Loop-Generated Neutrino Masses in Composite Higgs Models
TLDR
In this paper, a composite scotogenic model for neutrino masses is presented, which are generated via loops of $ \mathbb{Z}_2$-odd composite scalars.Abstract:
We present a composite scotogenic model for neutrino masses, which are generated via loops of $\mathbb{Z}_2$-odd composite scalars. We considered three different approaches to the couplings of the neutrinos (including three right-handed singlets) and the composite sector: ETC-like four-fermion interactions, fundamental partial compositeness and fermion partial compositeness. In all cases, the model can feature sizeable couplings and remain viable with respect to various experimental constraints if the three $ \mathbb{Z}_2 $-odd right-handed neutrinos have masses between the TeV and the Planck scales. Additionally, the lightest $\mathbb{Z}_2$-odd composite scalar can play the role of Dark Matter, either via thermal freeze-out or as an asymmetric relic. This mechanism can be featured in a variety of models based on vacuum misalignment. For concreteness, we demonstrate it in a composite two-Higgs scheme based on $SU(6)/Sp(6)$.read more
Citations
More filters
Posted Content
Meson spectrum of Sp(4) lattice gauge theory with two fundamental Dirac fermions.
Ed Bennett,Deog Ki Hong,Jong-Wan Lee,C.-J. David Lin,Biagio Lucini,Maurizio Piai,Davide Vadacchino +6 more
TL;DR: In this paper, the meson spectrum of the Sp(4) lattice gauge theory coupled to two fundamental flavors of dynamical Dirac fermions was calculated and the resulting meson masses and decay constants were fit to a low-energy effective field theory built along the ideas of hidden local symmetry.
Journal ArticleDOI
Muon (g − 2) and W-boson mass Anomaly in a Model Based on Z4 Symmetry with Vector like Fermion
TL;DR: In this article , the connection between neutrino masses, dark matter, muon (g − 2) and W-boson mass anomaly within a single coherent framework based on Z4 extension of the scotogenic model with vector like lepton (VLL).
Journal ArticleDOI
Technically natural Higgs boson from Planck scale
TL;DR: In this paper , a partially composite Higgs model with compositeness scaling up to the Planck scale is proposed. But the model is based on a small vacuum misalignment.
References
More filters
Journal ArticleDOI
Review of Particle Physics
Claude Amsler,Michael Doser,Mario Antonelli,D. M. Asner,K. S. Babu,Howard Baer,H. R. Band,R. M. Barnett,E. Bergren,J. Beringer,G. Bernardi,Willi Bertl,H. Bichsel,Otmar Biebel,Philippe Bloch,E. Blucher,S. Blusk,Robert N. Cahn,Marcela Carena,Marcela Carena,C. Caso,Augusto Ceccucci,Debadi Chakraborty,Mingshui Chen,R. S. Chivukula,G. A. Cowan,O. I. Dahl,Giancarlo D'Ambrosio,Thibault Damour,A. de Gouvêa,Thomas DeGrand,Bogdan A. Dobrescu,Manuel Drees,D. A. Edwards,Semen Eidelman,Victor Daniel Elvira,Jens Erler,V. V. Ezhela,Jonathan L. Feng,W. Fetscher,Brian D. Fields,B. Foster,Thomas K. Gaisser,L. A. Garren,H.