Conformal density of a canonical scalar field
= Conformal density of a canonical scalar field
{title2=$T_{00}=a^2\rho$}
For $ds^2=a^2(d\tau^2-d\mathbf x^2)$ and a homogeneous canonical scalar, $\rho=\phi'^2/(2a^2)+V$ is the physical density, whereas $T_{00}=a^2\rho$. At $w=-1/3$, the kinetic and potential energies are $K=\rho/3$ and $V=2\rho/3$, so $\phi'^2=2a^2\rho/3=2T_{00}/3$. A single power of $\phi'$ cannot replace the square in this energy identity.
// Target: cosmology.bigb