# Cosmological principle

Unsolved problem in physics:

Is the universe homogeneous and isotropic at large enough scales, as claimed by the cosmological principle and assumed by all models that use the Friedmann–Lemaître–Robertson–Walker metric, including the current version of the ΛCDM model, or is the universe inhomogeneous or anisotropic?[1][2][3]

In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throughout the universe, and should, therefore, produce no observable irregularities in the large-scale structuring over the course of evolution of the matter field that was initially laid down by the Big Bang.

## Definition

Astronomer William Keel explains:

The cosmological principle is usually stated formally as 'Viewed on a sufficiently large scale, the properties of the universe are the same for all observers.' This amounts to the strongly philosophical statement that the part of the universe which we can see is a fair sample, and that the same physical laws apply throughout. In essence, this in a sense says that the universe is knowable and is playing fair with scientists.[4]

The cosmological principle depends on a definition of "observer," and contains an implicit qualification and two testable consequences.

"Observers" means any observer at any location in the universe, not simply any human observer at any location on Earth: as Andrew Liddle puts it, "the cosmological principle [means that] the universe looks the same whoever and wherever you are."[5]

The qualification is that variation in physical structures can be overlooked, provided this does not imperil the uniformity of conclusions drawn from observation: the Sun is different from the Earth, our galaxy is different from a black hole, some galaxies advance toward rather than recede from us, and the universe has a "foamy" texture of galaxy clusters and voids, but none of these different structures appears to violate the basic laws of physics.

The two testable structural consequences of the cosmological principle are homogeneity and isotropy. Homogeneity means that the same observational evidence is available to observers at different locations in the universe ("the part of the universe which we can see is a fair sample"). Isotropy means that the same observational evidence is available by looking in any direction in the universe ("the same physical laws apply throughout"[dubious ]). The principles are distinct but closely related, because a universe that appears isotropic from any two (for a spherical geometry, three) locations must also be homogeneous.

## Origin

The cosmological principle is first clearly asserted in the Philosophiæ Naturalis Principia Mathematica (1687) of Isaac Newton.[dubious ] In contrast to earlier classical or medieval cosmologies, in which Earth rested at the center of universe, Newton conceptualized the Earth as a sphere in orbital motion around the Sun within an empty space that extended uniformly in all directions to immeasurably large distances. He then showed, through a series of mathematical proofs on detailed observational data of the motions of planets and comets, that their motions could be explained by a single principle of "universal gravitation" that applied as well to the orbits of the Galilean moons around Jupiter, the Moon around the Earth, the Earth around the Sun, and to falling bodies on Earth. That is, he asserted the equivalent material nature of all bodies within the Solar System, the identical nature of the Sun and distant stars and thus the uniform extension of the physical laws of motion to a great distance beyond the observational location of Earth itself.

## Implications

Since the 1990s, observations have shown that, if one assumes the cosmological principle, then around 68% of the mass–energy density of the universe can be attributed to dark energy, which led to the development of the ΛCDM model.[6][7][8]

Observations show that more distant galaxies are closer together and have lower content of chemical elements heavier than lithium.[9] Applying the cosmological principle, this suggests that heavier elements were not created in the Big Bang but were produced by nucleosynthesis in giant stars and expelled across a series of supernovae explosions and new star formation from the supernovae remnants, which means heavier elements would accumulate over time. Another observation is that the furthest galaxies (earlier time) are often more fragmentary, interacting and unusually shaped than local galaxies (recent time), suggesting evolution in galaxy structure as well.

A related implication of the cosmological principle is that the largest discrete structures in the universe are in mechanical equilibrium. Homogeneity and isotropy of matter at the largest scales would suggest that the largest discrete structures are parts of a single indiscrete form, like the crumbs which make up the interior of a cake. At extreme cosmological distances, the property of mechanical equilibrium in surfaces lateral to the line of sight can be empirically tested; however, under the assumption of the cosmological principle, it cannot be detected parallel to the line of sight (see timeline of the universe).

Cosmologists agree that in accordance with observations of distant galaxies, a universe must be non-static if it follows the cosmological principle. In 1923, Alexander Friedmann set out a variant of Albert Einstein's equations of general relativity that describe the dynamics of a homogeneous isotropic universe.[10][11] Independently, Georges Lemaître derived in 1927 the equations of an expanding universe from the General Relativity equations.[12] Thus, a non-static universe is also implied, independent of observations of distant galaxies, as the result of applying the cosmological principle to general relativity.

## Criticism

Karl Popper criticized the cosmological principle on the grounds that it makes "our lack of knowledge a principle of knowing something". He summarized his position as:

the “cosmological principles” were, I fear, dogmas that should not have been proposed.[13]

## Observations

Although the universe is inhomogeneous at smaller scales, according to the ΛCDM model it ought to be isotropic and statistically homogeneous on scales larger than 250 million light years. However, recent findings have suggested that violations of the cosmological principle exist in the universe and thus have called the ΛCDM model into question, with some authors suggesting that the cosmological principle is now obsolete and the Friedmann–Lemaître–Robertson–Walker metric breaks down in the late universe.[1]

### Violations of isotropy

The cosmic microwave background (CMB) is predicted by the ΛCDM model to be isotropic, that is to say that its intensity is about the same whichever direction we look at.[14] However, recent findings have called the cosmological principle in ΛCDM model into question. Data from the Planck Mission shows hemispheric bias in 2 respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The European Space Agency (the governing body of the Planck Mission) has concluded that these anisotropies are, in fact, statistically significant and can no longer be ignored.[15] Nevertheless, some authors say that the universe around Earth is isotropic at high significance by studies of the cosmic microwave background temperature maps.[16]

Furthermore, evidence from galaxy clusters,[2][3] quasars,[17] and type Ia supernovae[18] suggests that isotropy is violated on large scales.

