GWTC-4.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation
This paper analyzes 142 gravitational-wave sources from the GWTC-4.0 catalog to jointly estimate the Hubble constant as 75.4−9.1+12.8 km s−1 Mpc−1 and constrain deviations from general relativity in gravitational-wave propagation, finding results consistent with standard cosmology.
Original authors: The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration, A. G. Abac, I. Abouelfettouh, F. Acernese, K. Ackley, C. Adamcewicz, S. Adhicary, D. Adhikari, N. Adhikari, R. X. Adhikari, V. K. Adkins, S. Afroz, A. Agapito, D. Agarwal, M. Agathos, N. Aggarwal, S. Aggarwal, O. D. Aguiar, I. -L. Ahrend, L. Aiello, A. Ain, P. Ajith, T. Akutsu, S. Albanesi, W. Ali, S. Al-Kershi, C. Alléné, A. Allocca, S. Al-Shammari, P. A. Altin, S. Alvarez-Lopez, W. Amar, O. Amarasinghe, A. Amato, F. Amicucci, C. Amra, A. Ananyeva, S. B. Anderson, W. G. Anderson, M. Andia, M. Ando, M. Andrés-Carcasona, T. Andrić, J. Anglin, S. Ansoldi, J. M. Antelis, S. Antier, M. Aoumi, E. Z. Appavuravther, S. Appert, S. K. Apple, K. Arai, A. Araya, M. C. Araya, M. Arca Sedda, J. S. Areeda, N. Aritomi, F. Armato, S. Armstrong, N. Arnaud, M. Arogeti, S. M. Aronson, K. G. Arun, G. Ashton, Y. Aso, L. Asprea, M. Assiduo, S. Assis de Souza Melo, S. M. Aston, P. Astone, F. Attadio, F. Aubin, K. AultONeal, G. Avallone, E. A. Avila, S. Babak, C. Badger, S. Bae, S. Bagnasco, L. Baiotti, R. Bajpai, T. Baka, A. M. Baker, K. A. Baker, T. Baker, G. Baldi, N. Baldicchi, M. Ball, G. Ballardin, S. W. Ballmer, S. Banagiri, B. Banerjee, D. Bankar, T. M. Baptiste, P. Baral, M. Baratti, J. C. Barayoga, B. C. Barish, D. Barker, N. Barman, P. Barneo, F. Barone, B. Barr, L. Barsotti, M. Barsuglia, D. Barta, A. M. Bartoletti, M. A. Barton, I. Bartos, A. Basalaev, R. Bassiri, A. Basti, M. Bawaj, P. Baxi, J. C. Bayley, A. C. Baylor, P. A. Baynard II, M. Bazzan, V. M. Bedakihale, F. Beirnaert, M. Bejger, D. Belardinelli, A. S. Bell, D. S. Bellie, L. Bellizzi, W. Benoit, I. Bentara, J. D. Bentley, M. Ben Yaala, S. Bera, F. Bergamin, B. K. Berger, S. Bernuzzi, M. Beroiz, C. P. L. Berry, D. Bersanetti, T. Bertheas, A. Bertolini, J. Betzwieser, D. Beveridge, G. Bevilacqua, N. Bevins, R. Bhandare, R. Bhatt, D. Bhattacharjee, S. Bhattacharyya, S. Bhaumik, V. Biancalana, A. Bianchi, I. A. Bilenko, M. Bilicki, G. Billingsley, A. Binetti, S. Bini, C. Binu, S. Biot, O. Birnholtz, S. Biscoveanu, A. Bisht, M. Bitossi, M. -A. Bizouard, S. Blaber, J. K. Blackburn, L. A. Blagg, C. D. Blair, D. G. Blair, N. Bode, N. Boettner, G. Boileau, M. Boldrini, G. N. Bolingbroke, A. Bolliand, L. D. Bonavena, R. Bondarescu, F. Bondu, E. Bonilla, M. S. Bonilla, A. Bonino, R. Bonnand, A. Borchers, S. Borhanian, V. Boschi, S. Bose, V. Bossilkov, Y. Bothra, A. Boudon, L. Bourg, M. Boyle, A. Bozzi, C. Bradaschia, P. R. Brady, A. Branch, M. Branchesi, I. Braun, T. Briant, A. Brillet, M. Brinkmann, P. Brockill, E. Brockmueller, A. F. Brooks, B. C. Brown, D. D. Brown, M. L. Brozzetti, S. Brunett, G. Bruno, R. Bruntz, J. Bryant, Y. Bu, F. Bucci, J. Buchanan, O. Bulashenko, T. Bulik, H. J. Bulten, A. Buonanno, K. Burtnyk, R. Buscicchio, D. Buskulic, C. Buy, R. L. Byer, G. S. Cabourn