The interpretation of cosmological redshift as evidence for the expansion of space is a central component of the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological framework. In this paper, we compare FLRW cosmology with a stationary Taub-NUT gravitational-redshift cosmology using redshift-based observables. We discuss three possible discriminants: the Hubble diagram, redshift drift, and astrometric radial velocities. The supernova Hubble diagram is fit with both a Taub-NUT redshift-distance relation and a reference flat FLRW model. The fits show that present supernova redshift-distance data alone do not uniquely distinguish the two descriptions. However, future observations at high redshift (z > 2) may provide an observational means of distinguishing between the two cosmological theories. In addition, redshift drift provides a direct future observational test: expanding FLRW models predict a systematic, nonzero drift, whereas a stationary Taub-NUT model predicts zero cosmological drift for sources at fixed coordinate distance. Astrometric radial velocities are included for conceptual completeness, but quantitative estimates show that they are not practical at cosmological distances.
References
[1]
Riess, A.G., Filippenko, A.V., Challis, P., Clocchiatti, A., Diercks, A., Garnavich, P.M., et al. (1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 116, 1009-1038. https://doi.org/10.1086/300499
[2]
Perlmutter, S., Aldering, G., Goldhaber, G., Knop, R.A., Nugent, P., Castro, P.G., etal. (1999) Measurements of Ω and λ from 42 High-Redshift Supernovae. The Astrophysical Journal, 517, 565-586. https://doi.org/10.1086/307221
[3]
Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., et al. (2020) Planck 2018 Results. VI. Cosmological Parameters. Astronomy & Astrophysics, 641, A6. https://doi.org/10.1051/0004-6361/201833910
[4]
Eisenstein, D.J., Zehavi, I., Hogg, D.W., Scoccimarro, R., Blanton, M.R., Nichol, R.C., et al. (2005) Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies. The Astrophysical Journal, 633, 560-574. https://doi.org/10.1086/466512
[5]
Hubble, E. (1929) A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae. Proceedings of the National Academy of Sciences, 15, 168-173. https://doi.org/10.1073/pnas.15.3.168
[6]
Friedmann, A. (1922) über die Krümmung des Raumes. Zeitschrift für Physik, 10, 377-386. https://doi.org/10.1007/BF01332580
[7]
Lema？tre, G. (1927) Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques. Annales de la Société Scientifique de Bruxelles, 47, 49-59. https://ui.adsabs.harvard.edu/abs/1927ASSB...47...49L
[8]
Hubble, E. and Tolman, R.C. (1935) Two Methods of Investigating the Nature of the Nebular Redshift. The Astrophysical Journal, 82, 302-337. https://doi.org/10.1086/143682
[9]
McGruder, C.H. (2024) Cosmology without the Cosmological Principle and without Violating the Copernican Principle: Taub-NUT Universe. Journal of Modern Physics, 15, 1069-1096. https://doi.org/10.4236/jmp.2024.158046
[10]
McGruder, C.H. (2024) Cosmological Gravitational Redshift, Spectral Shift and Time in the Taub-NUT Universe. Journal of Modern Physics, 15, 1448-1459. https://doi.org/10.4236/jmp.2024.159059
[11]
Sandage, A. (1962) The Change of Redshift and Apparent Luminosity of Galaxies Due to the Deceleration of Selected Expanding Universes. The Astrophysical Journal, 136, 319-333. https://doi.org/10.1086/147385
[12]
Loeb, A. (1998) Direct Measurement of Cosmological Parameters from the Cosmic Deceleration of Extragalactic Objects. The Astrophysical Journal, 499, L111-L114. https://doi.org/10.1086/311375
[13]
Uzan, J., Clarkson, C. and Ellis, G.F.R. (2008) Time Drift of Cosmological Redshifts as a Test of the Copernican Principle. Physical Review Letters, 100, Article 191303. https://doi.org/10.1103/physrevlett.100.191303
[14]
Martins, C.J.A.P. (2017) The Status of Varying Constants: A Review of the Physics, Searches and Implications. Reports on Progress in Physics, 80, Article 126902. https://doi.org/10.1088/1361-6633/aa860e
[15]
Pierel, J.D.R., Engesser, M., Coulter, D.A., DeCoursey, C., Siebert, M.R., Rest, A., et al. (2024) Discovery of an Apparent Red, High-Velocity Type Ia Supernova at z = 2.9 with JWST. TheAstrophysical Journal Letters, 971, L32. https://doi.org/10.3847/2041-8213/ad6908
[16]
Vinkó, J. and Reg？s, E. (2025) SN 2023adsy: A Normal Type Ia Supernova at z = 2.9. Astronomy & Astrophysics, 701, A70. https://doi.org/10.1051/0004-6361/202554209
[17]
Reg？s, E. and Vinkó, J. (2019) Detection and Classification of Supernovae beyond z～2 Redshift with the James Webb Space Telescope. The Astrophysical Journal, 874, Article 158. https://doi.org/10.3847/1538-4357/ab0a73
[18]
Weinberg, S. (1972) Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley.
[19]
Peebles, P.J.E. (1993) Principles of Physical Cosmology. Princeton University Press.
[20]
Goldhaber, G., Groom, D.E., Kim, A., Aldering, G., Astier, P., Conley, A., et al. (2001) Timescale Stretch Parameterization of Type Ia Supernova B‐Band Light Curves. The Astrophysical Journal, 558, 359-368. https://doi.org/10.1086/322460
[21]
Pepe, F., Cristiani, S., Rebolo, R., Santos, N.C., et al. (2021) ESPRESSO at VLT: On-sky Performance and First Results. Astronomy & Astrophysics, 645, A96.
