GWTC-4.0: Tests of General Relativity. II. Parameterized Tests

Abstract

In this second of three papers on tests of general relativity (GR) applied to the compact binary coalescence signals in the fourth Gravitational-Wave Transient Catalog (GWTC-4.0), we present the results of the parameterized tests of GR and constraints on line-of-sight acceleration. We include events up to and including the first part of the fourth observing run (O4a) of the LIGO Virgo KAGRA detectors. As in the other two papers in this series, we restrict our analysis to the 42 confident signals, measured by at least two detectors, that have false alarm rates $\le 10^{-3} \mathrm{yr}^{-1}$ from O4a, in addition to the 49 such events from previous observing runs. This paper focuses on the eight tests that constrain parameterized deviations from the expected GR (or unaccelerated) values. These include modifications of post-Newtonian (PN) parameters, spin-induced quadrupole moments different from those of a binary black hole, and possible dispersive or birefringent propagation effects. Overall, we find no evidence for physics beyond GR, for spin-induced quadrupole moments different from those of a Kerr black hole in GR, or for line of sight acceleration, with more than 90% of the events including the null result (no deviation) within their 90% credible intervals. We discuss possible systematics affecting the other events and tests, even though they are statistically not surprising, given noise. We improve the bounds on deviations from the GR PN coefficients by factors of 1.2-5.5 and provide illustrative translations to constraints on some modified theories. Also, we update the bound on the mass of the graviton, at 90% credibility, to $m_g \leq 1.92\times 10^{-23} \mathrm{eV}/c^2$. Thus, we see that GR holds, and many of the bounds on possible deviations derived from our events are the best to date.

Figures (16)

• Figure 1: Results for the magnitudes of the inspiral deviation coefficients (from $-1$PN to $3.5$PN) in terms of 90% upper limits, compared with previous combined results from GWTC-2.0 LIGOScientific:2020tif and GWTC-3.0 LIGOScientific:2021sio, as appropriate. The horizontal stripes mark the results from individual events obtained with the SEOBNRv5HM_ROM waveform model using the FTI analysis. Marginalizing over all results from O4a (GWTC-3.0), while assuming that all events share the same values for the violation coefficients, results in the filled (unfilled) red diamonds for the SEOBNRv5HM_ROM waveform model. These bounds cannot be directly compared due to changes in the tapering frequency and waveform model used in the analysis. Marginalizing over all results from GWTC-4.0 (GWTC-2.0) for the IMRPhenomXPHM (IMRPhenomPv2) waveform model using the TIGER analysis results in the filled (unfilled) blue squares. The dark and light orange stripes highlight BBH GW230627_015337GW230518_125908GW230518_125908GW230529_181500GW230529_181500GW230531_141100GW230531_141100GW230601_224134GW230601_224134GW230603_174756GW230603_174756GW230605_065343GW230605_065343GW230606_004305GW230606_004305GW230606_024545GW230606_024545GW230608_205047GW230608_205047GW230609_010824GW230609_010824GW230609_064958GW230609_064958GW230615_160825GW230615_160825GW230618_102550GW230618_102550GW230624_113103GW230624_113103GW230624_214944GW230624_214944GW230625_211655GW230625_211655GW230627_015337GW230627_015337GW230628_231200GW230628_231200GW230630_070659GW230630_070659GW230630_125806GW230630_125806GW230630_234532GW230630_234532GW230702_162025GW230702_162025GW230702_185453GW230702_185453GW230704_021211GW230704_021211GW230704_212616GW230704_212616GW230706_104333GW230706_104333GW230707_124047GW230707_124047GW230708_053705GW230708_053705GW230708_071859GW230708_071859GW230708_230935GW230708_230935GW230709_063445GW230709_063445GW230709_122727GW230709_122727GW230712_090405GW230712_090