Constraining interacting dark energy with CMB and BAO future surveys

In this paper, we perform a forecast analysis to test the capacity of future baryon acoustic oscillation (BAO) and cosmic microwave background (CMB) experiments to constrain phenomenological interacting dark energy models using the Fisher matrix formalism. We consider a Euclid-like experiment, in which BAO measurements are one of the main goals, to constrain the cosmological parameters of alternative cosmological models. Moreover, additional experimental probes can more efficiently provide information on the parameters forecast, justifying also the inclusion in the analysis of a future ground-based CMB experiment mainly designed to measure the polarization signal with high precision. In the interacting dark energy scenario, a coupling between dark matter and dark energy modifies the conservation equations such that the fluid equations for both constituents are conserved as the total energy density of the dark sector. In this context, we consider three phenomenological models that have been deeply investigated in literature over the past years. We find that the combination of both CMB and BAO information can break degeneracies among the dark sector parameters for all three models, although to different extents. We find powerful constraints on, for example, the coupling constant when comparing it with present limits for two of the models, and their future statistical $3\sigma$ bounds could potentially exclude the null interaction for the combination of probes that is considered. However, for one of the models, the constraint on the coupling parameter does not improve the present result (achieved using a large combination of surveys), and a larger combination of probes appears to be necessary to eventually claim whether or not interaction is favored in that context.

Figure 1

Plots of the CMB temperature power spectrum (upper panel) and matter power spectrum (lower panel) for three different coupling parameters ${\xi }_2$ for model 1. The other parameters assume the fiducial values given in Sec. 3, Table 3. In particular, $w_{\mathrm{DE}}=-0.9434$.

Figure 2

Plots of the CMB temperature power spectrum (upper panel) and matter power spectrum (lower panel) for three different coupling parameters ${\xi }_2$ for model 2. The other parameters assume the fiducial values given in Sec. 3, Table 4. In particular, $w_{\mathrm{DE}}=-1.087$.

Figure 3

Plots of the CMB temperature power spectrum (upper panel) and matter power spectrum (lower panel) for three different coupling parameters ${\xi }_1$ for model 3. The other parameters assume the fiducial values given in Sec. 3, Table 5. In particular, $w_{\mathrm{DE}}=-1.06$.

Figure 4

Plots of the growth rate ($f$; top panel), the root-mean-square matter fluctuations today in linear theory at a characteristic length scale of $8\mathrm{Mpc}/h$ (${\sigma }_8$; middle panel), and their product ($f{\sigma }_8$; bottom panel) as a function of redshift ($z$). The orange curve represents $\mathrm{\Lambda }\mathrm{CDM}$ with Planck-like fiducial values for the cosmological parameters (see Ref. [2]). For models 1, 2, and 3 (green, red, and blue curves, respectively), the fiducial values were taken following the best fit values of Ref. [17], also shown in Tables 3, 4, 5 of our manuscript.

Figure 5

Fisher forecast contours for model 1 with CMB and BAO information using AdvACT (red curves) and Euclid (blue curves) experimental setups, respectively. The dashed curves represent 68% C. L., and the solid curves represent 99.9% C. L. The combined contours are shown by the green filled ellipses. Similarly, the darker ellipses represent 68% C. L., and the fainter ones represent 99.9% C. L. See Table 3 for numerical values.

Figure 6

Correlation matrix computed according to Eq. (18) for AdvACT (left), Euclid (center), and their combination (right) for model 1. The color in each cell indicates the correlation between two model parameters, ranging from 0 (completely independent) to $\pm 1$ [completely (anti)correlated].

Figure 7

Fisher forecast contours for model 2. The convention used to denote the various cases is described in Fig. 5. See also Table 4 for numerical values.

Figure 8

Correlation matrix computed according to Eq. (18) for AdvACT (left), Euclid (center), and their combination (right) for model 2. The color in each cell indicates the correlation between two model parameters, ranging from 0 (completely independent) to $\pm 1$ [completely (anti)correlated].

Figure 9

Fisher forecast contours for model 3. The convention used to denote the various cases is described in Fig. 5. See also Table 5 for numerical values.

Figure 10

Correlation matrix computed according to Eq. (18) for AdvACT (left), Euclid (center), and their combination (right) for model 3. The color in each cell indicates the correlation between two model parameters, ranging from 0 (completely independent) to $\pm 1$ [completely (anti)correlated].