General Relativity: An Introduction for Physicists · Problem 16.4

Inflationary cosmology — Hobson, Efstathiou & Lasenby

Physics · scalar-field-equation-of-motion

Problem

Show that the equation of motion for a scalar field with potential

V(\phi)

\ddot{\phi} + 3H\dot{\phi} + \frac{dV}{d\phi} = 0.

Hence find the general solution for a free scalar field

\phi

, for which

V = \tfrac{1}{2}m^2\phi^2

, in the case where

H

is approximately constant.