405GW230717_102139GW230717_102139GW230721_222634GW230721_222634GW230723_084820GW230723_084820GW230723_101834GW230723_101834GW230726_002940GW230726_002940GW230728_083628GW230728_083628GW230729_082317GW230729_082317GW230731_215307GW230731_215307GW230803_033412GW230803_033412GW230805_034249GW230805_034249GW230806_204041GW230806_204041GW230807_205045GW230807_205045GW230811_032116GW230811_032116GW230814_061920GW230814_061920GW230814_230901GW230814_230901GW230817_212349GW230817_212349GW230819_171910GW230819_171910GW230820_212515GW230820_212515GW230822_230337GW230822_230337GW230823_142524GW230823_142524GW230824_033047GW230824_033047GW230824_135331GW230824_135331GW230825_041334GW230825_041334GW230830_064744GW230830_064744GW230831_015414GW230831_015414GW230831_134621GW230831_134621GW230902_122814GW230902_122814GW230902_172430GW230902_172430GW230902_224555GW230902_224555GW230904_051013GW230904_051013GW230904_152545GW230904_152545GW230911_195324GW230911_195324GW230914_111401GW230914_111401GW230919_215712GW230919_215712GW230920_064709GW230920_064709GW230920_071124GW230920_071124GW230922_020344GW230922_020344GW230922_040658GW230922_040658GW230924_124453GW230924_124453GW230925_143957GW230925_143957GW230927_043729GW230927_043729GW230927_153832GW230927_153832GW230928_215827GW230928_215827GW230930_110730GW230930_110730GW231001_140220GW231001_140220GW231002_143916GW231002_143916GW231004_232346GW231004_232346GW231005_021030GW231005_021030GW231005_091549GW231005_091549GW231005_144455GW231005_144455GW231008_142521GW231008_142521GW231013_135504GW231013_135504GW231014_040532GW231014_040532GW231018_233037GW231018_233037GW231020_142947GW231020_142947GW231026_130704GW231026_130704GW231028_153006GW231028_153006GW231029_111508GW231029_111508GW231102_052214GW231102_052214GW231102_071736GW231102_071736GW231102_232433GW231102_232433GW231104_133418GW231104_133418GW231108_125142GW231108_125142GW231110_040320GW231110_040320GW231113_122623GW231113_122623GW231113_150041GW231113_150041GW231113_200417GW231113_200417GW231114_043211GW231114_043211GW231118_005626GW231118_005626GW231118_071402GW231118_071402GW231118_090602GW231118_090602GW231119_075248GW231119_075248GW231120_022103GW231120_022103GW231123_135430GW231123_135430GW231126_010928GW231126_010928GW231127_165300GW231127_165300GW231129_081745GW231129_081745GW231204_090648GW231204_090648GW231206_010629GW231206_010629GW231206_233134GW231206_233134GW231206_233901GW231206_233901GW231213_111417GW231213_111417GW231220_173406GW231220_173406GW231221_135041GW231221_135041GW231223_032836GW231223_032836GW231223_075055GW231223_075055GW231223_202619GW231223_202619GW231224_024321GW231224_024321GW231226_101520GW231226_101520GW231230_170116GW231230_170116GW231231_120147GW231231_120147GW231231_154016GW231231_154016GW240104_164932GW240104_164932GW240105_151143GW240105_151143GW240107_013215GW240107_013215GW240109_050431GW240109_050431[???] and NSBH GW230518_125908GW230518_125908GW230518_125908GW230529_181500GW230529_181500GW230531_141100GW230531_141100GW230601_224134GW230601_224134GW230603_174756GW230603_174756GW230605_065343GW230605_065343GW230606_004305GW230606_004305GW230606_024545GW230606_024545GW230608_205047GW230608_205047GW230609_010824GW230609_010824GW230609_064958GW230609_064958GW230615_160825GW230615_160825GW230618_102550GW230618_102550GW230624_113103GW230624_113103GW230624_214944GW230624_214944GW230625_211655GW230625_211655GW230627_015337GW230627_015337GW230628_231200GW230628_231200GW230630_070659GW230630_070659GW230630_125806GW230630_125806GW230630_234532GW230630_234532GW230702_162025GW230702_162025GW230702_185453GW230702_185453GW230704_021211GW230704_021211GW230704_212616GW230704_212616GW230706_104333GW230706_104333GW230707_124047GW230707_124047GW230708_053705GW230708_053705GW230708_071859GW230708_071859GW230708_230935GW230708_230935GW230709_063445GW230709_063445GW230709_122727GW230709_122727GW230712_090405