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Inflaton action in an expanding universe

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)] .

The field Euler-Lagrange equation is

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

Table of contents 119 4
- Inflationary scalar Fourier mode Inflaton action in an expanding universe 97 3
  - Canonically rescaled de Sitter scalar mode Inflationary scalar Fourier mode 77 2
    - Bunch-Davies vacuum Canonically rescaled de Sitter scalar mode 61 1
      - Scale-invariant inflationary power spectrum Bunch-Davies vacuum 39

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