Gravitational waves in warped compactifications
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Springer
Received: November 21, Revised: March 2, Accepted: May 24, Published: June 16,
2019 2020 2020 2020
David Andriota,b and Dimitrios Tsimpisc a
Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, Austria b Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland c Institut de Physique des Deux Infinis de Lyon, Universit´e de Lyon, UCBL, UMR 5822, CNRS/IN2P3, 4 rue Enrico Fermi, 69622 Villeurbanne Cedex, France
E-mail: [email protected], [email protected] 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. Keywords: Classical Theories of Gravity, p-branes, Flux compactifications, Superstring Vacua ArXiv ePrint: 1911.01444
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)100
JHEP06(2020)100
Gravitational waves in warped compactifications
Contents 1
2 Kaluza-Klein gravitational waves and p-brane backgrounds 2.1 Spectrum for a warped background 2.2 p-branes in D = 10 2.3 General D and gravitational wave background
3 4 5 7
3 Generalized Green’s functions and the warp factor 3.1 Warmup: warp factor from dipoles with d = 3 3.2 Generalized Green’s functions 3.3 Normalisation of H: the constant piece
9 9 10 11
4 Kaluza-Klein spectrum of gravitational waves 4.1 Stringy background: a type IIB example 4.2 Standard Kaluza-Klein spectrum, deviation, and physical regime 4.3 Numerical evaluation of the spectrum for d = 1, 2, 3
15 16 17 19
5 Summary and discussion
25
A Study of the generalized Green’s function A.1 Behaviour close to the source A.2 The d = 2 case
28 28 31
B Alternative numerical method for the d = 1 spectrum
32
1
Introduction
The observation of gravitational waves of astrophysical origin by the LIGO and Virgo collaboration [1] has opened a new era where we have at hand an independent experimental device to scrutinize nature and test our theories. The prospects of gravitational wave observations are flourishing: much is expected from the advanced LIGO and Virgo, but also from the upcoming KAGRA, IndIGO, SKA, eLISA, as well as the awaited results of PTAs, BICEP3, etc. It is then legitimate to ask ourselves whether new fundamental physics can be probed through these observations [2–7]. Here, we are interested in the question of extra dimensions. Consider gravitational waves that ha
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