The CWKB approach to non-reflecting potential and cosmological implications

TL;DR

This paper uses the complex trajectory WKB method to analyze non-reflecting potentials, clarifies previous misconceptions, and explores implications for particle production and cosmology in different spacetime models.

Contribution

It introduces a detailed CWKB approach to non-reflecting potentials, emphasizing the role of repeated reflections and linking results to cosmological scenarios.

Findings

Repeated reflections are crucial for non-reflecting conditions.

CWKB results align with Bogolubov transformation techniques.

Implications for particle production in cosmological models.

Abstract

We discuss the method of calculating the reflection coefficient using complex trajectory WKB (CWKB) approximation. This enables us to give an interpretation of non-reflecting nature of the potential under certain conditions and clarify some points, reported incorrectly elsewhere [vs:ejp] for the potential $U(x)=-U_0cosh^2(x/a)$. We show that the repeated reflectios between the turning points are essential, which most authors overlooked, in obtaining the non-reflecting c ondition. We find that the considered repeated reflection paths are in conformity with Bogolubov transformation technique. We discuss the implications of the results when applied to the particle production scenario, considering $x$ as a time variable and also stress the cosmological implications of the result with reference to radiation domonated and de Sitter spacetime.