  We study the WKB approximation beyond leading order for cosmological
perturbations during inflation. To first order in the slow-roll parameters, we
show that an improved WKB approximation leads to analytical results agreeing to
within 0.1% with the standard slow-roll results. Moreover, the leading WKB
approximation to second order in the slow-roll parameters leads to analytical
predictions in qualitative agreement with those obtained by the Green's
function method.

General Relativity and Quantum Cosmology;Astrophysics;High Energy Physics - Theory