Copernican principle

Unsolved problem in physics:

Are cosmological observations made from Earth representative of observations from the average position in the universe?

Figure 'M' (for Latin *Mundus*) from Johannes Kepler's 1617–1621 *Epitome Astronomiae Copernicanae*, showing the Earth as belonging to just one of any number of similar stars

In physical cosmology, the Copernican principle states that humans, on the Earth or in the Solar System, are not privileged observers of the universe,^[1] that observations from the Earth are representative of observations from the average position in the universe. Named for Copernican heliocentrism, it is a working assumption that arises from a modified cosmological extension of Copernicus' argument of a moving Earth.^[2]

Origin and implications

Hermann Bondi named the principle after Copernicus in the mid-20th century, although the principle itself dates back to the 16th-17th century paradigm shift away from the Ptolemaic system, which placed Earth at the center of the universe. Copernicus proposed that the motion of the planets could be explained by reference to an assumption that the Sun is centrally located and stationary in contrast to the geocentrism. He argued that the apparent retrograde motion of the planets is an illusion caused by Earth's movement around the Sun, which the Copernican model placed at the centre of the universe. Copernicus himself was mainly motivated by technical dissatisfaction with the earlier system and not by support for any mediocrity principle.^[3] Although the Copernican heliocentric model is often described as "demoting" Earth from its central role it had in the Ptolemaic geocentric model, it was successors to Copernicus, notably the 16th century Giordano Bruno, who adopted this new perspective. The Earth's central position had been interpreted as being in the "lowest and filthiest parts". Instead, as Galileo said, the Earth is part of the "dance of the stars" rather than the "sump where the universe's filth and ephemera collect".^[4]^[5] In the late 20th Century, Carl Sagan asked, "Who are we? We find that we live on an insignificant planet of a humdrum star lost in a galaxy tucked away in some forgotten corner of a universe in which there are far more galaxies than people."^[6]

While the Copernican principle is derived from the negation of past assumptions, such as geocentrism, heliocentrism, or galactocentrism which state that humans are at the center of the universe, the Copernican principle is stronger than acentrism, which merely states that humans are not at the center of the universe. The Copernican principle assumes acentrism and also states that human observers or observations from Earth are representative of observations from the average position in the universe. Michael Rowan-Robinson emphasizes the Copernican principle as the threshold test for modern thought, asserting that: "It is evident that in the post-Copernican era of human history, no well-informed and rational person can imagine that the Earth occupies a unique position in the universe."^[7]

Most modern cosmology is based on the assumption that the cosmological principle is almost, but not exactly, true on the largest scales. The Copernican principle represents the irreducible philosophical assumption needed to justify this, when combined with the observations. If one assumes the Copernican principle and observes that the universe appears isotropic or the same in all directions from the vantage point of Earth, then one can infer that the universe is generally homogeneous or the same everywhere (at any given time) and is also isotropic about any given point. These two conditions make up the cosmological principle.^[7]

In practice, astronomers observe that the universe has heterogeneous or non-uniform structures up to the scale of galactic superclusters, filaments and great voids. In the current Lambda-CDM model, the predominant model of cosmology in the modern era, the universe is predicted to become more and more homogeneous and isotropic when observed on larger and larger scales, with little detectable structure on scales of more than about 260 million parsecs.^[8] However, recent evidence from galaxy clusters,^[9]^[10] quasars,^[11] and type Ia supernovae^[12] suggests that isotropy is violated on large scales. Furthermore, various large-scale structures have been discovered, such as the Clowes–Campusano LQG, the Sloan Great Wall,^[13] U1.11, the Huge-LQG, the Hercules–Corona Borealis Great Wall,^[14] and the Giant Arc,^[15] all which indicate that homogeneity might be violated.

On scales comparable to the radius of the observable universe, we see systematic changes with distance from Earth. For instance, at greater distances, galaxies contain more young stars and are less clustered, and quasars appear more numerous. If the Copernican principle is assumed, then it follows that this is evidence for the evolution of the universe with time: this distant light has taken most of the age of the universe to reach Earth and shows the universe when it was young. The most distant light of all, cosmic microwave background radiation, is isotropic to at least one part in a thousand.