Davies, R. Cabrita, V. Cáceres-Barbosa, L. Cadonati, G. Cagnoli, C. Cahillane, A. Calafat, T. A. Callister, E. Calloni, S. R. Callos, M. Canepa, G. Caneva Santoro, K. C. Cannon, H. Cao, L. A. Capistran, E. Capocasa, E. Capote, G. Capurri, G. Carapella, F. Carbognani, M. Carlassara, J. B. Carlin, T. K. Carlson, M. F. Carney, M. Carpinelli, G. Carrillo, J. J. Carter, G. Carullo, A. Casallas-Lagos, J. Casanueva Diaz, C. Casentini, S. Y. Castro-Lucas, S. Caudill, M. Cavaglià, R. Cavalieri, A. Ceja, G. Cella, P. Cerdá-Durán, E. Cesarini, N. Chabbra, W. Chaibi, A. Chakraborty, P. Chakraborty, S. Chakraborty, S. Chalathadka Subrahmanya, J. C. L. Chan, M. Chan, K. Chang, S. Chao, P. Charlton, E. Chassande-Mottin, C. Chatterjee, Debarati Chatterjee, Deep Chatterjee, M. Chaturvedi, S. Chaty, K. Chatziioannou, A. Chen, A. H. -Y. Chen, D. Chen, H. Chen, H. Y. Chen, S. Chen, Yanbei Chen, Yitian Chen, H. P. Cheng, P. Chessa, H. T. Cheung, S. Y. Cheung, F. Chiadini, G. Chiarini, A. Chiba, A. Chincarini, M. L. Chiofalo, A. Chiummo, C. Chou, S. Choudhary, N. Christensen, S. S. Y. Chua, G. Ciani, P. Ciecielag, M. Cieślar, M. Cifaldi, B. Cirok, F. Clara, J. A. Clark, T. A. Clarke, P. Clearwater, S. Clesse, F. Cleva, E. Coccia, E. Codazzo, P. -F. Cohadon, S. Colace, E. Colangeli, M. Colleoni, C. G. Collette, J. Collins, S. Colloms, A. Colombo, C. M. Compton, G. Connolly, L. Conti, T. R. Corbitt, I. Cordero-Carrión, S. Corezzi, N. J. Cornish, I. Coronado, A. Corsi, R. Cottingham, M. W. Coughlin, A. Couineaux, P. Couvares, D. M. Coward, R. Coyne, A. Cozzumbo, J. D. E. Creighton, T. D. Creighton, P. Cremonese, S. Crook, R. Crouch, J. Csizmazia, J. R. Cudell, T. J. Cullen, A. Cumming, E. Cuoco, M. Cusinato, L. V. Da Conceição, T. Dal Canton, S. Dal Pra, G. Dálya, B. D'Angelo, S. Danilishin, S. D'Antonio, K. Danzmann, K. E. Darroch, L. P. Dartez, R. Das, A. Dasgupta, V. Dattilo, A. Daumas, N. Davari, I. Dave, A. Davenport, M. Davier, T. F. Davies, D. Davis, L. Davis, M. C. Davis, P. Davis, E. J. Daw, M. Dax, J. De Bolle, M. Deenadayalan, J. Degallaix, M. De Laurentis, F. De Lillo, S. Della Torre, W. Del Pozzo, A. Demagny, F. De Marco, G. Demasi, F. De Matteis, N. Demos, T. Dent, A. Depasse, N. DePergola, R. De Pietri, R. De Rosa, C. De Rossi, M. Desai, R. DeSalvo, A. DeSimone, R. De Simone, A. Dhani, R. Diab, M. C. Díaz, M. Di Cesare, G. Dideron, T. Dietrich, L. Di Fiore, C. Di Fronzo, M. Di Giovanni, T. Di Girolamo, D. Diksha, J. Ding, S. Di Pace, I. Di Palma, D. Di Piero, F. Di Renzo, Divyajyoti, A. Dmitriev, J. P. Docherty, Z. Doctor, N. Doerksen, E. Dohmen, A. Doke, A. Domiciano