Paper detail

On exact solutions for quantum particles with spin S= 0, 1/2, 1 and de Sitter event horizon

Exact wave solutions for particles with spin 0, 1/2 and 1 in the static coordinates of the de Sitter space-time model are examined in detail. Firstly, for a scalar particle, two pairs of linearly independent solutions are specified explicitly: running and standing waves. A known algorithm for calculation of the reflection coefficient $R_{εj}$ on the background of the de Sitter space-time model is analyzed. It is shown that the determination of R_{εj} requires an additional constrain on quantum numbers ερ/ \hbar c >> j, where ρis a curvature radius. When taken into account of this condition, the R_{εj} vanishes identically. It is claimed that the calculation of the reflection coefficient R_{εj} is not required at all because there is no barrier in an effective potential curve on the background of the de Sitter space-time. The same conclusion holds for arbitrary particles with higher spins, it is demonstrated explicitly with the help of exact solutions for electromagnetic and Dirac fields.