Cosmic Inflation — Slow-Roll Potential & Power Spectrum

Inflaton field rolling down V(φ). Slow-roll parameters ε,η determine primordial scalar/tensor power spectra P_s(k), P_t(k).

Inflaton potential V(φ) and field trajectory
Primordial power spectrum P(k) — scalar (yellow) & tensor (red)

Inflationary Model

ε=— η=— | n_s=— r=—
Slow-roll: ε = (M_Pl²/2)(V'/V)², η = M_Pl²(V''/V). Inflation: ε≪1. Spectral index: n_s = 1−6ε+2η. Tensor-to-scalar ratio: r = 16ε. CMB constraint: n_s ≈ 0.965, r < 0.036 (Planck 2018).