# Gravitational Waves as a Probe of the Extra Dimension

## TL;DR

This paper investigates how gravitational waves can reveal the presence of extra dimensions by analyzing the spectrum of Kaluza-Klein modes resulting from a 5-dimensional Einstein-Hilbert action compactified on a circle.

## Contribution

It provides a theoretical framework for how massive KK modes from extra dimensions can generate observable gravitational wave signatures.

## Key findings

- Massive KK modes act as stochastic GW sources.
- Characteristic frequencies depend on the size of the extra dimension.
- Order estimations suggest potential detectability with current bounds.

## Abstract

We consider the Einstein-Hilbert action without cosmological constant in 5-dimensions and implement the Kaluza-Klein (KK) reduction by compactifying the fifth direction on a circle of small but finite radius. For non-zero compactification radius, the 4- dimensional spectrum contains massless and massive KK modes. For the massive KK modes, we retain four KK tensor and one KK scalar modes after a gauge fixing. We treat those massive KK modes as stochastic sources of gravitational wave (GW) with characteristic dependences of the frequencies on the size of the extra dimension. Using the observational bounds on the size of the extra dimension and on the characteristic strain, we make an order estimation on the frequencies and amplitudes of the massive KK modes that can contribute to the GW.