The evidence for a spatially flat Universe
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ABSTRACT We use a new and statistically powerful Planck likelihood to show that the Planck temperature and polarization spectra are consistent with a spatially flat Universe, in contrast to recent claims in the literature. When combined with other astrophysical data, particularly geometrical measurements of baryon acoustic oscillations, our likelihood constrains the Universe to be spatially flat to extremely high precision. We deduce a curvature density parameter ΩK = 0.0004 ± 0.0018 in good agreement with the 2018 results of the Planck team. In the context of inflationary cosmology, the observations offer strong support for models of inflation with a large number of e-foldings and disfavour models of incomplete inflation.
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Gómez-Valent, A. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.043528 · Cited by 33 · see citing works
Constraining the curvature density parameter in cosmology
Mukherjee, P., & Banerjee, N. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.063516 · Cited by 32 · see citing works
Cao, S., Zajaček, M., Panda, S., Martínez‐Aldama, M. L., Czerny, B., & Ratra, B. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac2325 · Cited by 32 · see citing works
Constraining spatial curvature with large-scale structure
Bel, J., Larena, J., Maartens, R., Marinoni, C., & Pèrenon, L. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/09/076 · Cited by 32 · see citing works
Analyzing the geometrical and dynamical parameters of modified Teleparallel-Gauss–Bonnet model
Lohakare, S. V., Mishra, B., Maurya, S. K., & Singh, K. N. (2022) · Physics of the Dark Universe · doi:10.1016/j.dark.2022.101164 · Cited by 32 · see citing works
Cosmological constraints from H ii starburst galaxy, quasar angular size, and other measurements
Cao, S., Ryan, J., & Ratra, B. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab3304 · Cited by 31 · see citing works
Dynamical Systems Analysis of f(Q) Gravity
Böhmer, C. G., Jensko, E., & Lazkoz, R. (2023) · Universe · doi:10.3390/universe9040166 · Cited by 30 · see citing works
Comparing Compressed and Full-Modeling analyses with FOLPS: implications for DESI 2024 and beyond
Noriega, H. E., Avilés, A., Gil-Marín, H., Ramírez-Solano, S., Fromenteau, S., Vargas-Magaña, M., Aguilar, J., Ahlen, S. P., Alves, O., Brieden, S., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/01/136 · Cited by 30 · see citing works
D’Amico, G., & Kaloper, N. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/08/058 · Cited by 30 · see citing works
What is flat ΛCDM, and may we choose it?
Anselmi, S., Carney, M. F., Giblin, J. T., Kumar, S., Mertens, J. B., O'Dwyer, M., Starkman, G. D., & Tian, C. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/02/049 · Cited by 29 · see citing works
Khadka, N., Zajaček, M., Prince, R., Panda, S., Czerny, B., Martínez‐Aldama, M. L., Jaiswal, V. K., & Ratra, B. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad1040 · Cited by 29 · see citing works
Lorentzian vacuum transitions: Open or closed universes?
Céspedes, S., de Alwis, S. P., Muia, F., & Quevedo, F. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.026013 · Cited by 27 · see citing works
Do reverberation-measured Hβ quasars provide a useful test of cosmology?
Khadka, N., Martínez‐Aldama, M. L., Zajaček, M., Czerny, B., & Ratra, B. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac914 · Cited by 26 · see citing works
High redshift Λ CDM cosmology: To bin or not to bin?
Colgáin, E. Ó., Sheikh-Jabbari, M. M., & Solomon, R. M. (2023) · Physics of the Dark Universe · doi:10.1016/j.dark.2023.101216 · Cited by 26 · see citing works
Khadka, N., Zajaček, M., Panda, S., Martínez‐Aldama, M. L., & Ratra, B. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac1940 · Cited by 25 · see citing works
Towards a new model-independent calibration of Gamma-Ray Bursts
Favale, A., Dainotti, M. G., Gómez-Valent, A., & Migliaccio, M. (2024) · Journal of High Energy Astrophysics · doi:10.1016/j.jheap.2024.10.010 · Cited by 25 · see citing works
Measuring cosmic curvature with non-CMB observations
Wu, P.-J., & Zhang, X. (2025) · Physical review. D/Physical review. D. · doi:10.1103/sn3q-q589 · Cited by 24 · see citing works
Anselmi, S., Starkman, G. D., & Renzi, A. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.123506 · Cited by 24 · see citing works
High H 0 Values from CMB E-mode Data: A Clue for Resolving the Hubble Tension?