GW230712_090405GW230717_102139GW230717_102139GW230721_222634GW230721_222634GW230723_084820GW230723_084820GW230723_101834GW230723_101834GW230726_002940GW230726_002940GW230728_083628GW230728_083628GW230729_082317GW230729_082317GW230731_215307GW230731_215307GW230803_033412GW230803_033412GW230805_034249GW230805_034249GW230806_204041GW230806_204041GW230807_205045GW230807_205045GW230811_032116GW230811_032116GW230814_061920GW230814_061920GW230814_230901GW230814_230901GW230817_212349GW230817_212349GW230819_171910GW230819_171910GW230820_212515GW230820_212515GW230822_230337GW230822_230337GW230823_142524GW230823_142524GW230824_033047GW230824_033047GW230824_135331GW230824_135331GW230825_041334GW230825_041334GW230830_064744GW230830_064744GW230831_015414GW230831_015414GW230831_134621GW230831_134621GW230902_122814GW230902_122814GW230902_172430GW230902_172430GW230902_224555GW230902_224555GW230904_051013GW230904_051013GW230904_152545GW230904_152545GW230911_195324GW230911_195324GW230914_111401GW230914_111401GW230919_215712GW230919_215712GW230920_064709GW230920_064709GW230920_071124GW230920_071124GW230922_020344GW230922_020344GW230922_040658GW230922_040658GW230924_124453GW230924_124453GW230925_143957GW230925_143957GW230927_043729GW230927_043729GW230927_153832GW230927_153832GW230928_215827GW230928_215827GW230930_110730GW230930_110730GW231001_140220GW231001_140220GW231002_143916GW231002_143916GW231004_232346GW231004_232346GW231005_021030GW231005_021030GW231005_091549GW231005_091549GW231005_144455GW231005_144455GW231008_142521GW231008_142521GW231013_135504GW231013_135504GW231014_040532GW231014_040532GW231018_233037GW231018_233037GW231020_142947GW231020_142947GW231026_130704GW231026_130704GW231028_153006GW231028_153006GW231029_111508GW231029_111508GW231102_052214GW231102_052214GW231102_071736GW231102_071736GW231102_232433GW231102_232433GW231104_133418GW231104_133418GW231108_125142GW231108_125142GW231110_040320GW231110_040320GW231113_122623GW231113_122623GW231113_150041GW231113_150041GW231113_200417GW231113_200417GW231114_043211GW231114_043211GW231118_005626GW231118_005626GW231118_071402GW231118_071402GW231118_090602GW231118_090602GW231119_075248GW231119_075248GW231120_022103GW231120_022103GW231123_135430GW231123_135430GW231126_010928GW231126_010928GW231127_165300GW231127_165300GW231129_081745GW231129_081745GW231204_090648GW231204_090648GW231206_010629GW231206_010629GW231206_233134GW231206_233134GW231206_233901GW231206_233901GW231213_111417GW231213_111417GW231220_173406GW231220_173406GW231221_135041GW231221_135041GW231223_032836GW231223_032836GW231223_075055GW231223_075055GW231223_202619GW231223_202619GW231224_024321GW231224_024321GW231226_101520GW231226_101520GW231230_170116GW231230_170116GW231231_120147GW231231_120147GW231231_154016GW231231_154016GW240104_164932GW240104_164932GW240105_151143GW240105_151143GW240107_013215GW240107_013215GW240109_050431GW240109_050431[???], respectively, when they give the best individual event constraints on the inspiral parameters. The green circles show the bounds obtained with BNS GW170817 LIGOScientific:2018dkp and NSBH GW230529GW230529GW230529_181500GW230518_125908GW230518GW230529_181500GW230529GW230531_141100GW230531GW230601_224134GW230601GW230603_174756GW230603GW230605_065343GW230605GW230606_004305GW230606_00GW230606_024545GW230606_02GW230608_205047GW230608GW230609_010824GW230609_01GW230609_064958GW230609_06GW230615_160825GW230615GW230618_102550GW230618GW230624_113103GW230624_11GW230624_214944GW230624_21GW230625_211655GW230625GW230627_015337GW230627GW230628_231200GW230628GW230630_070659GW230630_07GW230630_125806GW230630_12GW230630_234532GW230630_23GW230702_162025GW230702_16GW230702_185453GW230702_18GW230704_021211GW230704_02GW230704_212616GW230704_21GW230706_104333GW230706GW230707_124047GW230707GW230708_053705GW230708_05GW230708_071859GW230708_07GW230708_230935GW230708_23GW230709_063445GW230709_06GW230