-J. Gerber,G. Gerbier,Tony Gherghetta,Gian F. Giudice,Maury Goodman,Christoph Grab,Andrei Gritsan,Jean-Francois Grivaz,D. E. Groom,Martin Grunewald,Atul Gurtu,Atul Gurtu,Th. Gutsche,Howard E. Haber,K. Hagiwara,C. A. Hagmann,K. G. Hayes,J.J. Hernández-Rey,Ken Ichi Hikasa,Ian Hinchliffe,A Höcker,Joey Huston,P. Igo-Kemenes,John David Jackson,Kurtis F Johnson,T. Junk,D. Karlen,B. Kayser,D. Kirkby,S. R. Klein,I.G. Knowles,Christopher Kolda,R. Kowalewski,P. Kreitz,B. Krusche,Yu V. Kuyanov,Younghoon Kwon,Ofer Lahav,Paul Langacker,Andrew R. Liddle,Zoltan Ligeti,Chi Lin,Tony Liss,L. S. Littenberg,Jeff C. Liu,K. S. Lugovsky,S. B. Lugovsky,H. Mahlke,Michelangelo L. Mangano,T Mannel,Aneesh V. Manohar,William J. Marciano,Alan D. Martin,A. Masoni,David Milstead,Ramon Miquel,Klaus Mönig,Hitoshi Murayama,Hitoshi Murayama,Hitoshi Murayama,Koji Nakamura,Meenakshi Narain,Paolo Nason,S. Sánchez Navas,P. Nevski,Yosef Nir,Keith A. Olive,Luc Pape,C. Patrignani,John A. Peacock,A. Piepke,G. Punzi,Arnulf Quadt,Stuart Raby,Georg G. Raffelt,B. N. Ratcliff,B. Renk,Paul William Richardson,S. Roesler,S. Rolli,Anatoli Romaniouk,L. J. Rosenberg,Jonathan L. Rosner,C.T. Sachrajda,Y. Sakai,Subir Sarkar,Fabio Sauli,O. Schneider,Douglas Scott,W. G. Seligman,Michael H. Shaevitz,Torbjörn Sjöstrand,J. G. Smith,George F. Smoot,Stefan M Spanier,H. Spieler,Achim Stahl,Todor Stanev,Sophia L. Stone,T. Sumiyoshi,Masaharu Tanabashi,John Terning,Maksym Titov,N. P. Tkachenko,Nils A. Tornqvist,Daniel Tovey,G.H. Trilling,T. G. Trippe,German Valencia,K. van Bibber,Manuella Vincter,Petr Vogel,D. R. Ward,Taizan Watari,Bryan R. Webber,Georg Weiglein,James D. Wells,M R Whalley,A. Wheeler,C. G. Wohl,Lincoln Wolfenstein,J. Womersley,C. L. Woody,Ron L. Workman,A. Yamamoto,W-M. Yao,Oleg Zenin,Jie Zhang,Ren-Yuan Zhu,P A Zyla,G. Harper,V. S. Lugovsky,P. Schaffner +176 more
TL;DR: This biennial Review summarizes much of particle physics, using data from previous editions.
Journal ArticleDOI
Planck 2015 results - XIII. Cosmological parameters
Peter A. R. Ade,Nabila Aghanim,Monique Arnaud,M. Ashdown,J. Aumont,Carlo Baccigalupi,A. J. Banday,A. J. Banday,R. B. Barreiro,James G. Bartlett,James G. Bartlett,N. Bartolo,N. Bartolo,E. Battaner,Richard A. Battye,K. Benabed,Alain Benoit,A. Benoit-Lévy,A. Benoit-Lévy,J.-P. Bernard,J.