arXiv subjects

Marcel van der Westhuizen

Publications and source records attributed to Marcel van der Westhuizen.

6 recordsLinked to original sources

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 $Q = 3H(δ_{\rm dm}ρ_{\rm dm} + δ_{\rm de}ρ_{\rm de})$, 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

Late-time Background Constraints on Linear and Non-linear Interacting Dark Energy after DESI DR2

In this study, we present observational constraints on a class of phenomenological interacting dark energy (IDE) models that admit analytical solutions for the Hubble parameter $H(z)$. We consider a set of five linear and three non-linear IDE scenarios, encompassing both interactions proportional to the dark matter and/or dark energy densities, as well as non-linear combinations of the two. For all eight IDE models, we find a better fit than $Λ$CDM from a $Δχ^2$ analysis for both combinations of datasets considered. When using the Akaike Information Criterion ($Δ$AIC), we find a similarly improved fit in all cases, except for one dataset combination in $Q=3Hδρ_{\rm de}$. Our analysis also shows a preference for sign-switching interactions, with energy transfer from dark energy to dark matter at low redshift, reversing direction at higher redshift. These results should be interpreted with caution, as the latter direction of energy transfer is accompanied by negative dark energy densities in the past, which may be unphysical. Models that do not allow sign-changing behaviour instead show a preference for energy flow from dark matter to dark energy, and hence negative dark energy densities. The only exceptions are $Q=3Hδρ_{\rm de}$ and $Q=3Hδ\left(\tfrac{ρ_{\rm de}^2}{ρ_{\rm dm}+ρ_{\rm de}}\right)$, which exhibit energy flow in the opposite direction. Furthermore, for all interactions considered, we find a phantom-divide crossing in the effective dark energy equation of state $w^{\rm eff}_{\rm de}$, with the dark energy density decreasing ($w^{\rm eff}_{\rm de}>-1$) at present and at low redshift, while increasing ($w^{\rm eff}_{\rm de}<-1$) in the past at high redshift. These results highlight the promising, but problematic, nature of dark sector interactions, as well as the need to extend the analysis using early-time physics and datasets.

astro-ph.CO↗

arXiv2025

III. Interacting Dark Energy: Summary of Models, Pathologies, and Constraints

We present an overview of the main results from our two companion papers that are relevant for observational constraints on interacting dark energy (IDE) models. We provide analytical solutions for the dark matter and dark energy densities, $ρ_{\rm dm}$ and $ρ_{\rm de}$, as well as the normalized Hubble function $h(z)$, for eight IDE models. These include five linear IDE models, namely $Q=3H(δ_{\rm dm} ρ_{\rm dm} + δ_{\rm de} ρ_{\rm de})$ and four special cases: $Q=3Hδ(ρ_{\rm dm}+ρ_{\rm de})$, $Q=3Hδ(ρ_{\rm dm}-ρ_{\rm de})$, $Q=3Hδρ_{\rm dm}$, and $Q=3Hδρ_{\rm de}$, together with three non-linear IDE models: $Q=3Hδ\left( \tfrac{ρ_{\rm dm} ρ_{\rm de}}{ρ_{\rm dm}+ρ_{\rm de}} \right)$, $Q=3Hδ\left( \tfrac{ρ_{\rm dm}^2}{ρ_{\rm dm}+ρ_{\rm de}} \right)$, and $Q=3Hδ\left( \tfrac{ρ_{\rm de}^2}{ρ_{\rm dm}+ρ_{\rm de}} \right)$. For these eight models, we present conditions to avoid imaginary, undefined, and negative energy densities. In seven of the eight cases, negative densities arise if energy flows from DM to DE, implying a strong theoretical preference for energy transfer from DE to DM. We also provide conditions to avoid future big rip singularities and evaluate how each model addresses the coincidence problem in both the past and the future. Finally, we propose a set of approaches and simplifying assumptions that can be used when constraining IDE models, by defining regimes that restrict the parameter space according to the behavior researchers are willing to tolerate.

