General Relativity: An Introduction for Physicists · Problem 16.6

Inflationary cosmology — Hobson, Efstathiou & Lasenby

Physics · inflation-condition-slow-roll

Problem

Show that, in general, R¨=R(H˙+H2).\ddot{R} = R(\dot{H} + H^2). Show that H˙>0\dot{H} > 0 only if p<−ρp < -\rho, which is forbidden by the weak energy condition (see Exercise 8.8). Hence show that, for inflation to occur, one requires −H˙H2<1,-\frac{\dot{H}}{H^2} < 1, and thus that the first slow-roll parameter must obey ϵ<1\epsilon < 1.

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