### Violations of homogeneity

The cosmological principle implies that at a sufficiently large scale, the universe is homogeneous. Based on N-body simulations in a ΛCDM universe, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales of 260/h Mpc or more.[19]

A number of observations have been reported to be in conflict with predictions of maximal structure sizes:

• The Clowes–Campusano LQG, discovered in 1991, has a length of 580 Mpc, and is marginally larger than the consistent scale.
• The Sloan Great Wall, discovered in 2003, has a length of 423 Mpc,[20] which is only just consistent with the cosmological principle.
• U1.11, a large quasar group discovered in 2011, has a length of 780 Mpc, and is two times larger than the upper limit of the homogeneity scale.
• The Huge-LQG, discovered in 2012, is three times longer than, and twice as wide as is predicted possible according to these current models, and so challenges our understanding of the universe on large scales.
• In November 2013, a new structure 10 billion light years away measuring 2000–3000 Mpc (more than seven times that of the SGW) has been discovered, the Hercules–Corona Borealis Great Wall, putting further doubt on the validity of the cosmological principle.[21]
• In September 2020, a 4.9σ conflict was found between the kinematic explanation of the CMB dipole and the measurement of the dipole in the angular distribution of a flux-limited, all-sky sample of 1.36 million quasars.[22]
• In June 2021, the Giant Arc was discovered, a structure spanning approximately 1000 Mpc.[23] It is located 2820 MPc away and consists of galaxies, galactic clusters, gas, and dust.

However, as pointed out by Seshadri Nadathur in 2013 using statistical properties,[24] the existence of structures larger than the homogeneous scale (260/h Mpc by Yadav's estimation[19]) does not necessarily violate the cosmological principle in the ΛCDM model (see Huge-LQG#Dispute).

The homogeneity of the cosmic microwave background over cosmological scales is still a matter of debate.[25]

## CMB dipole

Unsolved problem in physics:

Is the CMB dipole purely kinematic, or does it signal anisotropy of the universe, resulting in the breakdown of the FLRW metric and the cosmological principle?[1]

As stated above, it is true that the cosmic microwave background provides a snapshot of an isotropic and homogeneous universe. Nevertheless, what is often not advertised is that there is a dipole anisotropy in the cosmic microwave background. The amplitude of the dipole exceeds the amplitudes of the other temperature fluctuations, and for this reason, it is subtracted on the assumption that it is a Doppler effect, or simply due to relative motion. In recent years this assumption has been tested and current results suggest our motion with respect to distant radio galaxies [26] and quasars [27] differs from our motion with respect to the cosmic microwave background. The same conclusion has been reached in recent studies of the Hubble diagram of Type Ia supernovae[28] and quasars.[29] This contradicts the cosmological principle and challenges the assumption that the CMB dipole is simply due to relative motion.

This potential misinterpretation of the CMB dipole is hinted at through a number of other observations. First, even within the cosmic microwave background, there are curious directional alignments [30] and an anomalous parity asymmetry [31] that may have an origin in the CMB dipole.[32] Separately, the CMB dipole direction has emerged as a preferred direction in studies of alignments in quasar polarizations,[33] scaling relations in galaxy clusters,[34][35] strong lensing time delay,[36] Type Ia supernovae,[37] and quasars & gamma-ray bursts as standard candles.[38] The fact that all these independent observables, based on different physics, are tracking the CMB dipole direction suggests that the Universe is anisotropic in the direction of the CMB dipole.

## Perfect cosmological principle

The perfect cosmological principle is an extension of the cosmological principle, and states that the universe is homogeneous and isotropic in space and time. In this view the universe looks the same everywhere (on the large scale), the same as it always has and always will. The perfect cosmological principle underpins Steady State theory and emerges[clarification needed] from chaotic inflation theory.[39][40][41]

## References

1. ^ a b c Elcio Abdalla; Guillermo Franco Abellán; et al. (11 Mar 2022), Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies, arXiv:2203.06142v1
2. ^ a b Lee Billings (April 15, 2020). "Do We Live in a Lopsided Universe?". Scientific American. Retrieved March 24, 2022.
3. ^ a b 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. doi:10.1051/0004-6361/201936602. S2CID 215238834. Retrieved 24 March 2022.
4. ^ William C. Keel (2007). The Road to Galaxy Formation (2nd ed.). Springer-Praxis. p. 2. ISBN 978-3-540-72534-3.
5. ^ Andrew Liddle (2003). An Introduction to Modern Cosmology (2nd ed.). John Wiley & Sons. p. 2. ISBN 978-0-470-84835-7.
6. ^ Ellis, G. F. R. (2009). "Dark energy and inhomogeneity". Journal of Physics: Conference Series. 189: 012011. doi:10.1088/1742-6596/189/1/012011.
7. ^ Jacques Colin; Roya Mohayaee; Mohamed Rameez; Subir Sarkar (20 November 2019). "Evidence for anisotropy of cosmic acceleration". Astronomy and Astrophysics. 631: L13. arXiv:1808.04597. doi:10.1051/0004-6361/201936373. S2CID 208175643. Retrieved 25 March 2022.
8. ^ Redd (2013)
9. ^ Image:CMB Timeline75.jpg – NASA (public domain image)
10. ^ Alexander Friedmann (1923). Die Welt als Raum und Zeit (The World as Space and Time). Ostwalds Klassiker der exakten Wissenschaften. ISBN 978-3-8171-3287-4. OCLC 248202523..
11. ^ Ėduard Abramovich Tropp; Viktor Ya. Frenkel; Artur Davidovich Chernin (1993). Alexander A. Friedmann: The Man who Made the Universe Expand. Cambridge University Press. p. 219. ISBN 978-0-521-38470-4.
12. ^ Lemaître, