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

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 $\mathrm{\Lambda }\mathrm{CDM}$ 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.

Figure 1

Gaussian processes reconstruction of $D(z)$, $D^{\prime }(z)$ (top), and $D^{\prime \prime }(z)$, $D^{\prime \prime \prime }(z)$ (bottom) obtained from a mock data set of future DES and assuming the $\mathrm{\Lambda }\mathrm{CDM}$ model with ${\mathrm{\Omega }}_{m0}=0.3$ (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 $\mathrm{\Lambda }\mathrm{CDM}$ model with ${\mathrm{\Omega }}_{m0}=0.3$. The shaded blue regions are the 68% and 95% C.L. of the reconstruction.

Figure 3

Gaussian processes reconstruction of $D(z)$, $D^{\prime }(z)$ (top), and $D^{\prime \prime }(z)$, $D^{\prime \prime \prime }(z)$ (bottom) obtained from a mock data set of future DES and assuming a toy decaying vacuum model: ${\rho }_{\mathrm{DE}}=3\alpha H$ with $w=-1$ and ${\mathrm{\Omega }}_{m0}=0.3$ (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 $\mathrm{\Lambda }\mathrm{CDM}$ 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: ${\rho }_{\mathrm{DE}}=3\alpha H$ with $w=-1$ and ${\mathrm{\Omega }}_{m0}=0.3$ (green line). The shaded blue regions are the 68% and 95% C.L. of the reconstruction. The $\mathrm{\Lambda }\mathrm{CDM}$ model is also shown (red dotted).

Figure 5

Gaussian processes reconstruction of $D(z)$, $D^{\prime }(z)$ (top), and $D^{\prime \prime }(z)$, $D^{\prime \prime \prime }(z)$ (bottom) obtained from Union 2.1 data sets. The shaded blue regions are the 68% and 95% C.L. of the reconstruction. The $\mathrm{\Lambda }\mathrm{CDM}$ model (red line) is also shown.

Figure 6

Reconstruction of $\tilde{q}(z)$ from Union 2.1 data sets. The shaded blue regions are the 68% and 95% C.L. of the reconstruction. The red line corresponds to the $\mathrm{\Lambda }\mathrm{CDM}$ model.

Figure 7

Reconstructions of $\tilde{q}(z)$ for the $w\mathrm{CDM}$ model and CPL parametrization. (a) $w=-0.7$; (b) $w=-0.8$; (c) $w=-0.9$; (d) $w=-1.006\pm 0.045$ from Planck 2015; (e) $w(a)=w_0+w_a(1-a)$ with $w_0=-1.046_{-0.170}^{+0.179}$ and $w_a=0.14_{-0.76}^{+0.60}$; (f) $w=-1.1$; (g) $w=-1.2$; (h) $w=-1.3$. The shaded blue regions are the 68% and 95% C.L. for the reconstruction.