-P. Bernard,Marco Bersanelli,Marco Bersanelli,P. Bielewicz,P. Bielewicz,J. J. Bock,Anna Bonaldi,Laura Bonavera,J. R. Bond,Julian Borrill,Julian Borrill,François R. Bouchet,Francois Boulanger,M. Bucher,Carlo Burigana,Carlo Burigana,R. C. Butler,Erminia Calabrese,Jean-François Cardoso,Jean-François Cardoso,Jean-François Cardoso,A. Catalano,A. Catalano,Anthony Challinor,A. Chamballu,A. Chamballu,A. Chamballu,Ranga-Ram Chary,H. C. Chiang,H. C. Chiang,Jens Chluba,P. R. Christensen,Sarah E. Church,David L. Clements,S. Colombi,L. P. L. Colombo,L. P. L. Colombo,C. Combet,A. Coulais,B. P. Crill,A. Curto,A. Curto,F. Cuttaia,Luigi Danese,R. D. Davies,R. J. Davis,P. de Bernardis,A. de Rosa,G. de Zotti,G. de Zotti,Jacques Delabrouille,F.-X. Désert,E. Di Valentino,Clive Dickinson,Jose M. Diego,Klaus Dolag,Klaus Dolag,H. Dole,H. Dole,S. Donzelli,Olivier Doré,Marian Douspis,A. Ducout,A. Ducout,Jo Dunkley,X. Dupac,George Efstathiou,F. Elsner,F. Elsner,Torsten A. Enßlin,H. K. Eriksen,Marzieh Farhang,Marzieh Farhang,James R. Fergusson,Fabio Finelli,Olivier Forni,Olivier Forni,M. Frailis,A. A. Fraisse,E. Franceschi,A. Frejsel,S. Galeotta,S. Galli,K. Ganga,C. Gauthier,C. Gauthier,M. Gerbino,M. Gerbino,M. Gerbino,Tuhin Ghosh,M. Giard,M. Giard,Y. Giraud-Héraud,Elena Giusarma,E. Gjerløw,J. González-Nuevo,J. González-Nuevo,Krzysztof M. Gorski,Krzysztof M. Gorski,Serge Gratton,A. Gregorio,A. Gregorio,Alessandro Gruppuso,Jon E. Gudmundsson,Jon E. Gudmundsson,Jon E. Gudmundsson,Jan Hamann,Jan Hamann,F. K. Hansen,Duncan Hanson,Duncan Hanson,Duncan Hanson,D. L. Harrison,George Helou,Sophie Henrot-Versille,C. Hernández-Monteagudo,D. Herranz,S. R. Hildebrandt,E. Hivon,Michael P. Hobson,W. A. Holmes,Allan Hornstrup,W. Hovest,Zhiqi Huang,Kevin M. Huffenberger,G. Hurier,Andrew H. Jaffe,T. R. Jaffe,T. R. Jaffe,W. C. Jones,Mika Juvela,E. Keihänen,Reijo Keskitalo,Theodore Kisner,R. Kneissl,R. Kneissl,J. Knoche,Lloyd Knox,Martin Kunz,Martin Kunz,Martin Kunz,Hannu Kurki-Suonio,Guilaine Lagache,Guilaine Lagache,Anne Lähteenmäki,Anne Lähteenmäki,J.-M. Lamarre,Anthony Lasenby,Massimiliano Lattanzi,Charles R. Lawrence,J. P. Leahy,R. Leonardi,Julien Lesgourgues,Julien Lesgourgues,François Levrier,Antony Lewis,Michele Liguori,Michele Liguori,P. B. Lilje,M. Linden-Vørnle,M. López-Caniego,M. López-Caniego,Philip Lubin,J. F. Macías-Pérez,G. Maggio,Davide Maino,Davide Maino,N. Mandolesi,N. Mandolesi,A. Mangilli,A. Mangilli,A. Marchini,Michele Maris,Peter G. Martin,M. Martinelli,E. Martínez-González,Silvia Masi,Sabino Matarrese,Sabino Matarrese,P. McGehee,Peter Meinhold,Alessandro Melchiorri,Jean-Baptiste Melin,L. Mendes,A. Mennella,A. Mennella,M. Migliaccio,Marius Millea,Subhasish Mitra,Subhasish Mitra,M.-A. Miville-Deschênes,M.-A. Miville-Deschênes,A. Moneti,L. Montier,L. Montier,Gianluca Morgante,Daniel J. Mortlock,Adam Moss,Dipak Munshi,J. A. Murphy,Pavel Naselsky,Federico Nati,Paolo Natoli,Paolo Natoli,Calvin B. Netterfield,Hans Ulrik Nørgaard-Nielsen,F. Noviello,Dmitry Novikov,I. D. Novikov,I. D. Novikov,C. A. Oxborrow,F. Paci,L. Pagano,F. Pajot,Roberta Paladini,Daniela Paoletti,Bruce Partridge,F. Pasian,G. Patanchon,T. J. Pearson,O. Perdereau,L. Perotto,Francesca Perrotta,Valeria Pettorino,F. Piacentini,M. Piat,E. Pierpaoli,Davide Pietrobon,Stéphane Plaszczynski,Etienne Pointecouteau,Etienne Pointecouteau,G. Polenta,G. Polenta,L. Popa,G. W. Pratt,G. Prézeau,Simon Prunet,J.