Gravitational waves as a probe of the extra dimension

Abstract

We consider the Einstein-Hilbert action without a cosmological constant in five dimensions and implement the Kaluza-Klein (KK) reduction by compactifying the fifth direction on a circle of small but finite radius. For a nonzero compactification radius, the four-dimensional spectrum contains massless and massive KK modes. For the massive KK modes, we retain four KK tensor modes and one KK scalar mode after gauge fixing. We treat those massive KK modes as stochastic sources of gravitational waves (GWs) with characteristic dependence 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 GWs.