= Homogeneous massive-scalar equation in an expanding universe
{c}
{title2=$\ddot\phi+3H\dot\phi+m^2\phi=0$}
A canonical spatially homogeneous field with $V=m^2\phi^2/2$ obeys $\ddot\phi+3H\dot\phi+m^2\phi=0$. The $3H\dot\phi$ term expresses dilution of field <momentum> by expansion. Conservation of its stress energy gives this equation wherever $\dot\phi\ne0$; the canonical field equation is needed to fix an identically stationary interval, while continuity extends a regular solution across isolated turning points.
Back to article page
