Gravitational waves in warped compactifications

David Andriot,Dimitrios Tsimpis

doi:10.1007/jhep06(2020)100

Abstract

We study gravitational waves propagating on a warped Minkowski space-time with D − 4 compact extra dimensions. While Kaluza-Klein scales are typically too high for any current detection, we analyse how the warp factor changes the Kaluza-Klein spectrum of gravitational waves. To that end we provide a complete and explicit expression for the warp factor, as well as the Green’s function, on a d-dimensional torus. This expression differs from that of braneworld models and should find further uses in string compactifications. We then evaluate the Kaluza-Klein spectrum of gravitational waves. Our preliminary numerical results indicate not only a deviation from the standard toroidal spectrum, but also that the first masses get lowered due to the warp factor.

Highlights

Space-time, e.g. Minkowski, parameterized by xμ, together with D − 4 extra dimensions parameterized by yp, with metric ds2D = e2A(y) gμν dxμdxν + gpqdypdyq
We study gravitational waves propagating on a warped Minkowski space-time with D − 4 compact extra dimensions
In standard models, the Kaluza-Klein 4d gravitational waves have a mass or frequency too high to be detected with current instruments: the observational upper bound of 10−4 m on the size of an extra dimension leads to a frequency 108 times bigger than the LIGO sensitivity bound [8, 16]

Summary

Kaluza-Klein gravitational waves and p-brane backgrounds

We first introduce four-dimensional Kaluza-Klein gravitational waves on a warped Minkowski background with extra dimensions. We identify the eigenfunction equation relevant to determine their spectrum. We present the p-brane solutions that will serve as the background. We consider non-compact or compact extra dimensions, and discuss the related definitions of the warp factor. We first give them in a D = 10 string context, and more generally in arbitrary D dimensions. We rewrite the eigenfunction (spectrum) equation on such backgrounds with toroidal extra dimensions

Spectrum for a warped background

General D and gravitational wave background

Generalized Green’s functions and the warp factor

Generalized Green’s functions

Normalisation of H: the constant piece

Kaluza-Klein spectrum of gravitational waves

Stringy background: a type IIB example

Summary and discussion

A Study of the generalized Green’s function

Behaviour close to the source