 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-3/14a/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

\frac{a ¨}{a} = - \frac{4 π G}{3 c ^{2}} (ρ + 3 P) .

ρ + 3 P = 2 \dot{ϕ}^{2} - 2 V (ϕ),

and hence

\frac{a ¨}{a} = \frac{8 π G}{3 c ^{2}} [V (ϕ) - \dot{ϕ}^{2}] .

An inflationary phase occurs precisely when potential energy dominates enough that

V (ϕ) > \dot{ϕ}^{2} .

 New to topics? Read the docs here!