Evidence for interacting dark energy from BOSS

The result presented by the BOSS-SDSS Collaboration measuring the baryon acoustic oscillations of the Lyman-alpha forest from high-redshift quasars indicates a $2.5\sigma$ departure from the standard $\mathrm{\Lambda }$-cold-dark-matter model. This is the first time that the evolution of dark energy at high redshifts has been measured, and the current results cannot be explained by simple generalizations of the cosmological constant. We show here that a simple phenomenological interaction in the dark sector provides a good explanation for this deviation, naturally accommodating the Hubble parameter obtained by BOSS, $H(z=2.34)=222\pm 7\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. By performing a global fit of the parameters with the inclusion of this new data set together with the Planck data for the interacting model, we are able to show that some interacting models have constraints for $H(2.34)$ and $D_{\mathrm{A}}(2.34)$ that are compatible with the ones obtained by the BOSS Collaboration, showing a better concordance than $\mathrm{\Lambda }\mathrm{CDM}$. We also show that the interacting models that have a small positive coupling constant, which helps alleviate the coincidence problem, are compatible with the cosmological observations. Adding the likelihood of these new baryon acoustic oscillations data shows an improvement in the global fit, although it is not statistically significant. The coupling constant could not be fully constrained by the data sets used, but the dark energy equation of state shows a slight preference for a value different from a cosmological constant.

Figure 1

We plot $H(z=2.34)$ as a function of the coupling $\xi$ (corresponding to ${\xi }_2$ for models I and II and to ${\xi }_1$ for model III). The interacting models correspond to the colored lines since they depend on the free parameter $\xi$, the coupling constant. The left panel represents the Hubble parameter calculated using the cosmological parameters from Table 2 and with ${\omega }_{\mathrm{DE}}=-1$. The right panel represents $H(2.34)$ using the parameters found in Ref. [27] (including ${\omega }_{\mathrm{DE}}\ne -1$; see Table X for model I, Table XI for model II, and Table XII for model III) obtained from $\text{Planck}+\mathrm{BAO}+\mathrm{SnIa}+H_0$. The dashed gray line is the BOSS measured value of $H(2.34)=222\pm 7\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$, and the shaded areas represent $1\sigma$ and $2\sigma$ deviations from this average. For the sake of comparison, the green star represents $H(2.34)=238\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$, the value expected for $\mathrm{\Lambda }\mathrm{CDM}$ given the cosmological parameters in Table 2.

Figure 2

Plot of the 68.3% and 95.5% likelihood contours in $D_{\mathrm{A}}(z=2.34)/r_{\mathrm{d}}\times D_H(z=2.34)/r_{\mathrm{d}}$ comparing the BOSS combined (autocorrelation and cross-correlation) contour in black with the results for the interacting models from the runs using Planck data in blue. Interacting Model II is shown in the left panel and Model III in the right panel. The green lines show the best fit values for $\mathrm{\Lambda }\mathrm{CDM}$.

Figure 3

Contour plot of the EoS for dark energy ($\omega$) vs the coupling constant between dark energy and dark matter ($\xi$). In purple, we present the interacting model II, and in gray, we present the interacting model III fitted to the Planck data. The cosmological constant $\mathrm{\Lambda }$ of $\mathrm{\Lambda }\mathrm{CDM}$ corresponds to $\omega =-1$, and it is depicted by the dashed black horizontal line.