gr-qc↗

arXiv2025

Compartmentalization in the Dark Sector of the Universe after DESI DR2 BAO data

We consider a non-linear interaction between the dark matter and dark energy components of the universe. In particular, within the FLRW geometry, where dark matter is described by a dust fluid and dark energy by an ideal gas with a constant equation of state parameter, we introduce energy transfer between the two fluids. The effective cosmological fluid leads to a unified dynamical dark energy model with the feature that the Hubble function admits an analytic expression. We study this model using the DESI DR2 Baryonic Acoustic Oscillations data and the Supernova data from Pantheon+. The interacting model fits the data better than the $Λ$CDM model, with $χ_{\text{model}}^{2}-χ_{Λ\text{CDM}}^{2}=-5$. Using the Akaike Information Criterion to compare the two models, we derive $\text{AIC}_{\operatorname{model}}-\text{AIC}_{Λ\text{CDM}}=-1$, from which we conclude that the interacting model is marginally better supported by the data than the $Λ$CDM, but the difference is not statistically significant.

astro-ph.CO↗

arXiv2025

I. Linear Interacting Dark Energy: Analytical Solutions and Theoretical Pathologies

Interacting dark energy (IDE) models, in which dark matter (DM) and dark energy (DE) exchange energy through a non-gravitational interaction, have long been proposed as candidates to address key challenges in modern cosmology. These include the coincidence problem, the $H_0$ and $S_8$ tensions, and, more recently, the hints of dynamical dark energy reported by the DESI collaboration. Given the renewed interest in IDE models, it is crucial to fully understand their parameter space when constraining them observationally, especially with regard to the often-neglected issues of negative energy densities and future big rip singularities. In this work, we present a comparative study of the general linear interaction $Q=3H(δ_{\rm dm}ρ_{\rm dm} + δ_{\rm de}ρ_{\rm de})$ and four special cases: $Q=3Hδ(ρ_{\rm dm}+ρ_{\rm de})$, $Q=3Hδ(ρ_{\rm dm}-ρ_{\rm de})$, $Q=3Hδρ_{\rm dm}$, and $Q=3Hδρ_{\rm de}$. For these five models, we perform a dynamical system analysis and derive new conditions that ensure positive, real, and well-defined energy densities throughout cosmic evolution, as well as criteria to avoid future big rip singularities. We obtain exact analytical solutions for $ρ_{\rm{dm}}$, $ρ_{\rm{de}}$, the effective equations of state ($w_{\mathrm{eff}}^{\rm{dm}}$, $w_{\mathrm{eff}}^{\rm{de}}$, $w_{\mathrm{eff}}^{\rm{tot}}$), and a reconstructed dynamical DE equation of state $\tilde{w}$. Using these results, we examine phantom crossings, address the coincidence problem, and apply the statefinder diagnostic to distinguish between models. We show that energy transfer from DM to DE inevitably produces negative energy densities and make future singularities more likely, while transfer from DE to DM avoids these pathologies and is thus theoretically favored.

gr-qc↗

arXiv2025

II. Non-Linear Interacting Dark Energy: Analytical Solutions and Theoretical Pathologies

We investigate interacting dark energy (IDE) models with phenomenological, non-linear interaction kernels $Q$, specifically $Q_{1}=3Hδ\left(\frac{ρ_{\rm dm}ρ_{\rm de}}{ρ_{\rm dm}+ρ_{\rm de}}\right)$, $Q_{2}=3Hδ\left(\frac{ρ_{\rm dm}^2}{ρ_{\rm dm}+ρ_{\rm de}}\right)$, and $Q_{3}=3Hδ\left(\frac{ρ_{\rm de}^2}{ρ_{\rm dm}+ρ_{\rm de}}\right)$. Using dynamical system techniques developed in our companion paper on linear kernels, we derive new conditions that ensure positive and well-defined energy densities, as well as criteria to avoid future big rip singularities. We find that for $Q_{1}$, all densities remain positive, while for $Q_{2}$ and $Q_{3}$ negative values of either DM or DE are unavoidable if energy flows from DM to DE. We also show that for $Q_{1}$ and $Q_{2}$ a big rip singularity always arises in the phantom regime $w<-1$, whereas for $Q_{3}$ this fate may be avoided if energy flows from DE to DM. In addition, we provide new exact analytical solutions for $ρ_{\rm dm}$ and $ρ_{\rm de}$ in the cases of $Q_{2}$ and $Q_{3}$, and obtain new expressions for the effective equations of state of DM, DE, the total fluid, and the reconstructed dynamical DE equation of state ($w_{\rm dm}^{\rm eff}$, $w_{\rm de}^{\rm eff}$, $w_{\rm tot}^{\rm eff}$, and $\tilde{w}$). Using these results, we discuss phantom crossings, evaluate how each kernel addresses the coincidence problem, and apply statefinder diagnostics to compare the models. These findings extend the theoretical understanding of non-linear IDE models and provide analytical tools for future observational constraints.

gr-qc↗