have $$q=\frac{1+3w}2\, ,$$ and the eigenvalues are $$\lambda_{k}=1+3w\, , \quad \lambda_{\Lambda}=3(1+w)\, , \quad
\lambda_{\lambda}=-3(1+w)\, , \quad \lambda_C = 3 w - 1 \, .$$

[**(2)**]{}  The Milne case, or $(\Omega_{\rho}, \Omega_{k},
\Omega_{\Lambda}, \Omega_{\lambda},\Omega_C) = (0,1,0,0,0)$. We have $$q=0\, ,$$ and the eigenvalues are $$\lambda_{\rho}=-(1+3w)\, , \quad \lambda_{\Lambda}=2\, , \quad
\lambda_{\lambda}=-2(2+3w)\, , \quad \lambda_C = - 2 \, .$$

[**(3)**]{}  The de Sitter case, or $(\Omega_{\rho}, \Omega_{k},
\Omega_{\Lambda}, \Omega_{\lambda}, \Omega_C) = (0,0,1,0,0)$. We have $$q=-1\, ,$$ and the eigenvalues are $$\lambda_{\rho}=-3(1+w)\, , \quad \lambda_{k}=-2\, , \quad
\lambda_{\lambda}=-6(1+w)\, , \quad \lambda_C = - 4 \, .$$

[**(4)**]{}  The case considered in [@BDEL], or $(\Omega_{\rho},
\Omega_{k}, \Omega_{\Lambda}, \Omega_{\lambda}, \Omega_C) = (0,0,0,1,0)$. We have $$q=2+3w\, ,$$ and the eigenvalues are $$\lambda_{\rho}=3(1+w)\, , \quad \lambda_{k}=2(2+3w)\, , \quad
\lambda_{\Lambda}=6(1+w)\, , \quad \lambda_C = 2 (1 + 3w) \, .$$

[**(5)**]{}  The dark-radiation case, or $(\Omega_{\rho}, \Omega_{k},
\Omega_{\Lambda}, \Omega_{\lambda}, \Omega_C) = (0,0,0,0,1)$. We have $$q = 1\, ,$$ and the eigenvalues are $$\lambda_{\rho} = 1 - 3w \, , \quad \lambda_{k} = 2\, , \quad \lambda_\Lambda =
4 \, , \quad \lambda_{\lambda} = - 2(1 + 3w) \, .$$

All these results for the case $m = 0$ were obtained in [@CS].

The case $m\neq 0$
------------------