-L. Puget,Jörg P. Rachen,Jörg P. Rachen,William T. Reach,Rafael Rebolo,Rafael Rebolo,M. Reinecke,Mathieu Remazeilles,Mathieu Remazeilles,Mathieu Remazeilles,C. Renault,A. Renzi,I. Ristorcelli,I. Ristorcelli,Graca Rocha,C. Rosset,M. Rossetti,M. Rossetti,G. Roudier,G. Roudier,G. Roudier,B. Rouillé d'Orfeuil,Michael Rowan-Robinson,Jose Alberto Rubino-Martin,Jose Alberto Rubino-Martin,Ben Rusholme,Najla Said,Valentina Salvatelli,Valentina Salvatelli,Laura Salvati,M. Sandri,D. Santos,M. Savelainen,Giorgio Savini,Douglas Scott,Michael Seiffert,Paolo Serra,E. P. S. Shellard,Locke D. Spencer,M. Spinelli,V. Stolyarov,V. Stolyarov,V. Stolyarov,R. Stompor,R. Sudiwala,R. A. Sunyaev,R. A. Sunyaev,D. Sutton,A.-S. Suur-Uski,J.-F. Sygnet,J. A. Tauber,Luca Terenzi,Luca Terenzi,L. Toffolatti,L. Toffolatti,L. Toffolatti,M. Tomasi,M. Tomasi,M. Tristram,Tiziana Trombetti,Tiziana Trombetti,M. Tucci,J. Tuovinen,Marc Türler,G. Umana,Luca Valenziano,Jussi-Pekka Väliviita,F. Van Tent,P. Vielva,Fabrizio Villa,L. A. Wade,Benjamin D. Wandelt,Benjamin D. Wandelt,Ingunn Kathrine Wehus,Ingunn Kathrine Wehus,Martin White,Simon D. M. White,Althea Wilkinson,D. Yvon,Andrea Zacchei,Andrea Zonca +337 more
TL;DR: In this article, the authors present a cosmological analysis based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation.
Journal ArticleDOI
Planck 2015 results. XIII. Cosmological parameters
Peter A. R. Ade,Nabila Aghanim,Monique Arnaud,M. Ashdown,J. Aumont,Carlo Baccigalupi,A. J. Banday,R. B. Barreiro,James G. Bartlett,N. Bartolo,E. Battaner,Richard A. Battye,K. Benabed,Alain Benoit,A. Benoit-Lévy,J.-P. Bernard,Marco Bersanelli,P. Bielewicz,J. J. Bock,Anna Bonaldi,Laura Bonavera,J. R. Bond,Julian Borrill,François R. Bouchet,F. Boulanger,M. Bucher,Carlo Burigana,R. C. Butler,Erminia Calabrese,Jean-François Cardoso,A. Catalano,Anthony Challinor,A. Chamballu,Ranga-Ram Chary,H. C. Chiang,Jens Chluba,P. R. Christensen,Sarah E. Church,David L. Clements,S. Colombi,L. P. L. Colombo,C. Combet,A. Coulais,B. P. Crill,A. Curto,F. Cuttaia,Luigi Danese,R. D. Davies,R. J. Davis,P. de Bernardis,A. de Rosa,G. de Zotti,Jacques Delabrouille,F.