Bondi and Thomas Gold used the Copernican principle to argue for the perfect cosmological principle which maintains that the universe is also homogeneous in time, and is the basis for the steady-state cosmology.^[16] However, this strongly conflicts with the evidence for cosmological evolution mentioned earlier: the universe has progressed from extremely different conditions at the Big Bang, and will continue to progress toward extremely different conditions, particularly under the rising influence of dark energy, apparently toward the Big Freeze or Big Rip.

Since the 1990s the term has been used (interchangeably with "the Copernicus method") for J. Richard Gott's Bayesian-inference-based prediction of duration of ongoing events, a generalized version of the Doomsday argument.^{[clarification needed]}

Tests of the principle

The Copernican principle has never been proven, and in the most general sense cannot be proven, but it is implicit in many modern theories of physics. Cosmological models are often derived with reference to the cosmological principle, slightly more general than the Copernican principle, and many tests of these models can be considered tests of the Copernican principle.^[17]

Historical

Before the term Copernican principle was even coined, past assumptions, such as geocentrism, heliocentrism, and galactocentrism, which state that Earth, the Solar System, or the Milky Way respectively were located at the center of the universe, were shown to be false. The Copernican Revolution dethroned Earth to just one of many planets orbiting the Sun. Proper motion was mentioned by Halley. William Herschel found that the Solar System is moving through space within our disk-shaped Milky Way galaxy. Edwin Hubble showed that the Milky Way galaxy is just one of many galaxies in the universe. Examination of the galaxy's position and motion in the universe led to the Big Bang theory and the whole of modern cosmology.

Modern tests

Recent and planned tests relevant to the cosmological and Copernican principles include:

time drift of cosmological redshifts;^[18]
modelling the local gravitational potential using reflection of cosmic microwave background (CMB) photons;^[19]
the redshift dependence of the luminosity of supernovae;^[20]
the kinetic Sunyaev–Zeldovich effect in relation to dark energy;^[21]
cosmic neutrino background;^[22]
the integrated Sachs–Wolfe effect^[23]
testing the isotropy and homogeneity of the CMB;^[24]^[25]^[26]^[27]^[28]
Some authors claim that the KBC Void violates the cosmological principle and thus the Copernican principle.^[29] However, other authors claim that the KBC void is consistent with the cosmological principle and the Copernican principle.^[30]

Physics without the principle

The standard model of cosmology, the Lambda-CDM model, assumes the Copernican principle and the more general cosmological principle. Some cosmologists and theoretical physicists have created models without the cosmological or Copernican principles to constrain the values of observational results, to address specific known issues in the Lambda-CDM model, and to propose tests to distinguish between current models and other possible models.

A prominent example in this context is inhomogeneous cosmology, to model the observed accelerating universe and cosmological constant. Instead of using the current accepted idea of dark energy, this model proposes the universe is much more inhomogeneous than currently assumed, and instead, we are in an extremely large low-density void.^[31] To match observations we would have to be very close to the centre of this void, immediately contradicting the Copernican principle.

While the Big Bang model in cosmology is sometimes said to derive from the Copernican principle in conjunction with redshift observations, the Big Bang model can still be assumed to be valid in absence of the Copernican principle, because the cosmic microwave background, primordial gas clouds, and the structure, evolution, and distribution of galaxies all provide evidence, independent of the Copernican principle, in favor of the Big Bang. However, the key tenets of the Big Bang model, such as the expansion of the universe, become assumptions themselves akin to the Copernican principle, rather than derived from the Copernican principle and observations.

