Large-scale (in-) stability Analysis of an Exactly Solved Coupled Dark-Energy Model

TL;DR

The paper analyzes a non-gravitational interaction between dark matter and dark energy in a flat FLRW universe, focusing on an exactly solvable Q ∝ \dot{\rho}_t coupling. It derives analytic background solutions for both IDE (w_x ≠ -1) and IVS (w_x = -1), and performs a thorough perturbation analysis to assess large-scale stability. Using Planck 2015 data plus diverse late-time probes, the authors constrain the coupling parameter ξ to be very small, with ΛCDM consistently favored by Bayesian evidence. The work also discusses the impact on H_0 tension, finding partial relief for IDE but not for IVS, and highlights that the background remains effectively ΛCDM-like while perturbations carry the distinctive signatures of the interaction. Overall, ΛCDM remains the preferred model given current observations, though the framework clarifies how tiny dark-sector couplings would modify cosmological evolution and structure formation.

Abstract

Assuming a non-gravitational interaction amongst the dark fluids of our universe namely, the dark matter and dark energy, we study a specific interaction model in the background of a spatially flat Friedmann-Lemaître-Robertson-Walker geometry. The interaction model, as we found, solves the background evolution in an analytic way when the dark energy takes a constant barotropic equation of state, $w_x$. In particular, we analyze two separate interaction scenarios, namely, when the dark energy is a fluid other than the vacuum energy (i.e., $w_x \neq -1$) and when it is vacuum energy itself (i.e., $w_x = -1$). We found that the interacting model with $w_x \neq -1$ produces stable perturbation at large scales for $w_x < -1$ with the coupling strength $ξ<0$. Both the scenarios have been constrained with the latest astronomical data having distinct origin. The analyses show that a very small interaction with coupling strength is allowed and within 68.3\% confidence-region, $ξ=0$ is recovered. The analyses further show that a large coupling strength significantly affects the large scale dynamics of the universe while according to the observational data the interaction models are very well consistent with the $Λ$-cosmology. Furthermore, we observe that for the vacuum interaction scenario, the tension on $H_0$ is not released while for the interacting dark energy scenario with $w_x < -1$, the tension on $H_0$ seems to be released partially because of the high error bars in $H_0$. Finally, we close the work with the Bayesian evidence which shows that the $Λ$CDM cosmology is favored over the two interacting scenarios.

Figures (15)

• Figure 1: Color Online $-$ The behaviour of the IDE scenario in the large scales has been presented for different measures of the coupling parameter $\xi$. Left Panel: Here we display the evolutions of the CMB TT spectra for different values of the coupling parameter representing its strength. We see that with the increase in the magnitude of the coupling parameter, the interaction scenario effectively deviates from the usual non-interacting $\Lambda$CDM cosmology. We note that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM are almost indistinguishable from one another. Right Panel: Here, the relative deviation in the CMB TT spectra in compared to the non-interacting $\Lambda$CDM model has been shown. This confirms the observation as found in the left panel of this figure. In this figure, we observe that a very small difference between the curves presenting $\xi =-0.0001$ and $\Lambda$CDM exists but that is very hard to detect.
• Figure 2: Color Online $-$ The behaviour of the IDE scenario in the large scales has been presented for different measures of the coupling parameter. Left Panel: We show the evolutions of the matter power spectra for different coupling strengths of the interaction model. We find that with the increase of the coupling strength, the interaction scenario has a deviation from the usual non-interacting scenario (i.e., $\xi =0$) $\Lambda$CDM. Let us note that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM are almost indistinguishable from one another. Right Panel: The relative deviation in the matter power spectra in compared to the non-interacting $\Lambda$CDM model has been shown and we find similar observation as realized from its left panel. In this figure, we observe that a very small difference between the curves presenting $\xi =-0.0001$ and $\Lambda$CDM exists, and it is clearly visible.
• Figure 3: Color Online $-$Left Panel: The dynamical evolution of the quantity $\mathcal{H}_{\text{eff}}/\mathcal{H}$ has been depicted in presence of different coupling parameters of the interaction rate (\ref{['interaction']}). The curves from upper to lower respectively stand for $\Lambda$CDM ($\xi =0$) model, $\xi = -0.0001, -0.01, -0.03, -0.05$. We notice that the curves presenting non-interacting $\Lambda$CDM and $\xi= -0.0001$ are practically indistinguishable from one another. Right Panel: The evolution of the quantity $G_{\text{eff}}/G$ has been shown for different coupling parameters of the interaction rate (\ref{['interaction']}). The curves from lower to upper levels respectively stand for $\Lambda$CDM ($\xi =0$) model, $\xi = -0.0001, -0.01, -0.03, -0.05$. Similar to the left panel, here we also notice that the curves presenting $\Lambda$CDM and $\xi= -0.0001$ are practically indistinguishable from each other. From both the panels, we arrive at a common conclusion which states that, as $\xi$ increases (considering its magnitude), the model starts deviating from the non-interacting $\Lambda$CDM cosmology and the coupling parameter $\xi =-0.05$ can be safely excluded from the consideration.
• Figure 4: Color Online $-$ The evolution of growth rate for the cold dark matter in presence of the interaction rate (\ref{['interaction']}) has been shown for different values of the coupling strength. The curves from upper to lower respectively stand for the non-interacting $\Lambda$CDM model (where $\xi=0$) and with other coupling parameters $\xi= -0.0001, -0.01, -0.03, -0.05$. Here too, the curves for $\Lambda$CDM and $\xi= -0.0001$ are indistinguishable from one another. From the figure we observe that as long as the strength or magnitude of the coupling parameter increases, the growth rate for the cold dark matter sector significantly deviates from $\xi = 0$ (no-interaction, $\Lambda$CDM). The physical scenario indicates that with the increase of the coupling strength, the growth-rate for the cold dark matter decreases with the evolution of the universe.
• Figure 5: Color Online $-$ The behaviour of the interacting vacuum scenario (IVS) in the large scales has been presented for different measures of the coupling parameter $\xi$. Left Panel: In this plot, we show the evolutions of the CMB TT spectra for different coupling strengths of the interaction model. One can clearly see that as the magnitude or strength of the coupling parameter increases, te deviation of the interaction model becomes prominent from the non-interacting $\Lambda$CDM cosmology. We note that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM cannot be differentiated from one another. Right Panel: The relative deviation in the CMB TT spectra in compared to the non-interacting $\Lambda$CDM model has been shown here. From this plot, one can easily conclude that the increament in $\xi$ results in significant deviation from the corresponding non-interacting scenario. Here, we observe that the curves presenting $\xi =-0.0001$ and $\Lambda$CDM overlap with each other.