-X. Désert,E. Di Valentino,Clive Dickinson,Jose M. Diego,Klaus Dolag,H. Dole,S. Donzelli,Olivier Doré,Marian Douspis,A. Ducout,Jo Dunkley,X. Dupac,George Efstathiou,F. Elsner,Torsten A. Ensslin,H. K. Eriksen,Marzieh Farhang,James R. Fergusson,Fabio Finelli,Olivier Forni,M. Frailis,A. A. Fraisse,E. Franceschi,A. Frejsel,S. Galeotta,S. Galli,K. Ganga,C. Gauthier,Martina Gerbino,Tuhin Ghosh,M. Giard,Y. Giraud-Héraud,Elena Giusarma,E. Gjerløw,J. González-Nuevo,Krzysztof M. Gorski,Serge Gratton,A. Gregorio,Alessandro Gruppuso,Jon E. Gudmundsson,Jan Hamann,F. K. Hansen,Duncan Hanson,D. L. Harrison,George Helou,Sophie Henrot-Versille,C. Hernández-Monteagudo,D. Herranz,S. R. Hildebrandt,E. Hivon,Michael P. Hobson,W. A. Holmes,Allan Hornstrup,W. Hovest,Zhiqi Huang,Kevin M. Huffenberger,G. Hurier,Andrew H. Jaffe,T. R. Jaffe,W. C. Jones,Mika Juvela,E. Keihänen,Reijo Keskitalo,Theodore Kisner,R. Kneissl,J. Knoche,Lloyd Knox,Martin Kunz,Hannu Kurki-Suonio,Guilaine Lagache,Anne Lähteenmäki,J.-M. Lamarre,Anthony Lasenby,Massimiliano Lattanzi,Charles R. Lawrence,J. P. Leahy,R. Leonardi,Julien Lesgourgues,François Levrier,Antony Lewis,Michele Liguori,P. B. Lilje,M. Linden-Vørnle,M. López-Caniego,Philip Lubin,J. F. Macías-Pérez,G. Maggio,Davide Maino,N. Mandolesi,A. Mangilli,A. Marchini,Peter G. Martin,M. Martinelli,E. Martínez-González,Silvia Masi,Sabino Matarrese,Pasquale Mazzotta,P. McGehee,Peter Meinhold,Alessandro Melchiorri,J.-B. Melin,L. Mendes,A. Mennella,M. Migliaccio,M. Millea,S. Mitra,M.-A. Miville-Deschênes,A. Moneti,L. Montier,Gianluca Morgante,Daniel J. Mortlock,Adam Moss,Dipak Munshi,J. A. Murphy,Pavel Naselsky,Federico Nati,Paolo Natoli,Calvin B. Netterfield,Hans Ulrik Nørgaard-Nielsen,F. Noviello,Dmitry Novikov,I. D. Novikov,C. A. Oxborrow,F. Paci,L. Pagano,F. Pajot,R. Paladini,Daniela Paoletti,Bruce Partridge,F. Pasian,G. Patanchon,T. J. Pearson,O. Perdereau,L. Perotto,Francesca Perrotta,Valeria Pettorino,F. Piacentini,M. Piat,E. Pierpaoli,Davide Pietrobon,Stéphane Plaszczynski,Etienne Pointecouteau,G. Polenta,L. Popa,G. W. Pratt,G. Prézeau,Simon Prunet,J.-L. Puget,Jörg P. Rachen,William T. Reach,Rafael Rebolo,M. Reinecke,Mathieu Remazeilles,C. Renault,A. Renzi,I. Ristorcelli,Graca Rocha,C. Rosset,M. Rossetti,G. Roudier,B. Rouillé d'Orfeuil,Michael Rowan-Robinson,Jose Alberto Rubino-Martin,Ben Rusholme,Najla Said,Valentina Salvatelli,L. Salvati,M. Sandri,D. Santos,M. Savelainen,Giorgio Savini,Douglas Scott,Michael Seiffert,Paolo Serra,E. P. S. Shellard,Locke D. Spencer,M. Spinelli,V. Stolyarov,R. Stompor,R. Sudiwala,R. A. Sunyaev,D. Sutton,A.-S. Suur-Uski,J.-F. Sygnet,J. A. Tauber,Luca Terenzi,L. Toffolatti,M. Tomasi,M. Tristram,T. Trombetti,M. Tucci,J. Tuovinen,M. Turler,G. Umana,Luca Valenziano,Jussi-Pekka Väliviita,B. Van Tent,P. Vielva,Fabrizio Villa,L. A. Wade,Benjamin D. Wandelt,Ingunn Kathrine Wehus,Martin White,Simon D. M. White,Althea Wilkinson,D. Yvon,Andrea Zacchei,Andrea Zonca +260 more
TL;DR: In this paper, the authors present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB, which are consistent with the six-parameter inflationary LCDM cosmology.