References

^ Peacock, John A. (1998). Cosmological Physics. Cambridge University Press. p. 66. ISBN 978-0-521-42270-3.
^ Bondi, Hermann (1952). Cosmology. Cambridge University Press. p. 13.
^ Kuhn, Thomas S. (1957). The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Harvard University Press. Bibcode:1957crpa.book.....K. ISBN 978-0-674-17103-9.
^ Musser, George (2001). "Copernican Counterrevolution". Scientific American. 284 (3): 24. Bibcode:2001SciAm.284c..24M. doi:10.1038/scientificamerican0301-24a.
^ Danielson, Dennis (2009). "The Bones of Copernicus". American Scientist. 97 (1): 50–57. doi:10.1511/2009.76.50.
^ Sagan, Carl, Cosmos (1980) p. 193
^ ^a ^b Rowan-Robinson, Michael (1996). Cosmology (3rd ed.). Oxford University Press. pp. 62–63. ISBN 978-0-19-851884-6.
^ Yadav, Jaswant; Bagla, J. S.; Khandai, Nishikanta (25 February 2010). "Fractal dimension as a measure of the scale of homogeneity". Monthly Notices of the Royal Astronomical Society. 405 (3): 2009–2015. arXiv:1001.0617. Bibcode:2010MNRAS.405.2009Y. doi:10.1111/j.1365-2966.2010.16612.x. S2CID 118603499.
^ Billings, Lee (April 15, 2020). "Do We Live in a Lopsided Universe?". Scientific American. Retrieved March 24, 2022.
^ Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (8 April 2020). "Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX-T scaling relation". Astronomy & Astrophysics. 636 (April 2020): 42. arXiv:2004.03305. Bibcode:2020A&A...636A..15M. doi:10.1051/0004-6361/201936602. S2CID 215238834. Retrieved 24 March 2022.
^ Secrest, Nathan J.; von Hausegger, Sebastian; Rameez, Mohamed; Mohayaee, Roya; Sarkar, Subir; Colin, Jacques (February 25, 2021). "A Test of the Cosmological Principle with Quasars". The Astrophysical Journal Letters. 908 (2): L51. arXiv:2009.14826. Bibcode:2021ApJ...908L..51S. doi:10.3847/2041-8213/abdd40. S2CID 222066749.
^ Javanmardi, B.; Porciani, C.; Kroupa, P.; Pflamm-Altenburg, J. (August 27, 2015). "Probing the Isotropy of Cosmic Acceleration Traced By Type Ia Supernovae". The Astrophysical Journal Letters. 810 (1): 47. arXiv:1507.07560. Bibcode:2015ApJ...810...47J. doi:10.1088/0004-637X/810/1/47. S2CID 54958680. Retrieved March 24, 2022.
^ Gott, J. Richard III; et al. (May 2005). "A Map of the Universe". The Astrophysical Journal. 624 (2): 463–484. arXiv:astro-ph/0310571. Bibcode:2005ApJ...624..463G. doi:10.1086/428890. S2CID 9654355.
^ Horvath, I.; Hakkila, J.; Bagoly, Z. (2013). "The largest structure of the Universe, defined by Gamma-Ray Bursts". arXiv:1311.1104 [astro-ph.CO].
^ "Line of galaxies is so big it breaks our understanding of the universe".
^ Bondi, H.; Gold, T. (1948). "The Steady-State Theory of the Expanding Universe". Monthly Notices of the Royal Astronomical Society. 108 (3): 252–270. Bibcode:1948MNRAS.108..252B. doi:10.1093/mnras/108.3.252.
^ Clarkson, C.; Bassett, B.; Lu, T. (2008). "A General Test of the Copernican Principle". Physical Review Letters. 101 (1): 011301. arXiv:0712.3457. Bibcode:2008PhRvL.101a1301C. doi:10.1103/PhysRevLett.101.011301. PMID 18764099. S2CID 32735465.
^ Uzan, J. P.; Clarkson, C.; Ellis, G. (2008). "Time Drift of Cosmological Redshifts as a Test of the Copernican Principle". Physical Review Letters. 100 (19): 191303. arXiv:0801.0068. Bibcode:2008PhRvL.100s1303U. doi:10.1103/PhysRevLett.100.191303. PMID 18518435. S2CID 31455609.