Addison, G. E. (2021) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/abf56e · Cited by 24 · see citing works
The Symmetries of Quantum and Classical Information. The Ressurected “Ether" of Quantum InformationPreprint
Penchev, V. D. (2021) · SSRN Electronic Journal · doi:10.2139/ssrn.3861105 · Cited by 24 · see citing works
Cosmological dynamical systems in modified gravity
Böhmer, C. G., Jensko, E., & Lazkoz, R. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10412-y · Cited by 23 · see citing works
Nested sampling with any prior you like
Alsing, J., & Handley, W. J. (2021) · Monthly Notices of the Royal Astronomical Society Letters · doi:10.1093/mnrasl/slab057 · Cited by 22 · see citing works
Planck-PR4 anisotropy spectra show better consistency with general relativity
Specogna, E., Giarè, W., & Valentino, E. D. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.103510 · Cited by 21 · see citing works
Abbott, T. M. C., Acevedo, M., Adamów, M., Aguena, M., Alarcon, A., Allam, S., Alves, O., Andrade-Oliveira, F., Annis, J. T., Armstrong, P., et al. (2026) · Physical review. D/Physical review. D. · doi:10.1103/z2q4-qcdq · Cited by 21 · see citing works
Null test for cosmic curvature using Gaussian process*
Wu, P.-J., Qi, J.-Z., & Zhang, X. (2023) · Chinese Physics C · doi:10.1088/1674-1137/acc647 · Cited by 21 · see citing works
Inference products for "Finite inflation in curved space"
Hergt, L. T. (2022) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.6547871 · Cited by 21 · see citing works
Modified Gravity in the Presence of Matter Creation: Scenario for the Late Universe
Montani, G., Carlevaro, N., & Angelis, M. D. (2024) · Entropy · doi:10.3390/e26080662 · Cited by 20 · see citing works
The variance of the CMB temperature gradient: a new signature of a multiply connected Universe
Aurich, R., Buchert, T., France, M. J., & Steiner, F. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac27f0 · Cited by 20 · see citing works
Comparison of dark energy models using late-universe observations
Wu, P.-J. (2025) · Physical review. D/Physical review. D. · doi:10.1103/mcgb-ntwr · Cited by 19 · see citing works
KiDS-1000 Cosmology: Constraints beyond flat ΛCDM
Tröster, T., Asgari, M., Blake, C., Cataneo, M., Heymans, C., Hildebrandt, H., Joachimi, B., Sánchez, A. G., Wright, A. H., Bilicki, M., et al. (2021) · Springer Link (Chiba Institute of Technology) · doi:10.1051/0004-6361/202039805/pdf · Cited by 19 · see citing works
Analytical approximations for curved primordial power spectra
Thavanesan, A., Werth, D., & Handley, W. J. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.023519 · Cited by 18 · see citing works
Cosmological constraints on unimodular gravity models with diffusion
Landau, S. J., Benetti, M., Pérez, A., & Sudarsky, D. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.043524 · Cited by 17 · see citing works
Lapi, A., Boco, L., Cueli, M. M., Haridasu, B. S., Ronconi, T., Baccigalupi, C., & Danese, L. (2023) · The Astrophysical Journal · doi:10.3847/1538-4357/ad01bb · Cited by 17 · see citing works
Effect of Extinction on Quasar Luminosity Distances Determined from UV and X-Ray Flux Measurements
Zajaček, M., Czerny, B., Khadka, N., Martínez‐Aldama, M. L., Prince, R., Panda, S., & Ratra, B. (2024) · The Astrophysical Journal · doi:10.3847/1538-4357/ad11dc · Cited by 17 · see citing works
Reconstructing the matter power spectrum with future cosmic shear surveys
Preston, C., Amon, A., & Efstathiou, G. (2024) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stae1848 · Cited by 17 · see citing works
Self-citationA low Hubble constant from galaxy distribution observations
Holanda, R. F. L., Pordeus-da-Silva, G., & Pereira, S. H. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/09/053 · Cited by 17 · see citing works
Nonminimally coupled gravity constraints from DESI DR2 data
Pan, J., & Ye, G. (2026) · Physical review. D/Physical review. D. · doi:10.1103/hqwq-m19h · Cited by 16 · see citing works
Evidence of dynamical dark energy in a non-flat universe: current and future observations
Rezaei, M., Pan, S., Yang, W., & Mota, D. F. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/01/052 · Cited by 16 · see citing works
Constraining ΛCDM cosmological parameters with Einstein Telescope mock data
Califano, M., Martino, I. D., Vernieri, D., & Capozzıello, S. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac3230 · Cited by 16 · see citing works
Baryon acoustic oscillations from a different angle
Efstathiou, G. (2025) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staf906 · Cited by 15 · see citing works
Self-citationModel-independent Estimation of H 0 and Ω K from Strongly Lensed Fast Radio Bursts
Zhao, S., Liu, B., Li, Z., & Gao, H. (2021) · The Astrophysical Journal · doi:10.3847/1538-4357/abfa91 · Cited by 15 · see citing works
f(T) cosmology in the regime of quasar observations
Sandoval-Orozco, R., Escamilla‐Rivera, C., Briffa, R., & Said, J. L. (2023) · Physics of the Dark Universe · doi:10.1016/j.dark.2023.101407 · Cited by 15 · see citing works
- Authors
- Efstathiou, G., & Gratton, S.
- Affiliations
- University of Cambridge (GB)
- Corresponding author
- Efstathiou, George
- Gratton, Steven
- ORCID
- Efstathiou, George
- Venue
- Monthly Notices of the Royal Astronomical Society: Letters
- Publisher
- Oxford University Press (OUP)
- Published
- 2020-05-27
- Volume
- 496
- Issue
- 1
- Pages
- L91-L95
- ISSN
- 1745-3925 (ISSN-L)
- 1745-3933
- OpenAlex
- W3006133234
- Cited by
- 203
- References
- 41
- Citations by year
- 2026: 18 · 2025: 31 · 2024: 27 · 2023: 33 · 2022: 34 · 2021: 48 · 2020: 12
- FWCI
- 14.26
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Monthly Notices of the Royal Astronomical Society Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Science and Technology Facilities Council (ST/N000927/1)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
- Keywords
- baryon acoustic oscillations, cosmic inflation
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