Unimodular Diffusion and Interacting Vacuum Cosmology

Abstract

We investigate the correspondence between unimodular diffusion cosmology and interacting dark sector models at the background and linear perturbation levels. In the diffusion framework, the effective cosmological constant becomes time dependent, $Λ(t)$, sourced by a diffusion current. We show that at the background level this framework can be mapped onto interacting dark energy models with $w=-1$ and energy transfer $Q$. Using two common parameterizations, $Q = ξH ρ_{\rm de}$ and $Q = ξH ρ_{\rm dm}$, and data from supernovae, DESI BAO, cosmic chronometers, and CMB distance priors, we find $ξ= -0.0197 \pm 0.0076$ for the vacuum-coupled case, while the matter-coupled case gives a best-fit $ξ= 0.0018$ with comparable goodness of fit. At the level of linear perturbations, however, the diffusion framework is consistent only with interacting vacuum models having homogeneous energy transfer ($Q \propto ρ_{\rm de}$ with $δQ=0$), thereby breaking the degeneracy with more general interacting dark energy scenarios. Including redshift-space distortion data, we obtain $ξ= -0.0147 \pm 0.0075$, consistent with $Λ$CDM ($ξ=0$) at $2σ$. The inferred clustering amplitude is $S_8 = 0.782 \pm 0.026$ for the diffusion model, compared to $S_8 = 0.77 \pm 0.025$ for $Λ$CDM under the same dataset, indicating a modest but non-negligible impact on structure growth.

Figures (4)

• Figure 1: Evolution of the normalized dark matter density for interacting dark sector models. Left: interaction $Q=\xi H\rho_{\rm dm}$ showing the modified dilution law $\rho_{\rm dm}\propto a^{-3-\xi}$. Right: interaction $Q=\xi H\rho_{de}$ where the matter density evolution depends on the dark energy dynamics.
• Figure 2: Marginalized one and two-dimensional posterior distributions for $H_0$, $\Omega_{m0}$, $\Omega_{b0}$, and the interaction parameter $\xi$ obtained using background datasets ($H(z)$, Pantheon+ SNe, BAO, and CMB distance priors). The contours represent the $68\%$ and $95\%$ confidence regions for the two interaction prescriptions, $Q=\xi H\rho_{\rm dm}$ and $Q=\xi H\rho_{\rm de}$, used to represent the diffusion model at the background level.
• Figure 3: Left: One dimensional posterior distributions of the interaction parameter $\xi$ for the diffusion model $Q=\xi H \rho_\Lambda$ using background-only data and the combined background+RSD analysis. Right: Corresponding constraints on $S_8$ for $\Lambda$CDM and the diffusion model using the full dataset. Growth measurements mildly reduce the statistical preference for nonzero $\xi$ while inducing only a modest shift in $S_8$.
• Figure 4: Evolution of the growth-rate observable $f\sigma_8(z)$. The blue solid curve shows the best-fit prediction of the diffusion model, while the red dashed curve corresponds to the $\Lambda$CDM prediction obtained using the same dataset combination. Black points with error bars represent redshift-space distortion (RSD) measurements of $f\sigma_8$. The two models produce nearly identical growth histories within current observational uncertainties, indicating that present large-scale structure data do not strongly distinguish between diffusion-driven vacuum dynamics and the standard $\Lambda$CDM model.