^ Caldwell, R.; Stebbins, A. (2008). "A Test of the Copernican Principle". Physical Review Letters. 100 (19): 191302. arXiv:0711.3459. Bibcode:2008PhRvL.100s1302C. doi:10.1103/PhysRevLett.100.191302. PMID 18518434. S2CID 5468549.
^ Clifton, T.; Ferreira, P.; Land, K. (2008). "Living in a Void: Testing the Copernican Principle with Distant Supernovae". Physical Review Letters. 101 (13): 131302. arXiv:0807.1443. Bibcode:2008PhRvL.101m1302C. doi:10.1103/PhysRevLett.101.131302. PMID 18851434. S2CID 17421918.
^ Zhang, P.; Stebbins, A. (2011). "Confirmation of the Copernican principle through the anisotropic kinetic Sunyaev Zel'dovich effect". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 369 (1957): 5138–5145. Bibcode:2011RSPTA.369.5138Z. doi:10.1098/rsta.2011.0294. PMID 22084299.
^ Jia, J.; Zhang, H. (2008). "Can the Copernican principle be tested using the cosmic neutrino background?". Journal of Cosmology and Astroparticle Physics. 2008 (12): 002. arXiv:0809.2597. Bibcode:2008JCAP...12..002J. doi:10.1088/1475-7516/2008/12/002. S2CID 14320348.
^ Tomita, K.; Inoue, K. (2009). "Probing violation of the Copernican principle via the integrated Sachs–Wolfe effect". Physical Review D. 79 (10): 103505. arXiv:0903.1541. Bibcode:2009PhRvD..79j3505T. doi:10.1103/PhysRevD.79.103505. S2CID 118478786.
^ Clifton, T.; Clarkson, C.; Bull, P. (2012). "Isotropic Blackbody Cosmic Microwave Background Radiation as Evidence for a Homogeneous Universe". Physical Review Letters. 109 (5): 051303. arXiv:1111.3794. Bibcode:2012PhRvL.109e1303C. doi:10.1103/PhysRevLett.109.051303. PMID 23006164. S2CID 119278505.
^ Kim, J.; Naselsky, P. (2011). "Lack of Angular Correlation and Odd-Parity Preference in Cosmic Microwave Background Data". The Astrophysical Journal. 739 (2): 79. arXiv:1011.0377. Bibcode:2011ApJ...739...79K. doi:10.1088/0004-637X/739/2/79. S2CID 118580902.
^ Copi, C. J.; Huterer, D.; Schwarz, D. J.; Starkman, G. D. (2010). "Large-Angle Anomalies in the CMB". Advances in Astronomy. 2010: 1–17. arXiv:1004.5602. Bibcode:2010AdAst2010E..92C. doi:10.1155/2010/847541. S2CID 13823900.
^ Ade; et al. (Planck Collaboration) (2013). "Planck 2013 results. XXIII. Isotropy and Statistics of the CMB". Astronomy & Astrophysics. 571: A23. arXiv:1303.5083. Bibcode:2014A&A...571A..23P. doi:10.1051/0004-6361/201321534. S2CID 13037411.
^ Longo, Michael (2007). "Does the Universe Have a Handedness?". arXiv:astro-ph/0703325.
^ Haslbauer, M.; Banik, I.; Kroupa, P. (2020-12-21). "The KBC void and Hubble tension contradict LCDM on a Gpc scale – Milgromian dynamics as a possible solution". Monthly Notices of the Royal Astronomical Society. 499 (2): 2845–2883. arXiv:2009.11292. Bibcode:2020MNRAS.499.2845H. doi:10.1093/mnras/staa2348. ISSN 0035-8711.
^ Sahlén, Martin; Zubeldía, Íñigo; Silk, Joseph (2016). "Cluster–Void Degeneracy Breaking: Dark Energy, Planck, and the Largest Cluster and Void". The Astrophysical Journal Letters. 820 (1): L7. arXiv:1511.04075. Bibcode:2016ApJ...820L...7S. doi:10.3847/2041-8205/820/1/L7. ISSN 2041-8205. S2CID 119286482.
^ February, S.; Larena, J.; Smith, M.; Clarkson, C. (2010). "Rendering dark energy void". Monthly Notices of the Royal Astronomical Society. 405 (4): 2231. arXiv:0909.1479. Bibcode:2010MNRAS.405.2231F. doi:10.1111/j.1365-2966.2010.16627.x. S2CID 118518082.

