The superpotential method in cosmological inflation

Understand

Scalar field cosmological inflation has a first integral relating the Hubble function and the lagrangian of the scalar field(s), which is known under the names of "Hamilton-Jacobi approach" or "superpotential equation".

• Here we exploit the simplicity of this superpotential equation and use it as an alternative but equivalent cosmological evolution equation during inflation, replacing the Friedman-Robertson-Walker (FRW) equations.
• It turns out that all inflationary observables can be calculated directly from its solution (the superpotential).
• Further, the superpotential equation allows for a simple and direct calculation of the slow-roll expansion to arbitrary order and, in many cases, for an exact determination of the slow-roll attractor.