Interacting dark energy: Constraints and degeneracies

In standard cosmologies, dark energy (DE) interacts only gravitationally with dark matter (DM). There could be a nongravitational interaction in the dark sector, leading to changes in the effective DE equation of state, in the redshift dependence of the DM density and in structure formation. We use cosmic microwave background, baryon acoustic oscillation and supernova data to constrain a model where the energy transfer in the dark sector is proportional to the DE density. There are two subclasses, defined by the vanishing of momentum transfer either in the DM or the DE frame. We conduct a Markov-Chain Monte Carlo analysis to obtain best-fit parameters. The background evolution allows large interaction strengths, and the constraints from cosmic microwave background anisotropies are weak. The growth of DM density perturbations is much more sensitive to the interaction, and can deviate strongly from the standard case. However, the deviations are degenerate with galaxy bias and thus more difficult to constrain. Interestingly, the integrated Sachs-Wolfe signature is suppressed since the nonstandard background evolution can compensate for high growth rates. We also discuss the partial degeneracy between interacting DE and modified gravity, and how this can be broken.

Figure 1

CMB and total matter power spectra from the modified CAMB code for 3 $Q||u_c$ models with different values of $\Gamma$ but identical values of their remaining parameters (see $\Gamma w\mathrm{CDM}$ A, B, C in Table ).

Figure 2

Smoothed 68% and 95% contours of the marginalized probability distribution for IDE model with $Q||u_c$ (left) and $Q||u_x$(right) in the range of stability, $w>-1$ and $\Gamma \ge 0$. Crosses identify models chosen to be analyzed in more detail (see Table ).

Figure 3

CMB and total matter power spectra from the modified CAMB code for the WMAP7 $w\mathrm{CDM}$ best-fit values and the $\Gamma w\mathrm{CDM}$ 1a, 1b, 2a, 2b models chosen from the 95% confidence range for further analysis (see Table ). The best-fit values of standard cosmological parameters were found using CosmoMC. Models 1a, 1b have $\Gamma =0.4H_0$ and $Q||u_c$ while 2a, 2b have $\Gamma =0.7H_0$ and $Q||u_x$.

Figure 4

Left: Normalized growth rates for $\Lambda \mathrm{CDM}$ and the same best-fit models as in Fig. 3. Right: The same models but showing a normalized combination of $a^2{\overline{\rho }}_c{\delta }_c$ which is important for the ISW effect.

Figure 5

Deviations from $\Lambda \mathrm{CDM}$ of the effective Hubble parameter (left) and effective Newton constant for ${\delta }_c$ (right), for the same best-fit models as in Fig. 3.

Figure 6

Comparison with $\Lambda \mathrm{CDM}$ of the effective DE equation of state (left) and the DM density (right), for the same best-fit models as in Fig. 3.

Figure 7

68% and 95% contours of the marginalized probability distribution for the $Q||u_c$ model (left) and $Q||u_x$ model (right). The dashed lines cross at the position of $\Lambda \mathrm{CDM}$, the crosses indicate the best-fits in each case and the circles indicate the median samples. Note that some areas appear only due to smoothing of the distributions (see Fig. 9).

Figure 8

68% and 95% contours of the marginalized probability distribution in the ${\Omega }_m-w$ plane for the $Q||u_c$ model (left) and $Q||u_x$ model (right).

Figure 9

Distributions of accepted steps in the MCMC chains for the models with $Q||u_c$ (left) and $Q||u_x$ (right).