Impact of Interacting Dark Energy on the Growth of Matter Density Perturbations: Observational Constraints from DESI and Multi-Probe Data

TL;DR

This work assesses the impact of a non-gravitational DM–DE coupling in a minimal IDE $w$CDM model on the growth of linear matter perturbations. It derives a second‑order expansion for the growth index γ(z) that explicitly includes the coupling α and develops an efficient $Ω_m(z)^{γ(z)}$ parameterization, enabling fast growth predictions for MCMC analyses. Through a joint analysis of Pantheon+ SNIa, CMB compressed priors, BAO from SDSS or DESI DR2, H(z), and RSD-derived $fσ_8$, the study finds α consistent with zero and w ≈ −1, with a bound $|Δγ| lesssim 0.03$ (3σ), effectively breaking the IDE–MG degeneracy and disfavoring MG models as the source of any observed γ deviation. The results reinforce ΛCDM as the consistent baseline and establish the growth index as a robust discriminator when coupled with precise background constraints, while providing a computationally efficient tool for future cosmological analyses.

Abstract

We investigate the impact of a non-gravitational interaction between dark matter and dark energy on the growth rate of matter density perturbations within the framework of a $w$CDM scenario, where the coupling is proportional to the dark energy density. To incorporate the effects of this interaction in cosmological analysis, we develop a parameterization for the growth rate based on a second-order approximation for the growth index $γ$ that explicitly includes the coupling constant $α$. This formalism reveals a theoretical degeneracy: the coupling induces a correction $Δγ\simeq 1.1α$, allowing an interacting dark energy model to mimic the growth index predicted by certain modified gravity theories. We confront the model with the latest multi-probe observations, including the Pantheon+ sample of Type~Ia supernovae, Baryon Acoustic Oscillation (BAO) data from the Sloan Digital Sky Survey (SDSS) and the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI), Cosmic Microwave Background (CMB) measurements, Hubble parameter $H(z)$ data, and redshift-space distortion (RSD) measurements, to simultaneously constrain the coupling strength $α$ and the dark energy equation of state $w$. Our analysis finds $α$ consistent with zero and $w$ with $-1$ at the $1σ$ confidence level, showing no statistical evidence for a departure from the standard $Λ$CDM cosmology. The observational constraints effectively break the theoretical degeneracy with modified gravity, limiting the possible interaction-induced shift in the growth index to $|Δγ|\lesssim 0.03$ ($3σ$). This establishes the growth index as a robust diagnostic for distinguishing between a non-minimal interaction in the dark sector and a genuine modification of gravity.

Figures (5)

• Figure 1: The impacts of the coupling $\alpha$ on the growth rate $f$, given $\Omega_{\rm{m},0}=0.31$ and $w=-1$.
• Figure 2: The relative difference between the growth rate $f$ and $\Omega_{\rm m}^{\gamma}$ for the constant $\gamma$ (left panel), and the same for the second-order approximation of $\gamma$ (right panel), while $\Omega_{\rm m,0}=0.31$ and $w=-1$.
• Figure 3: Triangular plot of the model parameters: 2D joint and 1D marginalized posterior distributions, showing constraints from the background-only SHCB$_{\rm SDSS}$ (red contours) and SHCB$_{\rm DESI}$ (blue contours) datasets, respectively.
• Figure 4: Triangular plot of the model parameters: 2D joint and 1D marginalized posterior distributions, showing constraints from the SHCB$_{\rm SDSS}$+RSD (red contours) and SHCB$_{\rm DESI}$+RSD (blue contours) datasets, respectively. The theoretical growth rate $f(z)$ is obtained via Method I.
• Figure 5: Triangular plot of the model parameters: 2D joint and 1D marginalized posterior distributions, showing constraints from the SHCB$_{\rm SDSS}$+RSD (red contours) and SHCB$_{\rm DESI}$+RSD (blue contours) datasets, respectively. The theoretical growth rate $f(z)$ is obtained via Method II.