709_122727GW230709_12GW230712_090405GW230712GW230717_102139GW230717GW230721_222634GW230721GW230723_084820GW230723_08GW230723_101834GW230723_10GW230726_002940GW230726GW230728_083628GW230728GW230729_082317GW230729GW230731_215307GW230731GW230803_033412GW230803GW230805_034249GW230805GW230806_204041GW230806GW230807_205045GW230807GW230811_032116GW230811GW230814_061920GW230814_06GW230814_230901GW230814_23GW230817_212349GW230817GW230819_171910GW230819GW230820_212515GW230820GW230822_230337GW230822GW230823_142524GW230823GW230824_033047GW230824_03GW230824_135331GW230824_13GW230825_041334GW230825GW230830_064744GW230830GW230831_015414GW230831_01GW230831_134621GW230831_13GW230902_122814GW230902_12GW230902_172430GW230902_17GW230902_224555GW230902_22GW230904_051013GW230904_05GW230904_152545GW230904_15GW230911_195324GW230911GW230914_111401GW230914GW230919_215712GW230919GW230920_064709GW230920_06GW230920_071124GW230920_07GW230922_020344GW230922_02GW230922_040658GW230922_04GW230924_124453GW230924GW230925_143957GW230925GW230927_043729GW230927_04GW230927_153832GW230927_15GW230928_215827GW230928GW230930_110730GW230930GW231001_140220GW231001GW231002_143916GW231002GW231004_232346GW231004GW231005_021030GW231005_02GW231005_091549GW231005_09GW231005_144455GW231005_14GW231008_142521GW231008GW231013_135504GW231013GW231014_040532GW231014GW231018_233037GW231018GW231020_142947GW231020GW231026_130704GW231026GW231028_153006GW231028GW231029_111508GW231029GW231102_052214GW231102_05GW231102_071736GW231102_07GW231102_232433GW231102_23GW231104_133418GW231104GW231108_125142GW231108GW231110_040320GW231110GW231113_122623GW231113_12GW231113_150041GW231113_15GW231113_200417GW231113_20GW231114_043211GW231114GW231118_005626GW231118_00GW231118_071402GW231118_07GW231118_090602GW231118_09GW231119_075248GW231119GW231120_022103GW231120GW231123_135430GW231123GW231126_010928GW231126GW231127_165300GW231127GW231129_081745GW231129GW231204_090648GW231204GW231206_010629GW231206_01GW231206_233134GW231206_2331GW231206_233901GW231206_2339GW231213_111417GW231213GW231220_173406GW231220GW231221_135041GW231221GW231223_032836GW231223_03GW231223_075055GW231223_07GW231223_202619GW231223_20GW231224_024321GW231224GW231226_101520GW231226GW231230_170116GW231230GW231231_120147GW231231_12GW231231_154016GW231231_15GW240104_164932GW240104GW240105_151143GW240105GW240107_013215GW240107GW240109_050431GW240109GW230814otherGW230814_061920GW230518_125908GW230518GW230529_181500GW230529GW230531_141100GW230531GW230601_224134GW230601GW230603_174756GW230603GW230605_065343GW230605GW230606_004305GW230606_00GW230606_024545GW230606_02GW230608_205047GW230608GW230609_010824GW230609_01GW230609_064958GW230609_06GW230615_160825GW230615GW230618_102550GW230618GW230624_113103GW230624_11GW230624_214944GW230624_21GW230625_211655GW230625GW230627_015337GW230627GW230628_231200GW230628GW230630_070659GW230630_07GW230630_125806GW230630_12GW230630_234532GW230630_23GW230702_162025GW230702_16GW230702_185453GW230702_18GW230704_021211GW230704_02GW230704_212616GW230704_21GW230706_104333GW230706GW230707_124047GW230707GW230708_053705GW230708_05GW230708_071859GW230708_07GW230708_230935GW230708_23GW230709_063445GW230709_06GW230709_122727GW230709_12GW230712_090405GW230712GW230717_102139GW230717GW230721_222634GW230721GW230723_084820GW230723_08GW230723_101834GW230723_10GW230726_002940GW230726GW230728_083628GW230728GW230729_082317GW230729GW230731_215307GW230731GW230803_033412GW230803GW230805_034249GW230805GW230806_204041GW230806GW230807_205045GW230807GW230811_032116GW230811GW230814_061920GW230814_06GW230814_230901GW230814_23GW230817_212349GW230817GW230819_171910GW230819GW230820_212515GW230820GW230822_230337GW230822GW230823_142524GW230823GW230824_033047GW230824_03GW230824_135331GW230824_13GW230825_041334GW230825GW230830_064744GW230830GW230831_015414GW230831_01GW230831_134621GW230831_13GW230902_122814GW230902_12GW230902_172430GW230902_