Journal ArticleDOI
APS : Review of Particle Physics, 2018-2019
Masaharu Tanabashi,Paul William Richardson,A Bettini,Andreas Vogt,L. Garren,A J Schwartz,K Terashi,M Karliner,R.S. Chivukula,Torbjörn Sjöstrand,J. Beringer,Siegfried Bethke,G. Gerbier,Paolo Nason,Herbert K. Dreiner,Younghoon Kwon,J. J. Beatty,E Pianori,M. Silari,John A. Peacock,Alessandro Cerri,A. de Gouvea,Ren-Yuan Zhu,Christian W. Bauer,T Mannel,Tony Liss,M. Pennington,Daniel Tovey,Fabio Sauli,Kurtis F Johnson,Stephen R. Sharpe,C. Hanhart,T. Sumiyoshi,J Anderson,Howard Baer,John Matthews,H. R. Gallagher,Debadi Chakraborty,Thomas DeGrand,L. R. Wiencke,Howard E. Haber,A Höcker,Filip Moortgat,Mario Antonelli,Arnulf Quadt,J Tanaka,P A Zyla,G. Venanzoni,Yoshinari Hayato,Giancarlo D'Ambrosio,C.T. Sachrajda,U Thoma,G Rybka,D. E. Groom,Matthias Neubert,Gavin P. Salam,H. Bichsel,E. J. Weinberg,Ken Ichi Hikasa,A Pomarol,Peter Skands,S. Sánchez Navas,D Wands,A Freitas,G Aielli,Zoltan Ligeti,Andreas Ringwald,P. Nevski,T Shutt,Maksym Titov,T Hyodo,David H. Weinberg,Sophia L. Stone,Kaustubh Agashe,Alberto Masoni,O Buchmuller,Douglas Scott,S L Zhu,L Fuller,S. Pagan Griso,Alan D. Martin,K. S. Lugovsky,Hitoshi Murayama,Kaoru Hagiwara,R A Ryutin,Manuel Drees,Christoph Grab,Sw. Banerjee,Brian D. Fields,M. C. Goodman,M A Bychkov,B. K. Heltsley,D A Dwyer,T. Basaglia,Chi Lin,Daniel de Florian,Georg G. Raffelt,H. Spieler,Frank Zimmermann,Jonas Rademacker,S. Rolli,C. Grojean,Burkert,Claude Amsler,J Lesgourgues,Th. Gutsche,J. Erler,Klaus Mönig,German Valencia,Y Gershtein,John Terning,J. G. Smith,J. Womersley,A Lusiani,J Ellis,Y. Sakai,A. Piepke,Eberhard Klempt,A. Stahl,K D Irwin,Andrei Gritsan,P Eerola,V A Petrov,George F. Smoot,Subir Sarkar,G P Zeller,William J. Marciano,Keith A. Olive,C. Patrignani,Ron L. Workman,Fabio Maltoni,G. Dissertori,Y Sumino,Christian Spiering,Yu V. Kuyanov,U G Meißner,Marcela Carena,B. Krusche,R E Mitchell,Timothy Gershon,Frank Krauss,Meenakshi Narain,N Varelas,Wolfgang Walkowiak,Ezhela,Kenneth G. Hayes,Augusto Ceccucci,Stefan Roesler,F Takahashi,J Hisano,Petr Vogel,M O Wascko,L Verde,S. T. Petcov,Michael Syphers,V I Belousov,Ofer Lahav,Oleg Zenin,C. L. Woody,Andrew R. Liddle,M D'Onofrio,Marumi Kado,Orin I. Dahl,S. R. Klein,M Moskovic,D. M. Asner,A. Gurtu,D. R. Ward,Mingshui Chen,S Heinemeyer,R. Kowalewski,A A Godizov,David Milstead,Manuella Vincter,S.I. Eidelman,R Firestone,L.J. Rosenberg,Martin Grunewald,K M Black,N. P. Tkachenko,Bogdan A. Dobrescu,Tony Gherghetta,W-M. Yao,S Willocq,R. M. Barnett,A Holtkamp,L. S. Littenberg,Michal Kreps,R S Thorne,O. Schneider,Paolo Molaro,W. Fetscher,Jamie Holder,Nils A. Tornqvist,E. Blucher,P. Schaffner,Uli Katz,Anatoli Romaniouk,P. de Jong,B. Foster,Sharma,Shoji Hashimoto,Kate Scholberg,R. G. Van de Water,T Skwarnicki,C. W. Walter,J. A. Parsons,Georg Weiglein,R. N. Cahn,Charles G Wohl,Jonathan L. Rosner,V. S. Lugovsky,B. N. Ratcliff,Martin White,Y. Nir,H J Gerber,S. P. Wakely,C Lippmann,Jack Laiho,Otmar Biebel,J.J. Hernández-Rey,Thibault Damour,G. Cowan,Y Makida,L. Tiator,Michael Doser,S. M. Spanier,S. B. Lugovsky,A Hebecker,Koji Nakamura,Aneesh V. Manohar +230 more
TL;DR: The complete review as discussed by the authors is published online on the website of the Particle Data Group (http://pdg.lbl.gov) and in a journal. Volume 1 is available in print as thePDG Book.
Book
The Early Universe
Edward W. Kolb,Michael S. Turner +1 more
TL;DR: In this article, the Robertson-Walker Metric is used to measure the radius of the Planck Epoch in the expanding universe, which is a measure of the number of atoms in the universe.