 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/iii/paper-53/1/ii/b/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

For

t > 0

\overset{a}{˙} = n t^{n - 1} > 0

and

\overset{a}{¨} = n (n - 1) t^{n - 2}

. Consequently inflation occurs exactly when $n > 1$ . The case

n = 1

is coasting, and

0 < n < 1

ϵ_{H} = - \dot{H} / H^{2} = 1/ n

, giving the same acceleration criterion

ϵ_{H} < 1

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