of derivatives of the total pressure and total energy with respect to the scalar as $$M^{2}=\frac{3H\left(P_{x,\phi}+\rho_{x,\phi}\right)+\dot{\rho}_{x,\phi}}{\dot{\phi}}\,.$$ One may wonder whether it is possible to invert Eqs  in order to obtain $\rho_{\text{m}}$ as a function of the functions $h_{1-5}$. If this were possible, and if all the $h_{1-5}$ were observable, then one could measure $\Omega_{\text{m}0}$, contrary to our claim in the text. In a future paper we will discuss in detail the observability of the functions $h_{1-5}$ and we will show that in fact it is not possible to obtain $\Omega_{\text{m}0}$ this way. Here it will suffice to notice that $h_{1}$ is completely degenerate with $\Omega_{\text{m}0}$ (see Eq. ); it turns out that $\rho_{\text{m}}$ is proportional to $1/h_{1}$ and therefore the fact that $h_{1}$ can only be measured up to $\Omega_{\text{m}0}$ implies the same degeneracy in $\rho_{\text{m}}$.

[^1]: A consistent theory is understood here to be a theory free of ghost and other catastrophic instabilities that can in general occur in generalized gravity and dark energy models.

[^2]: This class of Lagrangians includes such theories as $f(R)$ gravity, despite their naively fourth-order equations of motion. This is because we can always introduce the a priori hidden scalar explicitly through a Legendre 