[22]
Milakovi？, D., Lee, C.-C., Carswell, R.F., Webb, J.K., Molaro, P. and Pasquini, L. (2021) A New Era of Fine Structure Constant Measurements at High Redshift. Monthly Notices of the Royal Astronomical Society, 500, 1-21. https://doi.org/10.1093/mnras/staa3217
[23]
Cristiani, S., Porru, M., Guarneri, F., Calderone, G., Boutsia, K., Grazian, A., et al. (2023) Spectroscopy of QUBRICS Quasar Candidates: 1672 New Redshifts and a Golden Sample for the Sandage Test of the Redshift Drift. Monthly Notices of the Royal Astronomical Society, 522, 2019-2035. https://doi.org/10.1093/mnras/stad1007
[24]
Manzoor, R., Yousaf, M., Ikram, Z. and Siddiqa, A. (2026) Modified Observational Signatures of Gravitational Waves in Exponential f(T) Theory. The European Physical Journal C, 86, Article No. 193. https://doi.org/10.1140/epjc/s10052-026-15429-1
[25]
Donmez, O., Ghosh, S.G., Yousaf, M., Mustafa, G. and Atamurotov, F. (2026) Accretion Flow around Kerr Metric in the Infra-Red Limit of Asymptotically Safe Gravity. Journal of Cosmology and Astroparticle Physics, 2026, Article 45. https://doi.org/10.1088/1475-7516/2026/04/045
[26]
Donmez, O., Mustafa, G., Chaudhary, H., Yousaf, M., Bouzenada, A., Ditta, A. and Atamurotov, F. (2025) Relativistic Accretion Process onto Rotating Black Holes in Einstein-Euler-Heisenberg Nonlinear Electrodynamic Gravity. arXiv:2512.09845.
[27]
Singh, P., Kala, S., Nandan, H., Yousaf, M., Atamurotov, F. and Mustafa, G. (2026) Probing Strong-Gravity Chaos in Rotating Kerr-Bertotti-Robinson Black Holes. Chaos, Solitons & Fractals, 208, Article 118379. https://doi.org/10.1016/j.chaos.2026.118379
[28]
Lindegren, L. and Dravins, D. (2003) The Fundamental Definition of “Radial Velocity”. Astronomy & Astrophysics, 401, 1185-1201. https://doi.org/10.1051/0004-6361:20030181
[29]
Strauss, M.A. and Willick, J.A. (1995) The Density and Peculiar Velocity Fields of Nearby Galaxies. Physics Reports, 261, 271-431. https://doi.org/10.1016/0370-1573(95)00013-7
[30]
Carrick, J., Turnbull, S.J., Lavaux, G. and Hudson, M.J. (2015) Cosmological Parameters from the Comparison of Peculiar Velocities with Predictions from the 2M++ Density Field. Monthly Notices of the Royal Astronomical Society, 450, 317-332. https://doi.org/10.1093/mnras/stv547
[31]
Scrimgeour, M.I., Davis, T.M., Blake, C., Staveley-Smith, L., Magoulas, C., Springob, C.M., et al. (2016) The 6dF Galaxy Survey: Bulk Flows on 50-70 H？1 Mpc Scales. Monthly Notices of the Royal Astronomical Society, 455, 386-401. https://doi.org/10.1093/mnras/stv2146
[32]
Jackson, N. (2015) The Hubble Constant. Living Reviews in Relativity, 18, Article No. 2. https://doi.org/10.1007/lrr-2015-2
[33]
Einstein, A. (1917) Kosmologische Betrachtungen zur allgemeinen Relativit？tstheorie. Sitzungsberichte der K？niglich Preussischen Akademie der Wissenschaften, 8, 142-152. https://ui.adsabs.harvard.edu/abs/1917SPAW.......142E
[34]
de Sitter, W. (1917) On the Relativity of Inertia: Remarks Concerning Einstein’s Latest Hypothesis. Koninklijke Nederlandse Akademie van Wetenschappen Proceedings, 19, 1217-1225. https://ui.adsabs.harvard.edu/abs/1917KNAB...19.1217D
[35]
G？del, K. (1949) An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation. Reviews of Modern Physics, 21, 447-450. https://doi.org/10.1103/revmodphys.21.447
[36]
Segal, I.E. (1976) Mathematical Cosmology and Extragalactic Astronomy. Academic Press.
[37]
Ellis, G.F.R. and Maartens, R. (2004) The Emergent Universe: Inflationary Cosmology with No Singularity. Classical and Quantum Gravity, 21, 223-232. https://doi.org/10.1088/0264-9381/21/1/015
[38]
Einstein, A. (1911) über Den Einflu？ Der Schwerkraft Auf Die Ausbreitung Des Lichtes. Annalen der Physik, 340, 898-908. https://doi.org/10.1002/andp.19113401005
[39]
Ostermann, P. (2002) A Stationary Universe and the Basics of Relativity Theory. arXiv/0211054. https://arxiv.org/abs/physics/0211054
[40]
Potter, F. and Preston, H.G. (2007) Cosmological Redshift Interpreted as Gravitational Redshift. Progress in Physics, 2, 31-33.
[41]
Zwicky, F. (1929) On the Red Shift of Spectral Lines through Interstellar Space. Proceedings of the National Academy of Sciences of the United States of America, 15, 773-779.
[42]
Zwicky, F. (1957) Morphological Astronomy. Springer-Verlag.
[43]
Brynjolfsson, A. (2004) The Type Ia Supernovae and the Hubble’s Constant. arXiv:astro-ph/0407430. https://arxiv.org/abs/astro-ph/0407430
[44]
Ashmore, L. (2006) Recoil between Photons and Electrons Leading to the Hubble Constant and CMB. Galilean Electrodynamics, 17, 53-56.
