 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/iii/paper-55/5/a/solution

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

Differentiate the scalar-field Friedmann equation on the expanding branch

H > 0

2 H \dot{H} = \frac{Φ ˙}{3 M _{Pl}^{2}} (V^{'} + \ddot{Φ}) .

V^{'} + \ddot{Φ} = - 3 H \dot{Φ}

. Canceling

H

yields

2 M_{Pl}^{2} \dot{H} = - \dot{Φ}^{2} .

Thus the Hubble parameter cannot increase for a canonical homogeneous scalar field. The mass scale here is the reduced Planck mass.

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