Gravitational Waves as a Probe of the Extra Dimension

Understand

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.