For a spatially homogeneous canonical <scalar field>, spatial derivatives vanish. Reading the time and spatial components of its <energy-momentum tensor> in the comoving frame gives
$$
\boxed{\rho_\phi=\frac12\dot\phi^2+V(\phi)},
\qquad
\boxed{P_\phi=\frac12\dot\phi^2-V(\phi)}.
$$
Thus the kinetic term contributes equally to <energy density> and pressure, whereas the <scalar potential> contributes negative pressure.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 310 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-310/2/a/solution