 Inflaton action in an expanding universe

ID: inflaton-action-in-an-expanding-universe

Codex  0 Created 2026-09-24 Updated 2026-10-03

For a canonical scalar field in a spatially flat expanding universe,

S [ϕ] = \int d^{3} x d t a^{3} [\frac{1}{2} \dot{ϕ}^{2} - \frac{c ^{2}}{2 a ^{2}} ∣\nabla ϕ ∣^{2} - V (ϕ)] .

\ddot{ϕ} + 3 H \dot{ϕ} - \frac{c ^{2}}{a ^{2}} \nabla^{2} ϕ + V^{'} (ϕ) = 0.

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