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#### Investigating the relation between gravitational wave tests of general relativity

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##### Citation

Johnson-McDaniel, N. K., Ghosh, A., Ghonge, S., Saleem, M., Krishnendu, N. V., & Clark, J. A. (2022).
Investigating the relation between gravitational wave tests of general relativity.* Physical Review
D,* *105*: 044020. doi:10.1103/PhysRevD.105.044020.

Cite as: https://hdl.handle.net/21.11116/0000-0009-3F77-C

##### Abstract

Gravitational wave observations of compact binary coalescences provide

precision probes of strong-field gravity. There is thus now a standard set of

null tests of general relativity (GR) applied to LIGO-Virgo detections and many

more such tests proposed. However, the relation between all these tests is not

yet well understood. We start to investigate this by applying a set of standard

tests to simulated observations of binary black holes in GR and with

phenomenological deviations from GR. The phenomenological deviations include

self-consistent modifications to the energy flux in an effective-one-body (EOB)

model, the deviations used in the second post-Newtonian (2PN) TIGER and FTA

parameterized tests, and the dispersive propagation due to a massive graviton.

We consider four types of tests: residuals, inspiral-merger-ringdown

consistency, parameterized (TIGER and FTA), and modified dispersion relation.

We also check the consistency of the unmodeled reconstruction of the waveforms

with the waveform recovered using GR templates. These tests are applied to

simulated observations similar to GW150914 with both large and small deviations

from GR and similar to GW170608 just with small deviations from GR. We find

that while very large deviations from GR are picked up with high significance

by almost all tests, more moderate deviations are picked up by only a few

tests, and some deviations are not recognized as GR violations by any test at

the moderate signal-to-noise ratios we consider. Moreover, the tests that

identify various deviations with high significance are not necessarily the

expected ones. We also find that the 2PN (1PN) TIGER and FTA tests recover much

smaller deviations than the true values in the modified EOB (massive graviton)

case. Additionally, we find that of the GR deviations we consider, the

residuals test is only able to detect extreme deviations from GR. (Abridged)

precision probes of strong-field gravity. There is thus now a standard set of

null tests of general relativity (GR) applied to LIGO-Virgo detections and many

more such tests proposed. However, the relation between all these tests is not

yet well understood. We start to investigate this by applying a set of standard

tests to simulated observations of binary black holes in GR and with

phenomenological deviations from GR. The phenomenological deviations include

self-consistent modifications to the energy flux in an effective-one-body (EOB)

model, the deviations used in the second post-Newtonian (2PN) TIGER and FTA

parameterized tests, and the dispersive propagation due to a massive graviton.

We consider four types of tests: residuals, inspiral-merger-ringdown

consistency, parameterized (TIGER and FTA), and modified dispersion relation.

We also check the consistency of the unmodeled reconstruction of the waveforms

with the waveform recovered using GR templates. These tests are applied to

simulated observations similar to GW150914 with both large and small deviations

from GR and similar to GW170608 just with small deviations from GR. We find

that while very large deviations from GR are picked up with high significance

by almost all tests, more moderate deviations are picked up by only a few

tests, and some deviations are not recognized as GR violations by any test at

the moderate signal-to-noise ratios we consider. Moreover, the tests that

identify various deviations with high significance are not necessarily the

expected ones. We also find that the 2PN (1PN) TIGER and FTA tests recover much

smaller deviations than the true values in the modified EOB (massive graviton)

case. Additionally, we find that of the GR deviations we consider, the

residuals test is only able to detect extreme deviations from GR. (Abridged)