17GW230902_224555GW230902_22GW230904_051013GW230904_05GW230904_152545GW230904_15GW230911_195324GW230911GW230914_111401GW230914GW230919_215712GW230919GW230920_064709GW230920_06GW230920_071124GW230920_07GW230922_020344GW230922_02GW230922_040658GW230922_04GW230924_124453GW230924GW230925_143957GW230925GW230927_043729GW230927_04GW230927_153832GW230927_15GW230928_215827GW230928GW230930_110730GW230930GW231001_140220GW231001GW231002_143916GW231002GW231004_232346GW231004GW231005_021030GW231005_02GW231005_091549GW231005_09GW231005_144455GW231005_14GW231008_142521GW231008GW231013_135504GW231013GW231014_040532GW231014GW231018_233037GW231018GW231020_142947GW231020GW231026_130704GW231026GW231028_153006GW231028GW231029_111508GW231029GW231102_052214GW231102_05GW231102_071736GW231102_07GW231102_232433GW231102_23GW231104_133418GW231104GW231108_125142GW231108GW231110_040320GW231110GW231113_122623GW231113_12GW231113_150041GW231113_15GW231113_200417GW231113_20GW231114_043211GW231114GW231118_005626GW231118_00GW231118_071402GW231118_07GW231118_090602GW231118_09GW231119_075248GW231119GW231120_022103GW231120GW231123_135430GW231123GW231126_010928GW231126GW231127_165300GW231127GW231129_081745GW231129GW231204_090648GW231204GW231206_010629GW231206_01GW231206_233134GW231206_2331GW231206_233901GW231206_2339GW231213_111417GW231213GW231220_173406GW231220GW231221_135041GW231221GW231223_032836GW231223_03GW231223_075055GW231223_07GW231223_202619GW231223_20GW231224_024321GW231224GW231226_101520GW231226GW231230_170116GW231230GW231231_120147GW231231_12GW231231_154016GW231231_15GW240104_164932GW240104GW240105_151143GW240105GW240107_013215GW240107GW240109_050431GW240109GW230814singleGW230814_230901GW230518_125908GW230518GW230529_181500GW230529GW230531_141100GW230531GW230601_224134GW230601GW230603_174756GW230603GW230605_065343GW230605GW230606_004305GW230606_00GW230606_024545GW230606_02GW230608_205047GW230608GW230609_010824GW230609_01GW230609_064958GW230609_06GW230615_160825GW230615GW230618_102550GW230618GW230624_113103GW230624_11GW230624_214944GW230624_21GW230625_211655GW230625GW230627_015337GW230627GW230628_231200GW230628GW230630_070659GW230630_07GW230630_125806GW230630_12GW230630_234532GW230630_23GW230702_162025GW230702_16GW230702_185453GW230702_18GW230704_021211GW230704_02GW230704_212616GW230704_21GW230706_104333GW230706GW230707_124047GW230707GW230708_053705GW230708_05GW230708_071859GW230708_07GW230708_230935GW230708_23GW230709_063445GW230709_06GW230709_122727GW230709_12GW230712_090405GW230712GW230717_102139GW230717GW230721_222634GW230721GW230723_084820GW230723_08GW230723_101834GW230723_10GW230726_002940GW230726GW230728_083628GW230728GW230729_082317GW230729GW230731_215307GW230731GW230803_033412GW230803GW230805_034249GW230805GW230806_204041GW230806GW230807_205045GW230807GW230811_032116GW230811GW230814_061920GW230814_06GW230814_230901GW230814_23GW230817_212349GW230817GW230819_171910GW230819GW230820_212515GW230820GW230822_230337GW230822GW230823_142524GW230823GW230824_033047GW230824_03GW230824_135331GW230824_13GW230825_041334GW230825GW230830_064744GW230830GW230831_015414GW230831_01GW230831_134621GW230831_13GW230902_122814GW230902_12GW230902_172430GW230902_17GW230902_224555GW230902_22GW230904_051013GW230904_05GW230904_152545GW230904_15GW230911_195324GW230911GW230914_111401GW230914GW230919_215712GW230919GW230920_064709GW230920_06GW230920_071124GW230920_07GW230922_020344GW230922_02GW230922_040658GW230922_04GW230924_124453GW230924GW230925_143957GW230925GW230927_043729GW230927_04GW230927_153832GW230927_15GW230928_215827GW230928GW230930_110730GW230930GW231001_140220GW231001GW231002_143916GW231002GW231004_232346GW231004GW231005_021030GW231005_02GW231005_091549GW231005_09GW231005_144455GW231005_14GW231008_142521GW231008GW231013_135504GW231013GW231014_040532GW231014GW231018_233037GW231018GW231020_142947GW231020GW231026_130704GW231026GW231028_153006GW231028GW231029_111508