Bouncing of gravitons emitted from the brane to the bulk back to the brane

TL;DR

This paper investigates the behavior of gravitons emitted from a brane into the bulk in a cosmological model with one extra dimension, showing that under certain conditions they can return to the brane during early cosmology.

Contribution

It provides a detailed analysis of graviton geodesics in two different cosmological models, identifying conditions for gravitons to return to the brane.

Findings

Gravitons can return to the brane during early cosmology.

Conditions for graviton return depend on the model approach.

Coordinate transformations relate different modeling approaches.

Abstract

Solutions of geodesic equations describing propagation of gravitons in the bulk are studied in a cosmological model with one extra dimension. Brane with matter is embedded in the bulk. It is shown that in the period of early cosmology gravitons emitted from the brane to the bulk under certain conditions can return back to the brane. The model is discussed in two alternative approaches: (i) brane with static metric moving in the AdS space, and (ii) brane located at a fixed position in extra dimension with non-static metric. Transformation of coordinates from the one picture to another is performed. In both approaches conditions for gravitons emitted to the bulk to come back to the brane are found.