On the rest and flat limits of the scalar modes on the de Sitter spacetime

TL;DR

This paper redefines scalar mode functions on de Sitter spacetime to achieve natural frequency separation in rest frames and establishes criteria for phase factor choices, comparing results with existing literature.

Contribution

It introduces a new approach to define scalar modes with natural frequencies in de Sitter spacetime and sets criteria for phase factors, enhancing understanding of mode limits.

Findings

Mode functions are eigenfunctions of the energy operator in rest frames.

Criteria for phase factors ensure correct rest and flat limits.

Comparison with literature shows consistency and improvements.

Abstract

The scalar mode functions on the spatially flat FLRW chart of the de Sitter spacetime are redefined in order to obtain a natural frequencies separation in the special local charts where the momentum vanishes, called here (natural) rest frames. This can be done since in such frames the mode functions are eigenfunctions of the energy operator. Moreover, the most general criteria for choosing the suitable phase factors of the mode functions able to simultaneously determine the correct rest and flat limits are established. These results are compared to the different original choices from the literature. Pacs: 04.62.+v