 Scalar-field cosmology

A homogeneous canonical scalar field contributes energy density $\rho ={\dot{\phi }}^2/2+V$ and pressure $P={\dot{\phi }}^2/2-V$. When it is the only source in a spatially flat FLRW metric, the Friedmann equation is $3M_{\mathrm{Pl}}^2{H}^2=\rho$, and its evolution follows the scalar field equation of motion. Positive energy density implies $w\ge -1$ because $\rho +P={\dot{\phi }}^2\ge 0$, even if the scalar potential is negative.