[1] Peacock, John A. (1998). Cosmological Physics. Cambridge University Press. p. 66. ISBN 978-0-521-42270-3.

[2] Bondi, Hermann (1952). Cosmology. Cambridge University Press. p. 13.

[3] Kuhn, Thomas S. (1957). The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Harvard University Press. Bibcode:1957crpa.book.....K. ISBN 978-0-674-17103-9.

[4] Musser, George (2001). "Copernican Counterrevolution". Scientific American. 284 (3): 24. Bibcode:2001SciAm.284c..24M. doi:10.1038/scientificamerican0301-24a.

[5] Danielson, Dennis (2009). "The Bones of Copernicus". American Scientist. 97 (1): 50–57. doi:10.1511/2009.76.50.

[6] Sagan, Carl, Cosmos (1980) p. 193

[RowanRobinson1996-7] Rowan-Robinson, Michael (1996). Cosmology (3rd ed.). Oxford University Press. pp. 62–63. ISBN 978-0-19-851884-6.

[Yadav-8] Yadav, Jaswant; Bagla, J. S.; Khandai, Nishikanta (25 February 2010). "Fractal dimension as a measure of the scale of homogeneity". Monthly Notices of the Royal Astronomical Society. 405 (3): 2009–2015. arXiv:1001.0617. Bibcode:2010MNRAS.405.2009Y. doi:10.1111/j.1365-2966.2010.16612.x. S2CID 118603499.

[Billings-9] Billings, Lee (April 15, 2020). "Do We Live in a Lopsided Universe?". Scientific American. Retrieved March 24, 2022.

[Migkas_et_al-10] Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (8 April 2020). "Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX-T scaling relation". Astronomy & Astrophysics. 636 (April 2020): 42. arXiv:2004.03305. Bibcode:2020A&A...636A..15M. doi:10.1051/0004-6361/201936602. S2CID 215238834. Retrieved 24 March 2022.

[11] Secrest, Nathan J.; von Hausegger, Sebastian; Rameez, Mohamed; Mohayaee, Roya; Sarkar, Subir; Colin, Jacques (February 25, 2021). "A Test of the Cosmological Principle with Quasars". The Astrophysical Journal Letters. 908 (2): L51. arXiv:2009.14826. Bibcode:2021ApJ...908L..51S. doi:10.3847/2041-8213/abdd40. S2CID 222066749.

[12] Javanmardi, B.; Porciani, C.; Kroupa, P.; Pflamm-Altenburg, J. (August 27, 2015). "Probing the Isotropy of Cosmic Acceleration Traced By Type Ia Supernovae". The Astrophysical Journal Letters. 810 (1): 47. arXiv:1507.07560. Bibcode:2015ApJ...810...47J. doi:10.1088/0004-637X/810/1/47. S2CID 54958680. Retrieved March 24, 2022.

[apj624_2_463-13] Gott, J. Richard III; et al. (May 2005). "A Map of the Universe". The Astrophysical Journal. 624 (2): 463–484. arXiv:astro-ph/0310571. Bibcode:2005ApJ...624..463G. doi:10.1086/428890. S2CID 9654355.

[14] Horvath, I.; Hakkila, J.; Bagoly, Z. (2013). "The largest structure of the Universe, defined by Gamma-Ray Bursts". arXiv:1311.1104 [astro-ph.CO].

[15] "Line of galaxies is so big it breaks our understanding of the universe".

[BondiGold1948-16] Bondi, H.; Gold, T. (1948). "The Steady-State Theory of the Expanding Universe". Monthly Notices of the Royal Astronomical Society. 108 (3): 252–270. Bibcode:1948MNRAS.108..252B. doi:10.1093/mnras/108.3.252.

[clarkson-17] Clarkson, C.; Bassett, B.; Lu, T. (2008). "A General Test of the Copernican Principle". Physical Review Letters. 101 (1): 011301. arXiv:0712.3457. Bibcode:2008PhRvL.101a1301C. doi:10.1103/PhysRevLett.101.011301. PMID 18764099. S2CID 32735465.

[uzan-18] Uzan, J. P.; Clarkson, C.; Ellis, G. (2008). "Time Drift of Cosmological Redshifts as a Test of the Copernican Principle". Physical Review Letters. 100 (19): 191303. arXiv:0801.0068. Bibcode:2008PhRvL.100s1303U. doi:10.1103/PhysRevLett.100.191303. PMID 18518435. S2CID 31455609.

[caldwell-19] Caldwell, R.; Stebbins, A. (2008). "A Test of the Copernican Principle". Physical Review Letters. 100 (19): 191302. arXiv:0711.3459. Bibcode:2008PhRvL.100s1302C. doi:10.1103/PhysRevLett.100.191302. PMID 18518434. S2CID 5468549.

