth, providing $σ_8 = 0.744 \pm 0.0185$, lying below the $Λ$CDM value and moves in the direction preferred by weak lensing surveys. Since the interaction term is suppressed at high redshift, the pre-recombination sound horizon departs by less than $1\%$ from its $Λ$CDM value, suggesting that the alleviation of the tension dominantly originates from the late-time expansion rather than early-universe effects. We conclude that $Λ_s$CDM constitutes a phenomenologically viable interacting dark sector framework that addresses key cosmological tensions while remaining consistent with current precision data. }

astro-ph.CO↗

arXiv2026

Light Deflection and Greybody Bound Around a BTZ-ModMax Black Hole in Plasma Medium

We study the deflection of light in a homogeneous plasma medium around a BTZ-ModMax black hole, focusing on the effects of the ModMax nonlinear electrodynamics parameter and the cosmological constant. Using the Gauss-Bonnet theorem applied to the corresponding optical geometry in plasma, we derive a modified expression for the deflection angle and examine how plasma dispersion alters the gravitational lensing behavior. The influence of the ModMax parameter in the presence of homogeneous plasma is compared with its vacuum counterpart, as well as with the charged and static BTZ black hole cases, revealing distinct signatures arising from nonlinear electrodynamics. This work highlights the combined impact of homogeneous plasma, spacetime curvature, and nonlinear field dynamics on light deflection in lower-dimensional black hole geometries. We further study the greybody factor and analyze how the presence of homogeneous plasma and the ModMax parameter modifies the energy emission spectrum of the black hole. Our results demonstrate that both plasma effects and nonlinear electrodynamics significantly influence the transmission probabilities and emission rates, providing deeper insight into wave propagation and observational signatures in lower-dimensional black hole geometries.

gr-qc↗

arXiv2026

Cosmological Tensions as Consistency Conditions for f(Q) Gravity

Cosmology has entered a precision era in which discrepancies between independent datasets, most notably the $H_0$ and $S_8$ tensions, have become robust and statistically significant. These tensions are no longer isolated anomalies but increasingly appear as global consistency constraints on the underlying cosmological model, defining what we will refer to here as a \emph{consistency triangle} of background expansion ($H_0$), structure-growth amplitude ($S_8$), and the redshift-dependence of growth - summarised by the growth index $γ$, or equivalently the shape of $fσ_8(z)$. The third vertex is non-trivial because in modified-gravity scenarios with a redshift-dependent effective gravitational coupling, growth amplitude and growth shape evolve independently, breaking the rigid coupling characteristic of $Λ$CDM. In this work, we use $f(Q)$ gravity as a test case for this emerging paradigm. By drawing on a focused set of recent Bayesian and dynamical-system analyses of the three best-studied functional families - power-law, exponential, and logarithmic - we show that while $f(Q)$ models can alleviate individual tensions, the requirement of simultaneous consistency across $H_0$, $S_8$ and the growth index severely restricts the viable parameter space. A bulk-viscous extension is then briefly examined as a representative illustration of how additional matter-sector freedom is constrained by the same consistency requirement. Our reading of the current literature supports the view that cosmological tensions should be interpreted as global consistency conditions, and that viable extensions of $Λ$CDM must satisfy this multi-probe constraint \cite{CosmoVerse,DiValentino2025Corfu}. Within this framework, only a restricted subset of $f(Q)$ models remains competitive.

gr-qc↗

arXiv2026

Gravitational lensing around a Kerr-Sen black hole in plasma background

We investigate the gravitational lensing of massless particles around a Kerr-Sen black hole immersed in a magnetized, cold, pressureless plasma medium. Both homogeneous and inhomogeneous plasma distributions are considered in this study to mimic realistic astrophysical environments. The light deflection angle is computed, and the effects of the black hole's rotation and charge on light bending are analyzed in detail. The conditions for the circular photon orbits are also examined in both plasma configurations. A comparison with the vacuum case (i.e. zero plasma frequency) highlights the role of plasma in modifying the light propagation, and the results obtained provide a deeper insight into plasma effects which improve our understanding of observational signatures of rotating charged black holes.

gr-qc↗

arXiv2026

Testing the Coexistence of Dark Energy and Dark Matter with Late-time Observational Data

