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Constraints on the normal branch of DGP gravity from SPT galaxy clusters with DES and HST weak-lensing mass calibration and from Planck PR4 CMB anisotropies

S. M. L. Vogt1,2,3,*, S. Bocquet1, C. T. Davies1, J. J. Mohr1,4, F. Schmidt3, C.-Z. Ruan5, B. Li6, C. Hernández-Aguayo3, S. Grandis7 et al. (SPT and DES Collaborations)

S. Grandis7, L. E. Bleem8,9, M. Klein1,4, M. Aguena10,11, S. Allam12, F. Andrade-Oliveira13, D. Bacon14, D. Brooks15, R. Camilleri16, A. Carnero Rosell17,11,18, J. Carretero19, M. Costanzi20,10,21, L. N. da Costa11, M. E. da Silva Pereira22, J. De Vicente23, P. Doel15, J. García-Bellido24, P. Giles25, D. Gruen26, G. Gutierrez12, S. R. Hinton16, D. L. Hollowood27, D. J. James28, K. Kuehn29,30, S. Lee31, J. L. Marshall32, J. Mena-Fernández33, F. Menanteau34,35, R. Miquel36,19, J. Myles37, A. A. Plazas Malagón38,39, A. Porredon23,40, J. Prat41, C. L. Reichardt42, A. K. Romer25, E. Sanchez23, I. Sevilla-Noarbe23, M. Smith43, M. Soares-Santos44, E. Suchyta45, M. E. C. Swanson34, C. To46, V. Vikram47, and N. Weaverdyck48,49 (SPT and DES Collaborations)

  • 1University Observatory, LMU Faculty of Physics, Scheinerstraße 1, 81679 Munich, Germany
  • 2Excellence Cluster Origins, Boltzmannstraße 2, 85748 Garching, Germany
  • 3Max Planck Institute for Astrophysics, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany
  • 4Max Planck Institute for Extraterrestrial Physics, Giessenbachstraße 2, 85748 Garching, Germany
  • 5Institute of Theoretical Astrophysics, University of Oslo, 0315 Oslo, Norway
  • 6Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom
  • 7Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstraße 25/8, 6020 Innsbruck, Austria
  • 8High-Energy Physics Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, USA
  • 9Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
  • 10INAF-Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, I-34143 Trieste, Italy
  • 11Laboratório Interinstitucional de e-Astronomia—LIneA, Avenue Pastor Martin Luther King Jr, 126 Del Castilho, Nova América Offices, Torre 3000/sala 817 CEP: 20765-000, Brazil
  • 12Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, Illinois 60510, USA
  • 13Physik-Institut, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
  • 14Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom
  • 15Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom
  • 16School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia
  • 17Instituto de Astrofisica de Canarias, E-38205 La Laguna, Tenerife, Spain
  • 18Universidad de La Laguna, Departamento Astrrofisica, E-38206 La Laguna, Tenerife, Spain
  • 19Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona) Spain
  • 20Astronomy Unit, Department of Physics, University of Trieste, via Tiepolo 11, I-34131 Trieste, Italy
  • 21Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
  • 22Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
  • 23Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
  • 24Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain
  • 25Department of Physics and Astronomy, Pevensey Building, University of Sussex, Brighton, BN1 9QH, United Kingdom
  • 26University Observatory, LMU Faculty of Physics, Scheinerstraße 1, 81679 Munich, Germany
  • 27Santa Cruz Institute for Particle Physics, Santa Cruz, California 95064, USA
  • 28Center for Astrophysics | Harvard and Smithsonian, 60 Garden Street, Cambridge, Massachusetts 02138, USA
  • 29Australian Astronomical Optics, Macquarie University, North Ryde, NSW 2113, Australia
  • 30Lowell Observatory, 1400 Mars Hill Rd, Flagstaff, Arizona 86001, USA
  • 31Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, California 91109, USA
  • 32George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
  • 33Université Grenoble Alpes, CNRS, LPSC-IN2P3, 38000 Grenoble, France
  • 34Center for Astrophysical Surveys, National Center for Supercomputing Applications, 1205 West Clark Street, Urbana, Illinois 61801, USA
  • 35Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, Illinois 61801, USA
  • 36Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona, Spain
  • 37Department of Astrophysical Sciences, Princeton University, Peyton Hall, Princeton, New Jersey 08544, USA
  • 38Kavli Institute for Particle Astrophysics and Cosmology, P. O. Box 2450, Stanford University, Stanford, California 94305, USA
  • 39SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
  • 40Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute, German Centre for Cosmological Lensing, 44780 Bochum, Germany
  • 41Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-10691 Stockholm, Sweden
  • 42School of Physics, University of Melbourne, Parkville, VIC 3010, Australia
  • 43Physics Department, Lancaster University, Lancaster, LA1 4YB, United Kingdom
  • 44Physik-Institut, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
  • 45Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
  • 46Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA
  • 47Argone National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
  • 48Berkeley Center for Cosmological Physics, Department of Physics, University of California, Berkeley, California 94720, US
  • 49Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA

  • *Contact author: s.vogt@physik.lmu.de
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Phys. Rev. D 113, 123508 – Published 4 June, 2026

DOI: https://doi.org/10.1103/t189-srtj

Abstract

We present constraints on the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld gravity model from the abundance of massive galaxy clusters. On scales below the nDGP crossover scale rc, the nDGP model features an effective gravitylike fifth force that alters the growth of structure, leading to an enhancement of the halo mass function (HMF) on cluster scales. The enhanced cluster abundance allows for constraints on the nDGP model using cluster samples. We employ the South Pole Telescope (SPT) cluster sample, selected through the thermal Sunyaev-Zel’dovich effect with the SPT and with mass calibration using weak-lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample contains 1,005 clusters with redshifts 0.25<z<1.78, which are confirmed with the multicomponent matched filter algorithm using optical and near-infrared data. Weak-lensing data from DES and HST enable a robust mass measurement of the cluster sample. We use DES Year 3 data for 688 clusters with redshifts z<0.95, and HST data for 39 clusters with redshifts 0.6<z<1.7. We account for the enhancement in the HMF through a semi-analytic correction factor to the standard cosmology HMF derived from the spherical collapse model in the nDGP model. We then further calibrate this model using N-body simulations. In addition, for the first time, we analyze the primary CMB temperature and polarization anisotropy measurements from Planck PR4 within the nDGP model. We obtain a competitive constraint from the joint analysis of the SPT cluster abundance with the Planck PR4 data, and report an upper bound of 1/H0rc<1.41 at 95% when assuming a cosmology with massive neutrinos.

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Phys. Rev. D 113, 123508– Published 4 June, 2026
  • Received 8 December 2025
  • Accepted 5 May 2026
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