Inflaton φ rolling down V(φ) — slow-roll, de Sitter expansion a(t) ∝ e^(Ht)
During inflation, the inflaton field φ slowly rolls down V(φ) with φ̈ + 3Hφ̇ + V'(φ) = 0, where H² = V(φ)/(3M_Pl²). Slow-roll parameters ε = M_Pl²/2·(V'/V)² ≪ 1 and η = M_Pl²·V''/V set the CMB spectral tilt n_s ≈ 1 − 6ε + 2η. Planck 2018 measures n_s ≈ 0.965, favouring Starobinsky R² inflation.