The superpotential method in cosmological inflation. (arXiv:1901.02892v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Adam_C/0/1/0/all/0/1">C. Adam</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Varela_D/0/1/0/all/0/1">D. Varela</a>
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. 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.
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. 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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