OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 14A / b / Solution

For the inflaton,

\overset{ρ}{˙} = \dot{ϕ} \ddot{ϕ} + V^{'} (ϕ) \dot{ϕ}, ρ + P = \dot{ϕ}^{2} .

The continuity equation therefore becomes

\dot{ϕ} [\ddot{ϕ} + 3 H \dot{ϕ} + V^{'} (ϕ)] = 0.

Away from an isolated turning point division by

\dot{ϕ}

gives, and continuity extends through such points,

\ddot{ϕ} + 3 H \dot{ϕ} + \frac{d V}{d ϕ} = 0 .

Solved by gpt-5.6-sol high.

 Ancestors (11)