[clifton-20] Clifton, T.; Ferreira, P.; Land, K. (2008). "Living in a Void: Testing the Copernican Principle with Distant Supernovae". Physical Review Letters. 101 (13): 131302. arXiv:0807.1443. Bibcode:2008PhRvL.101m1302C. doi:10.1103/PhysRevLett.101.131302. PMID 18851434. S2CID 17421918.

[zhang-21] Zhang, P.; Stebbins, A. (2011). "Confirmation of the Copernican principle through the anisotropic kinetic Sunyaev Zel'dovich effect". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 369 (1957): 5138–5145. Bibcode:2011RSPTA.369.5138Z. doi:10.1098/rsta.2011.0294. PMID 22084299.

[jia-22] Jia, J.; Zhang, H. (2008). "Can the Copernican principle be tested using the cosmic neutrino background?". Journal of Cosmology and Astroparticle Physics. 2008 (12): 002. arXiv:0809.2597. Bibcode:2008JCAP...12..002J. doi:10.1088/1475-7516/2008/12/002. S2CID 14320348.

[tomita-23] Tomita, K.; Inoue, K. (2009). "Probing violation of the Copernican principle via the integrated Sachs–Wolfe effect". Physical Review D. 79 (10): 103505. arXiv:0903.1541. Bibcode:2009PhRvD..79j3505T. doi:10.1103/PhysRevD.79.103505. S2CID 118478786.

[bull-24] Clifton, T.; Clarkson, C.; Bull, P. (2012). "Isotropic Blackbody Cosmic Microwave Background Radiation as Evidence for a Homogeneous Universe". Physical Review Letters. 109 (5): 051303. arXiv:1111.3794. Bibcode:2012PhRvL.109e1303C. doi:10.1103/PhysRevLett.109.051303. PMID 23006164. S2CID 119278505.

[kim-25] Kim, J.; Naselsky, P. (2011). "Lack of Angular Correlation and Odd-Parity Preference in Cosmic Microwave Background Data". The Astrophysical Journal. 739 (2): 79. arXiv:1011.0377. Bibcode:2011ApJ...739...79K. doi:10.1088/0004-637X/739/2/79. S2CID 118580902.

[copi-26] Copi, C. J.; Huterer, D.; Schwarz, D. J.; Starkman, G. D. (2010). "Large-Angle Anomalies in the CMB". Advances in Astronomy. 2010: 1–17. arXiv:1004.5602. Bibcode:2010AdAst2010E..92C. doi:10.1155/2010/847541. S2CID 13823900.

[planck-27] Ade; et al. (Planck Collaboration) (2013). "Planck 2013 results. XXIII. Isotropy and Statistics of the CMB". Astronomy & Astrophysics. 571: A23. arXiv:1303.5083. Bibcode:2014A&A...571A..23P. doi:10.1051/0004-6361/201321534. S2CID 13037411.

[longo-28] Longo, Michael (2007). "Does the Universe Have a Handedness?". arXiv:astro-ph/0703325.

[Haslbauer-29] Haslbauer, M.; Banik, I.; Kroupa, P. (2020-12-21). "The KBC void and Hubble tension contradict LCDM on a Gpc scale – Milgromian dynamics as a possible solution". Monthly Notices of the Royal Astronomical Society. 499 (2): 2845–2883. arXiv:2009.11292. Bibcode:2020MNRAS.499.2845H. doi:10.1093/mnras/staa2348. ISSN 0035-8711.

[30] Sahlén, Martin; Zubeldía, Íñigo; Silk, Joseph (2016). "Cluster–Void Degeneracy Breaking: Dark Energy, Planck, and the Largest Cluster and Void". The Astrophysical Journal Letters. 820 (1): L7. arXiv:1511.04075. Bibcode:2016ApJ...820L...7S. doi:10.3847/2041-8205/820/1/L7. ISSN 2041-8205. S2CID 119286482.

[void-31] February, S.; Larena, J.; Smith, M.; Clarkson, C. (2010). "Rendering dark energy void". Monthly Notices of the Royal Astronomical Society. 405 (4): 2231. arXiv:0909.1479. Bibcode:2010MNRAS.405.2231F. doi:10.1111/j.1365-2966.2010.16627.x. S2CID 118518082.

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Copernican principle

Origin and implications

Tests of the principle

Historical

Modern tests

Physics without the principle

See also

References

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