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arXiv · 1901.02892

The superpotential method in cosmological inflation

C. Adam·D. Varela
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Abstract

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. It also allows for a power series expansion in the inflaton field which permits to estimate the radius of convergence of the slow-roll expansion. We consider several examples of single-field inflationary models to demonstrate the simplicity and usefulness of the method.

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C. Adam, D. Varela. 2019-01-09. The superpotential method in cosmological inflation. https://arxiv.org/abs/1901.02892

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