We investigate the viability of a cosmological scenario with interacting dark sector, which can describe the coexistence between dark energy and dark matter. The model possesses an analytical solution for the Hubble function and we constrain the free parameters by applying the newly released cosmic chronometers data (31 old data and 3 new data from DESI), the Baryonic Acoustic Oscillators from the Dark Energy Spectroscopic Instrument Survey (DESI DR2 BAO), along with Gamma-ray bursts (GRBs) and Supernova catalogues (Pantheon Plus, Union3, and DES-Dovekie). We find that the coexistence model fits the data sets in a better way than the reference models - the $Λ$CDM and $w$CDM models. The analysis shows that the coexistence scenario can provide a cosmologically viable model for the description of the late-time acceleration of the universe. Nevertheless, for large redshifts, the model has a similar behaviour to that of the $w$CDM model, as the introduction of the GRB data indicates in the statistical parameters. Finally, it is worth mentioning that the coexistence model provides a statistically smaller value for the $H_{0}$ parameter.

astro-ph.CO↗

arXiv2026

Diffusive dark fluids with Planck-2018 and DESI BAO DR2 Measurements

In this paper, we constrain the diffusive dark fluid cosmological model, which is the interacting dark energy framework, wherein energy is transferred between the two dark components through a diffusion process. We extended the work by S. Sahlu et al. (2026) by employing Cosmic Microwave Background (CMB) data from the Planck 2018 measurements in combination with Baryon Acoustic Oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) DR2 (2024).From the results, we found that the discrepancies in $H_0$ measurements are $0.0105σ$ and $1.29σ$ between the Planck 2018 value $(H_0 = 67.4\pm0.5\ \mathrm{km,s^{-1},Mpc^{-1}})$ and our diffusive model values, $H_0 = 67.3876^{+1.0765}_{-1.0709}$ and $68.3804^{+0.5639}_{-0.5852}$, respectively. We also the we observe that the effects of the interaction on cosmic evolution and structure formation; we emphasize this by computing the scale-dependent density contrast and the matter power spectrum, compared with the $Λ$CDM model.

astro-ph.CO↗

arXiv2026

Crunching, Bouncing, and Cyclical Cosmologies from Dark Sector Interactions

We present new mechanisms that produce either a future Big Crunch turnaround or a past non-singular bounce in flat FLRW cosmologies within general relativity at the background level, driven solely by non-gravitational interactions between dark matter (DM) and dark energy (DE). We study phenomenological interacting dark energy (IDE) models based on linear kernels of the form $Q = 3H(\delta_{\rm dm}\rho_{\rm dm} + \delta_{\rm de}\rho_{\rm de})$, focusing on parameter regimes with strong energy transfer from dark energy to dark matter. In this strong interacting regime, the interaction does not vanish when one component crosses zero density, allowing one of the dark-sector densities to become negative. The resulting sign changes can violate the energy conditions required for cosmological turnarounds in a flat universe, thereby enabling either (i) a maximum scale factor followed by recollapse into a big crunch, or (ii) a minimum non-zero scale factor corresponding to a bounce. We derive analytic conditions for these turnarounds and obtain closed-form expressions for the associated maximum or minimum scale factor. We also show that, in a closed universe, a special case of the same IDE framework can be tuned to yield a cyclic scenario. Although these strong interaction scenarios are unlikely to describe the observed Universe, they provide a concrete demonstration that exotic cosmological behaviour can arise naturally in underexplored regions of the parameter space of familiar IDE models.

astro-ph.CO↗

arXiv2026

Dynamics of the Bianchi~V cosmological model inspired by quintessential $α$-attractors

We investigate scalar-field cosmologies in the Bianchi V spacetime using a dynamical-systems framework. Motivated by representative $α$-attractor potentials - the E-model and T-model - we apply averaging theorems and amplitude--phase reductions to monomial potentials $\sim ϕ^{2n}$ of the scalar field, which approximate the attractor models near their minima, in the presence of matter with barotropic index $γ$. The reduced averaged system admits five generic isolated equilibria: Kasner vacua $\mathcal{K}_0^\pm$, the matter FLRW point $\mathcal{F}$, the scalar FLRW point $\mathcal{S}$, and the curvature Milne-type point $\mathcal{K}$, together with special families for tuned $(n,γ)$. We find that $\mathcal{K}_0^\pm$ are always sources, $\mathcal{F}$ is generically a saddle but can act as a sink for $γ<\min\{\tfrac{2n}{n+1},\tfrac{2}{3}\}$, $\mathcal{S}$ is a sink if $0 \tfrac{2}{3}$ and $n>\tfrac{1}{2}$. These results demonstrate that isotropic FLRW $α$-attractor models extend naturally to anisotropic Bianchi~V cosmologies: inflationary attractors remain robust, while the Milne-type curvature solution emerges as the late-time state.

gr-qc↗

arXiv2026

Constraining Quintessence Models with ISW-tSZ Cross-Correlations: A Comparative Analysis of Thawing, Tracker, and Scaling-Freezing Dynamics

We present constraints on quintessence dark energy models using the observational detection of the Integrated Sachs-Wolfe (ISW)--thermal Sunyaev-Zeldovich (tSZ) cross-correlation dataset. Our analysis compares three classes of quintessence dynamics: thawing, tracker, and scaling-freezing with the standard $Λ$CDM cosmology. Through a comprehensive likelihood analysis, we derive best-fit values and 68\% confidence intervals for key cosmological parameters, finding $Ω_{\rm m} = 0.322^{+0.027}_{-0.030}$ and $σ_8 = 0.735^{+0.045}_{-0.035}$ for $Λ$CDM, with deviations in alternative models consistent within $1σ$. For the thawing model, we consider an exponential potential with slope $λ= 0.736^{+0.270}_{-0.227}$, while for the tracker and scaling-freezing models, we use inverse axion-like and double exponential potentials, respectively. Observationally, the tracker model yields $n = 5.651^{+1.625}_{-1.604}$ and $f = 0.258^{+0.149}_{-0.096}$, and the scaling-freezing model gives $λ_1 = 0.405^{+0.293}_{-0.322}$ and $λ_2 = 23.226^{+7.975}_{-7.258}$. The dimensionless tSZ amplitude ($\widetilde{W}^{\rm SZ}$) and cosmic infrared background (CIB) parameters are tightly constrained across all models, providing additional insights into astrophysical foregrounds. Our results demonstrate the effectiveness of ISW--tSZ cross-correlations as a probe of dark energy dynamics, with the Thawing quintessence model yielding the lowest $χ^2_{\rm min}$ among the tested scenarios, and highlight the need for future high-precision measurements to distinguish between quintessence models and $Λ$CDM.

astro-ph.CO↗

arXiv2026

Kosmulator: A Python framework for cosmological inference with MCMC

We present Kosmulator, a modular and vectorised Python framework designed to accelerate the statistical testing of cosmological models. As the theoretical landscape expands beyond standard $Λ$CDM, implementing new expansion histories into traditional Einstein--Boltzmann solvers becomes a significant computational bottleneck. Kosmulator addresses this by leveraging array-native execution and efficient ensemble slice sampling (via Zeus) to perform rapid Bayesian inference. We validate the framework against the industry-standard Cobaya code using a combination of Type Ia Supernovae, Cosmic Chronometers, and Baryon Acoustic Oscillation (BAO) data. Our results demonstrate that Kosmulator reproduces Cobaya's posterior constraints to within $\leq0.3σ$ statistical agreement on $H_{0}$ and $Ω_{m}$ and $<0.6\%$ precision on $χ^{2}$, while achieving a $\sim 4.5\times$ reduction in wall-clock time on a single CPU core compared to a standard MPI-parallelised baseline. Furthermore, we showcase the framework's utility by constraining the implicit power-law $f(Q)$ "$f_1$CDM" model and demonstrating its automated model selection capabilities (AIC/BIC). Kosmulator is introduced as a "scientific sieve" for rapid hypothesis testing, allowing researchers to efficiently filter theoretical candidates before deploying high-precision resources.

astro-ph.CO↗

arXiv2026

Study of dynamical systems and large-scale structure

In this study, we employ dynamical systems methods to analyse the large-scale structure by considering two distinct interaction models (linear and non-linear) within the dark sector, associated with a specific dynamical dark energy model inspired by the Veneziano ghost theory in quantum chromodynamics (QCD). In these models, the dark energy density ($ρ_{DE}$) varies with the Hubble parameter ($H$), expressed as $ρ_{DE} = αH + βH^2$. After defining the dimensionless parameters, we present autonomous equations that allow us to find the trace $\text{Tr}(J)$ and the determinant $D(J)$. With these solutions, we demonstrate the presence of unstable, saddle, and stable fixed points, corresponding to the radiation-, matter-, and dark-energy-dominated eras, respectively. Our results suggest that these models are theoretically viable for representing the interaction between dark sector fluids.

gr-qc↗