Degeneracy between the dark components resulting from the fact that gravity only measures the total energy-momentum tensor

Gravity probes only the total energy-momentum tensor, which leads to a perfect degeneracy for generalized dark energy models. Because of this degeneracy, ${\Omega }_m$ cannot be measured. We demonstrate this explicitly by showing that the combination of cosmic microwave background and supernova data is compatible with very large and very small values of ${\Omega }_m$ for a specific family of dark energy models. We also show that for the same reason interacting dark energy is always equivalent to a family of noninteracting models. We argue that it is better to face this degeneracy and to parametrize the actual observables.

Figure 1

We try to determine ${\Omega }_m$ with the SNLS 1 yr data and the $R_{0.35}$ constraint from the baryon acoustic oscillations measured by SDSS LRG, but using an equation of state that exhibits a degeneracy between dark matter and dark energy. We find that the background data cannot determine ${\Omega }_m$.

Figure 2

This figure shows that supernova and CMB data together cannot measure ${\Omega }_m$ for generalized dark energy models. The filled contours show 1 and $2\sigma$ limits for a model with $c_s^2=0$, while the open contours show the limits for an effective scalar field model. The lower limit on ${\Omega }_m$ is due to the baryons which we know to exist.