De Souza, L. D'Onofrio, F. Donovan, K. L. Dooley, T. Dooney, S. Doravari, O. Dorosh, W. J. D. Doyle, M. Drago, J. C. Driggers, L. Dunn, U. Dupletsa, P. -A. Duverne, D. D'Urso, P. Dutta Roy, H. Duval, S. E. Dwyer, C. Eassa, M. Ebersold, T. Eckhardt, G. Eddolls, A. Effler, J. Eichholz, H. Einsle, M. Eisenmann, M. Emma, K. Endo, R. Enficiaud, L. Errico, R. Espinosa, M. Esposito, R. C. Essick, H. Estellés, T. Etzel, M. Evans, T. Evstafyeva, B. E. Ewing, J. M. Ezquiaga, F. Fabrizi, V. Fafone, S. Fairhurst, A. M. Farah, B. Farr, W. M. Farr, G. Favaro, M. Favata, M. Fays, M. Fazio, J. Feicht, M. M. Fejer, R. Felicetti, E. Fenyvesi, J. Fernandes, T. Fernandes, D. Fernando, S. Ferraiuolo, T. A. Ferreira, F. Fidecaro, P. Figura, A. Fiori, I. Fiori, M. Fishbach, R. P. Fisher, R. Fittipaldi, V. Fiumara, R. Flaminio, S. M. Fleischer, L. S. Fleming, E. Floden, H. Fong, J. A. Font, F. Fontinele-Nunes, C. Foo, B. Fornal, K. Franceschetti, F. Frappez, S. Frasca, F. Frasconi, J. P. Freed, Z. Frei, A. Freise, O. Freitas, R. Frey, W. Frischhertz, P. Fritschel, V. V. Frolov, G. G. Fronzé, M. Fuentes-Garcia, S. Fujii, T. Fujimori, P. Fulda, M. Fyffe, B. Gadre, J. R. Gair, S. Galaudage, V. Galdi, R. Gamba, A. Gamboa, S. Gamoji, D. Ganapathy, A. Ganguly, B. Garaventa, J. García-Bellido, C. García-Quirós, J. W. Gardner, K. A. Gardner, S. Garg, J. Gargiulo, X. Garrido, A. Garron, F. Garufi, P. A. Garver, C. Gasbarra, B. Gateley, F. Gautier, V. Gayathri, T. Gayer, G. Gemme, A. Gennai, V. Gennari, J. George, R. George, O. Gerberding, L. Gergely, Archisman Ghosh, Sayantan Ghosh, Shaon Ghosh, Shrobana Ghosh, Suprovo Ghosh, Tathagata Ghosh, J. A. Giaime, K. D. Giardina, D. R. Gibson, C. Gier, S. Gkaitatzis, J. Glanzer, F. Glotin, J. Godfrey, R. V. Godley, P. Godwin, A. S. Goettel, E. Goetz, J. Golomb, S. Gomez Lopez, B. Goncharov, G. González, P. Goodarzi, S. Goode, A. W. Goodwin-Jones, M. Gosselin, R. Gouaty, D. W. Gould, K. Govorkova, A. Grado, V. Graham, A. E. Granados, M. Granata, V. Granata, S. Gras, P. Grassia, J. Graves, C. Gray, R. Gray, G. Greco, A. C. Green, L. Green, S. M. Green, S. R. Green, C. Greenberg, A. M. Gretarsson, H. K. Griffin, D. Griffith, H. L. Griggs, G. Grignani, C. Grimaud, H. Grote, S. Grunewald, D. Guerra, D. Guetta, G. M. Guidi, A. R. Guimaraes, H. K. Gulati, F. Gulminelli, H. Guo, W. Guo, Y. Guo, Anuradha Gupta, I. Gupta, N. C. Gupta, S. K. Gupta, V. Gupta, N. Gupte, J. Gurs, N. Gutierrez, N. Guttman, F. Guzman, D. Haba, M. Haberland, S. Haino, E. D. Hall, E. Z. Hamilton, G. Hammond, M. Haney, J. Hanks, C. Hanna, M. D. Hannam, O. A. Hannuksela, A. G. Hanselman, H. Hansen, J. Hanson, S. Hanumasagar, R. Harada, A. R. Hardison, S. Harikumar, K. Haris, I. Harley-Trochimczyk, T. Harmark, J. Harms, G. M. Harry, I. W. Harry, J. Hart, B. Haskell, C. J. Haster, K. Haughian, H. Hayakawa, K. Hayama, M. C. Heintze, J. Heinze, J. Heinzel, H. Heitmann, F. Hellman, A. F. Helmling-Cornell, G. Hemming, O. Henderson-Sapir, M. Hendry, I. S. Heng, M. H. Hennig, C. Henshaw, M. Heurs, A. L. Hewitt, J. Heynen, J. Heyns, S. Higginbotham, S. Hild, S. Hill, Y. Himemoto, N. Hirata, C. Hirose, D. Hofman, B. E. Hogan, N. A. Holland, I. J. Hollows, D. E. Holz, L. Honet, D. J. Horton-Bailey, J. Hough, S. Hourihane, N. T. Howard, E. J. Howell, C. G. Hoy, C. A. Hrishikesh, P. Hsi, H. -F. Hsieh, H. -Y. Hsieh, C. Hsiung, S. -H. Hsu, W. -F. Hsu, Q. Hu, H. Y. Huang, Y. Huang, Y. T. Huang, A. D. Huddart, B. Hughey, V. Hui, S. Husa, R. Huxford, L. Iampieri, G. A. Iandolo, M. Ianni, G. Iannone, J. Iascau, K. Ide, R. Iden, A. Ierardi, S. Ikeda, H. Imafuku, Y. Inoue, G. Iorio, P. Iosif, M. H. Iqbal, J. Irwin, R. Ishikawa, M. Isi, K. S. Isleif, Y. Itoh, M. Iwaya, B. R. Iyer, C. Jacquet, P. -E. Jacquet, T. Jacquot, S. J. Jadhav, S. P. Jadhav, M. Jain, T. Jain, A. L. James, K. Jani, J. Janquart, N. N. Janthalur, S. Jaraba, P. Jaranowski, R. Jaume, W. Javed, A. Jennings, M. Jensen, W. Jia, J. Jiang, H. -B. Jin, G. R. Johns, N. A. Johnson, M. C. Johnston, R. Johnston, N. Johny, D. H. Jones, D. I. Jones, R. Jones, H. E. Jose, P. Joshi, S. K. Joshi, G. Joubert, J. Ju, L. Ju, K. Jung, J. Junker, V. Juste, H. B. Kabagoz, T. Kajita, I. Kaku, V. Kalogera, M. Kalomenopoulos, M. Kamiizumi, N. Kanda, S. Kandhasamy, G. Kang, N. C. Kannachel, J. B. Kanner, S. A. KantiMahanty, S. J. Kapadia, D. P. Kapasi, M. Karthikeyan, M. Kasprzack, H. Kato, T. Kato, E. Katsavounidis, W. Katzman, R. Kaushik, K. Kawabe, R. Kawamoto, D. Keitel, L. J. 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Meagher, R. Mechum, Q. Meijer, A. Melatos, C. S. Menoni, F. Mera, R. A. Mercer, L. Mereni, K. Merfeld, E. L. Merilh, J. R. Mérou, J. D. Merritt, M. Merzougui, C. Messick, B. Mestichelli, M. Meyer-Conde, F. Meylahn, A. Mhaske, A. Miani, H. Miao, C. Michel, Y. Michimura, H. Middleton, D. P. Mihaylov, A. L. Miller, S. J. Miller, M. Millhouse, E. Milotti, V. Milotti, Y. Minenkov, E. M. Minihan, Ll. M. Mir, L. Mirasola, M. Miravet-Tenés, C. -A. Miritescu, A. Mishra, C. Mishra, T. Mishra, A. L. Mitchell, J. G. Mitchell, S. Mitra, V. P. Mitrofanov, K. Mitsuhashi, R. Mittleman, O. Miyakawa, S. Miyoki, A. Miyoko, G. Mo, L. Mobilia, S. R. P. Mohapatra, S. R. Mohite, M. Molina-Ruiz, M. Mondin, M. Montani, C. J. Moore, D. Moraru, A. More, S. More, C. Moreno, E. A. Moreno, G. Moreno, A. Moreso Serra, S. Morisaki, Y. Moriwaki, G. Morras, A. Moscatello, M. Mould, B. Mours, C. M. Mow-Lowry, L. Muccillo, F. Muciaccia, D. 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Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