GW231029GW231102_052214GW231102_05GW231102_071736GW231102_07GW231102_232433GW231102_23GW231104_133418GW231104GW231108_125142GW231108GW231110_040320GW231110GW231113_122623GW231113_12GW231113_150041GW231113_15GW231113_200417GW231113_20GW231114_043211GW231114GW231118_005626GW231118_00GW231118_071402GW231118_07GW231118_090602GW231118_09GW231119_075248GW231119GW231120_022103GW231120GW231123_135430GW231123GW231126_010928GW231126GW231127_165300GW231127GW231129_081745GW231129GW231204_090648GW231204GW231206_010629GW231206_01GW231206_233134GW231206_2331GW231206_233901GW231206_2339GW231213_111417GW231213GW231220_173406GW231220GW231221_135041GW231221GW231223_032836GW231223_03GW231223_075055GW231223_07GW231223_202619GW231223_20GW231224_024321GW231224GW231226_101520GW231226GW231230_170116GW231230GW231231_120147GW231231_12GW231231_154016GW231231_15GW240104_164932GW240104GW240105_151143GW240105GW240107_013215GW240107GW240109_050431GW240109GW231123GW231123_135430GW230518_125908GW230518GW230529_181500GW230529GW230531_141100GW230531GW230601_224134GW230601GW230603_174756GW230603GW230605_065343GW230605GW230606_004305GW230606_00GW230606_024545GW230606_02GW230608_205047GW230608GW230609_010824GW230609_01GW230609_064958GW230609_06GW230615_160825GW230615GW230618_102550GW230618GW230624_113103GW230624_11GW230624_214944GW230624_21GW230625_211655GW230625GW230627_015337GW230627GW230628_231200GW230628GW230630_070659GW230630_07GW230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Sanger:2024axs when competitive; those two events are not included in the combined bounds. The blue upside-down triangles indicate bounds obtained with the double pulsar J0737$-$3039 Kramer:2021jcw when competitive. Starting from 1.5PN the pulsar bounds get much worse than the bounds from GW and are therefore not shown.
• Figure 2: Results for the magnitudes of the post-inspiral deviation coefficients using TIGER. The horizontal stripes mark the results from individual events obtained with the IMRPhenomXPHM waveform model. Marginalizing over all analyzed events in GWTC-4.0, while assuming that all events share the same values for the violation coefficients, results in the blue squares.
• Figure 3: The constraints on the GR violation parameters in the inspiral, marginalized over all analyzed events, in orange on the left for the SEOBNRv5HM_ROM waveform model (FTI analysis) and in blue on the right for the IMRPhenomXPHM waveform model (TIGER analysis). Consistency of GR corresponds to vanishing parameters (the horizontal line). Assuming independent violation parameters between events, using a hierarchical analysis, results in the filled probability densities. Instead, assuming that the violation parameters share the same values between different events leads to the unfilled distributions.
• Figure 4: Inferred hyperparameters $\mu$ and $\sigma$ of the GR violation coefficients. For each testing coefficient, the contours mark 90% credible regions. The inspiral parameters for the two waveform models SEOBNRv5HM_ROM (using the FTI analysis) and IMRPhenomXPHM (along with IMRPhenomPv2; using the TIGER analysis) are considered in the top and middle panel respectively. The bottom panel shows the post-inspiral parameters for the IMRPhenomXPHM waveform model. All contours enclose the GR expectation of $\mu=\sigma=0$; the $\delta\hat{\varphi}_{-2}$ values are rescaled $\times 500$ to improve visibility.
• Figure 5: The constraints on the GR violation parameters in the post-inspiral using TIGER, marginalized over all analyzed events in GWTC-4.0. Consistency of GR corresponds to vanishing parameters (the horizontal line). Assuming independent violation parameters between events, using a hierarchical analysis, results in the colored probability densities. Instead, assuming that the violation parameters share the same values between different events leads to the unfilled distributions.