Cosmic sign-reversal: non-parametric reconstruction of interacting dark energy with DESI DR2

TL;DR

This paper develops a model-independent, non-parametric reconstruction of vacuum energy interacting with cold dark matter, characterized by a time-varying coupling $\beta(z)$ in the IDE framework with $w=-1$. By binning $\beta(a)$ into 20 redshift bins and imposing a Gaussian smoothness prior, the authors reconstruct $\beta(z)$ from DESI DR2, Planck CMB, and multiple SNIa datasets without assuming a specific parameterization. The results reveal a sign reversal in the mean coupling over cosmic time, with early-time energy transfer from dark matter to dark energy and a late-time reversal, and show significant improvements in goodness-of-fit and Bayesian evidence relative to $\Lambda$CDM, notably for the DR2+DESY5 combination. A PCA indicates only three data-dominated degrees of freedom in $\beta(z)$, implying that the dynamical dark energy signal could be alternatively explained by IDE, underscoring the need for future observations to break this degeneracy between expansion history and growth history.

Abstract

A direct interaction between dark energy and dark matter provides a natural and important extension to the standard $Λ$CDM cosmology. We perform a non-parametric reconstruction of the vacuum energy ($w=-1$) interacting with cold dark matter using the cosmological data from DESI DR2, Planck CMB, and three SNIa samples (PP, DESY5, and Union3). By discretizing the coupling function $β(z)$ into 20 redshift bins and assuming a Gaussian smoothness prior, we reconstruct $β(z)$ without assuming any specific parameterization. The mean reconstructed $β(z)$ changes sign during cosmic evolution, indicating an energy transfer from cold dark matter to dark energy at early times and a reverse flow at late times. At high redshifts, $β(z)$ shows a $\sim 2σ$ deviation from $Λ$CDM. At low redshifts, the results depend on the SNIa sample: CMB+DESI and CMB+DESI+PP yield $β(z)$ consistent with zero within $2σ$, while CMB+DESI+DESY5 and CMB+DESI+Union3 prefer negative $β$ at $\sim2σ$. Both $χ^2$ tests and Bayesian analyses favor the $β(z)$ model, with CMB+DESI DR2+DESY5 showing the most significant support through the largest improvement in goodness of fit ($Δχ^2_{\rm MAP}=-17.76$) and strongest Bayesian evidence ($\ln\mathcal{B} = 5.98 \pm 0.69$). Principal component analysis reveals that the data effectively constrain three additional degrees of freedom in the $β(z)$ model, accounting for most of the improvement in goodness of fit. Our results demonstrate that the dynamical dark energy preference in current data can be equally well explained by such a sign-reversal interacting dark energy, highlighting the need for future observations to break this degeneracy.

Figures (6)

• Figure 1: Reconstructed evolution history of $\beta(z)$ with the mean value and 68% and 95% CL errors for the baseline CMB+DESI and its individual combinations with each SNIa dataset (PP, DESY5, and Union3). The blue solid lines and filled regions represent the DESI DR1-based reconstructions, while the red dashed lines show the DR2-based results. The black dashed lines denote the $\Lambda$CDM prediction ($\beta=0$).
• Figure 2: The Bayes factor $\ln \mathcal{B}$ results with 68% CL errors for different data combinations. The shaded regions correspond to the Jeffreys' scale thresholds for evidence interpretation: $|\ln\mathcal{B}|<1$ (inconclusive), $1\leq|\ln\mathcal{B}|<2.5$ (weak), $2.5\leq|\ln\mathcal{B}|<5$ (moderate), and $|\ln\mathcal{B}|\geq5$ (strong).
• Figure 3: The inverse eigenvalues of both the prior and the four posterior covariance matrices, ordered by the number of nodes in $e_i(z)$.
• Figure 4: The first three data-dominated eigenvectors $e_i(z)$ for the four DESI DR1-based data combinations.
• Figure 5: Reconstruction of $\beta(z)$ with the mean value (red line) and 68% and 95% CL errors (blue band) from a noiseless synthetic dataset generated assuming a $\Lambda$CDM cosmology ($\beta(z)=0$). The black dashed line indicates the true underlying model ($\beta=0$). The reconstruction is fully consistent with the null hypothesis, demonstrating the absence of significant biases or artefacts in our method.