gravity, but the fact that $\Omega_{\text{m0}}$ is not an observable was not discussed there. The quantity $R$ contains the term $Gf\sigma_{8}$, also denoted as $f\sigma_{8}(z)$ in the literature [@Percival:2008sh]. This term is often considered to be a directly observable quantity, but, as we have argued, this is only true if one assumes a model for DE, or at least a parametrized form of $\delta_{\text{t},0}$; otherwise, the model-independent observable combination is $P_{3}=R'/R$. It is important to realize that even a perfect knowledge of $P_{3}$ does not imply knowledge of $f$ since the equation $f'/f+f=P_{3}(k,z)$ cannot be solved without the unknown $k$-dependent initial condition for $f$. Finally, notice that we did not need to assume Gaussian fluctuations nor isotropy of the power spectrum.

Measurements of galaxy peculiar velocities and their time derivative directly estimate $\Psi$ through the Euler equation, which would give the quantity $V=\Omega_{\text{m0}}YG\sigma_{8}\delta_{\text{t,0}}\,$. Then one can form the observable, $L/V=1+\eta$, which measures the anisotropic stress. This new observable is not independent since it can be written in terms of $E,P_{2},P_{3}$ (see Eq. ). Moreover, the estimation of $V$ requires a delicate subtraction of the peculiar redshift from the cosmological redshift by using distance indicators such as Cepheids and therefore a 