Testing General Relativity Using Gravitational Waves: A Tutorial

Testing General Relativity Using Gravitational Waves: A Tutorial

Clifford Will Washington University, St. Louis Gravitational Wave Tests of Alternative Theories of Gravity in the Advanced Detector Era University of Wisconsin, Milwaukee, 26 May, 2010

Testing General Relativity Using Gravitational Waves: A Tutorial 

GW probe new sectors of the dynamics of a theory

 New phenomena can occur (negative energy flux, dipole radiation, v ≠1 propagation), even in theories that agree with GR at PN order  With compact objects as sources, additional effects can be present (violations of SEP, compositiondependent effects) 

Lessons of PPN formalism not obviously applicable



No obvious “parametrization” of GW  PPE templates (Yunes & Pretorius arXiv:0909.3328)  Mishra, Arun, Iyer & Sathyaprakash (arXiv:1005.0304)

 Must one plow through theory by theory?

Testing General Relativity Using Gravitational Waves: A Tutorial  Introduction  Propagation of gravitational waves: polarization  Propagation of gravitational waves: speed  Generation of gravitational waves: compact binaries  General relativity  Scalar-tensor gravity  Other alternative theories  Tests of alternative theories using matched filtering

University of Wisconsin, Milwaukee, 26 May, 2010

Propagation of Gravitational Waves: Polarization Invariant classification of Components of Riemann tensor

Re Ψ4

Φ2 2

Im Ψ4

Ψ2

Specific transformations under null rotations

Eardley et al, PRL 30,884, 1973 TEGP, 10.2

Re Ψ3

Im Ψ3

Measuring polarization with interferometers Wave propagation coordinates (z direction)

z

θ ψ Interferometer output

Beam pattern functions

x

φ

y

Measuring polarization with interferometers  How many interferometers are required to measure or bound all 6 modes?  How many if 5/6 are present (Ψ2 = 0)?  How many if 3/6 are present (Ψ2 = 0, Ψ3 = 0)?  What is gained by a 4th Asian/Southern Hemisphere IO?  Is the Wen-Schutz “redundancy veto” useful? See bibliography in Sec 6.2 of CBGRE

Testing General Relativity Using Gravitational Waves: A Tutorial  Introduction  Propagation of gravitational waves: polarization  Propagation of gravitational waves: speed  Generation of gravitational waves: compact binaries  General relativity  Scalar-tensor gravity  Other alternative theories  Tests of alternative theories using matched filtering

University of Wisconsin, Milwaukee, 26 May, 2010

Propagation of Gravitational Waves: Speed Why Speed could differ from “1”

massive graviton: v = 1 - (m /E ) g coupling to background fields: v = F(φ,K ,H gravity waves propagate off the brane 2 g

g

g

2

α

g

µν

αβ

)

Examples General relativity. For λ