The universe is expanding, and for decades, astronomers have been trying to measure exactly how fast. This rate of expansion, known as the Hubble constant, is a fundamental number that tells us the age and size of the cosmos. However, there is a persistent disagreement in the scientific community. One method, which looks at the afterglow of the Big Bang, suggests the universe is expanding at one speed. Another method, which measures the distance to nearby exploding stars, suggests it is expanding faster. This gap between the two measurements is one of the biggest puzzles in modern physics, hinting that our understanding of the universe might be incomplete.
To solve this, scientists have turned to a new kind of cosmic ruler: gravitational waves. These are ripples in the fabric of space-time caused by violent collisions between massive objects, such as black holes or neutron stars. When these objects crash together, they send out these ripples, which travel across the universe at the speed of light. By analyzing the shape of the wave, scientists can calculate exactly how far away the collision happened. This distance is known as the luminosity distance. The challenge is that the wave itself does not tell us how fast the source is moving away from us, which is the redshift. Without knowing the redshift, scientists cannot link the distance to the expansion rate of the universe.
A team of researchers from the LIGO, Virgo, and KAGRA collaborations has now taken a major step forward in solving this puzzle. They analyzed data from 142 gravitational wave events detected by their network of observatories. These events included collisions of black holes and neutron stars. Since most of these collisions do not produce visible light, the team had to use clever statistical methods to figure out where they happened. They treated the collection of events as a population, looking for patterns in the masses of the colliding objects. Just as a census can reveal the age structure of a city, the distribution of these cosmic masses contains clues about how far away the events are. They also cross-referenced the locations of these events with a massive catalog of galaxies, searching for potential host galaxies that could provide the missing redshift information.
The researchers combined these two approaches with a single, famous event that did produce light: a collision of two neutron stars that was seen in both gravitational waves and visible light. By merging the data from this single bright event with the statistical analysis of the 141 dark events, they arrived at a new estimate for the expansion rate of the universe. Their result is 75.4 kilometers per second per megaparsec. This number sits between the two previously conflicting values, though it leans closer to the faster rate measured by nearby stars. The uncertainty in this measurement is still significant, meaning the true value could reasonably be anywhere between roughly 62 and 88 kilometers per second per megaparsec, but the method itself is robust and independent of previous techniques.
