General Relativity: An Introduction for Physicists · Problem 16.15

Inflationary cosmology — Hobson, Efstathiou & Lasenby

Physics · perturbed-einstein-equations-inflation

Problem

Use your answers to Exercises 16.13 and 16.14 to show that the perturbed Einstein field equations yield only the two equations

\dot{\Phi} + H\Phi = \frac{1}{2}\dot{\phi}_0\,\delta\phi,

\left(\dot{\phi}_0^2 + 2\vec{\nabla}^2\right)\Phi = \dot{\phi}_0^2\frac{d}{dt}\left(\frac{\delta\phi}{\dot{\phi}_0}\right).