Reconstructing the interaction between dark energy and dark matter using Gaussian Processes

TL;DR

This work addresses whether a nonstandard interaction between dark energy and dark matter leaves a detectable imprint on the expansion history, without assuming a parametric form for the interaction. It introduces a nonparametric Gaussian Process framework to reconstruct the distance–redshift function $D(z)$ and its derivatives, enabling a model-independent recovery of the interaction term $Q(z)$ (via the derived $ ilde{q}(z)$) for a given $w$. Validation with mock data shows the method can distinguish ΛCDM from a toy decaying-vacuum model. Application to Union 2.1 data finds no evidence for interaction when $w=-1$, but allows nonzero interaction for larger deviations of $w$ from $-1$, revealing a degeneracy between $w$ and $Q$ and underscoring the potential need to incorporate growth data in future analyses.

Abstract

We present a nonparametric approach to reconstruct the interaction between dark energy and dark matter directly from SNIa Union 2.1 data using Gaussian processes, which is a fully Bayesian approach for smoothing data. In this method, once the equation of state ($w$) of dark energy is specified, the interaction can be reconstructed as a function of redshift. For the decaying vacuum energy case with $w=-1$, the reconstructed interaction is consistent with the standard $Λ$CDM model, namely, there is no evidence for the interaction. This also holds for the constant $w$ cases from $-0.9$ to $-1.1$ and for the Chevallier-Polarski-Linder (CPL) parametrization case. If the equation of state deviates obviously from $-1$, the reconstructed interaction exists at $95\%$ confidence level. This shows the degeneracy between the interaction and the equation of state of dark energy when they get constraints from the observational data.

Figures (7)

• Figure 1: Gaussian processes reconstruction of $D(z)$, $D'(z)$ ( top), and $D"(z)$, $D"'(z)$ ( bottom) obtained from a mock data set of future DES and assuming the $\Lambda$CDM model with $\Omega_{m0}=0.3$ (red line). The dashed blue line is the mean of the reconstruction and the shaded blue regions are the $68\%$ and $95\%$ C.L. of the reconstruction, respectively.
• Figure 2: Reconstruction of $\tilde{q}(z)$ (dashed line) from the mock data set of future DES and assuming the $\Lambda$CDM model with $\Omega_{m0}=0.3$. The shaded blue regions are the $68\%$ and $95\%$ C.L. of the reconstruction.
• Figure 3: Gaussian processes reconstruction of $D(z)$, $D'(z)$ ( top), and $D"(z)$, $D"'(z)$ ( bottom) obtained from a mock data set of future DES and assuming a toy decaying vacuum model: $\rho_{DE}=3\alpha H$ with $w=-1$ and $\Omega_{m0}=0.3$ (green line). The dashed blue line is the mean of the reconstructions and the shaded blue regions are the $68\%$ and $95\%$ C.L. of the reconstruction, respectively. The $\Lambda$CDM model is also shown (red dotted).
• Figure 4: Reconstruction of $\tilde{q}(z)$ from a mock data set of future DES and assuming a decaying-vacuum model: $\rho_{DE}=3\alpha H$ with $w=-1$ and $\Omega_{m0}=0.3$ (green line). The shaded blue regions are the $68\%$ and $95\%$ C.L. of the reconstruction. The $\Lambda$CDM model is also shown (red dotted).
• Figure 5: Gaussian precesses reconstruction of $D(z)$, $D'(z)$ ( top), and $D"(z)$, $D"'(z)$ ( bottom) obtained from Union 2.1 data sets. The shaded blue regions are the $68\%$ and $95\%$ C.L. of the reconstruction. The $\Lambda$CDM model (red line) is also shown.