Beyond measuring the expansion rate, the team also used this data to test the fundamental laws of gravity. Albert Einstein's theory of general relativity predicts that gravitational waves travel through the universe in a specific way, unaffected by the expansion of space in terms of their amplitude. Some alternative theories of gravity suggest that as these waves travel vast distances, they might lose energy or change in a way that makes them appear farther away than they actually are. The researchers checked for these deviations by comparing the distance measured by gravitational waves against the distance expected from standard cosmology. They found no evidence of such deviations. The data is consistent with Einstein's theory, suggesting that gravity behaves exactly as predicted even across the vast distances of the cosmos.
The study highlights both the power and the current limitations of this new field of astronomy. The researchers found that the most precise results came from using a comprehensive model that included all types of colliding objects, from the lightest neutron stars to the heaviest black holes. This approach allowed them to extract more information from the data than previous methods. However, the precision of the measurement is currently limited by how well the team can pinpoint the location of these events in the sky. During the period of observation used for this study, one of the key detectors was offline, which made it harder to narrow down the exact position of the collisions. As more detectors come online and as galaxy catalogs become more complete, the team expects these measurements to become much sharper.
This work represents a steady, independent path toward resolving the tension in our understanding of the universe. It does not yet definitively say which of the previous conflicting measurements is correct, but it proves that gravitational waves can serve as a reliable, self-calibrating tool for cosmology. As the network of detectors grows and the catalog of events expands, these cosmic ripples will continue to refine our picture of the universe, offering a fresh perspective on the forces that shape our existence. The path forward involves waiting for more collisions, better localization, and deeper galaxy maps, but the foundation for a new era of cosmic measurement has been firmly laid.
Technical Summary: GWTC-4.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation
Problem Statement
The primary objective of this work is to obtain independent measurements of the Hubble constant (H0) and to test General Relativity (GR) on cosmological scales using gravitational-wave (GW) data. A significant tension exists between early-Universe measurements of H0 derived from the Cosmic Microwave Background (CMB) and local measurements from Type Ia supernovae (the "Hubble tension"). While GWs from compact binary coalescences (CBCs) act as "standard sirens" providing a direct measure of luminosity distance, the source redshift cannot be determined from the GW signal alone due to a degeneracy with the binary masses. Previous analyses often relied on fixing population parameters or lacked the computational capacity to jointly infer cosmological and population properties when incorporating galaxy catalog data. This paper addresses these limitations by analyzing the full population of CBC candidates in the fourth LIGO–Virgo–KAGRA Collaboration (LVK) Gravitational-Wave Transient Catalog (GWTC-4.0).
Methodology
The analysis employs a hierarchical Bayesian framework to jointly infer cosmological parameters (specifically H0 in a flat ΛCDM model) and population-level properties of merging compact binaries. The methodology integrates two primary approaches to break the mass-redshift degeneracy:
Spectral Siren Method: This approach utilizes features in the source-frame mass distribution of CBCs (e.g., peaks, cutoffs, and the mass gap between neutron stars and black holes) to statistically infer redshifts. The authors utilize three phenomenological mass models:
- POWER LAW + PEAK (PLP): A power law with a smooth low-mass cutoff and a single Gaussian peak.
- MULTI PEAK (MLTP): An extension of PLP including a second Gaussian peak.
- FULLPOP-4.0: A unified model encompassing the full mass spectrum of Binary Neutron Stars (BNS), Neutron Star-Black Hole (NSBH), and Binary Black Hole (BBH) mergers, featuring a dip function to model the mass gap.
Dark Siren Method: This approach supplements the spectral siren method by identifying potential host galaxies within the GW localization volume using the GLADE+ all-sky galaxy catalog. The authors construct redshift priors by weighting galaxies based on their luminosity (luminosity-weighting, ϵ=1) or treating all galaxies equally (no-weighting, ϵ=0). They account for "out-of-catalog" galaxies using a Schechter function to model the missing population.
Data Selection
The analysis uses 142 CBC candidates from GWTC-4.0 with a false-alarm rate (FAR) <0.25 yr−1. This includes 137 BBH candidates and 5 candidates with at least one neutron star component. The multimessenger event GW170817 is treated separately as a "bright siren" (with a known electromagnetic counterpart) and combined a posteriori with the dark siren results. The analysis utilizes posterior samples generated with specific waveform approximants (e.g., IMRPHENOMXPHM) to ensure consistency, correcting for previously identified normalization errors in the likelihood function and calibration priors.
Key Contributions and Results
Hubble Constant (H0) Measurement:
By combining the dark siren analysis of 141 events (excluding GW170817 from the dark siren inference) with the bright siren GW170817, the authors report a median H0 of 75.4 km s−1 Mpc−1.- The 68.3% symmetric credible interval (CI) is −12.8+9.1 km s−1 Mpc−1.
- The 90% symmetric CI is −24.5+13.3 km s−1 Mpc−1.
- The analysis demonstrates that the FULLPOP-4.0 mass model provides the tightest constraints, improving upon single-population models (PLP and MLTP) by approximately 40–50%.
- The inclusion of the galaxy catalog (GLADE+) improves constraints on H0 by roughly 15% compared to the spectral siren method alone, though the mass spectrum features remain the dominant source of information.
Modified Gravitational-Wave Propagation:
The paper constrains deviations from GR that affect GW propagation, parameterized by the ratio of GW luminosity distance (DLGW) to electromagnetic luminosity distance (DLEM). Two parameterizations were tested:- Ξ0–n Parameterization: Describing the redshift evolution of the distance ratio. The authors find Ξ0=1.4−0.6+1.0 (68% CI) with a wide H0 prior, consistent with GR (Ξ0=1).
- αM Parameterization: Based on Horndeski gravity, constraining the rate of change of the effective Planck mass. The authors find cM=1.3−1.8+2.2 (68% CI) with a wide H0 prior, consistent with GR (cM=0).
These results show no evidence for modified gravity on cosmological scales and represent a 15–25% improvement in constraints over previous GWTC-3.0 analyses.
Systematic Robustness:
The study performs extensive robustness checks, varying mass models, galaxy weighting schemes, and numerical integration thresholds. The results are found to be robust against these variations, with the dominant systematic uncertainty arising from the choice of mass distribution model rather than galaxy catalog incompleteness or numerical thresholds.
Significance and Claims
The paper claims that the primary advancement of this work is the joint marginalization over cosmological and population hyperparameters while incorporating galaxy catalog information. Previous LVK analyses with galaxy catalogs relied on fixed population parameters, which could lead to overly optimistic constraints. By fully marginalizing over the mass distribution and merger rate evolution, this study provides a more statistically robust treatment of uncertainties.
The authors state that their results are consistent with both Planck CMB measurements and SH0ES local measurements within the 90% CI, though they do not resolve the existing tension. They emphasize that the FULLPOP-4.0 model, which unifies the analysis of BNS, NSBH, and BBH populations, is crucial for maximizing the constraining power of the data. Furthermore, the work demonstrates that GW events can serve as an independent probe of modified gravity, with constraints improving significantly due to the increased number of events in GWTC-4.0 and the inclusion of higher-redshift sources, even in the absence of a complete galaxy catalog at those distances.
The authors conclude that while current limitations (such as the lack of the Virgo detector during the O4a run and the incompleteness of the GLADE+ catalog at high redshifts) restrict the precision of the measurements, the methodology presented establishes a framework for future improvements. They anticipate that the addition of Virgo to the network and the release of deeper galaxy catalogs (e.g., UpGLADE, DESI, Euclid) will significantly enhance the precision of GW cosmology.
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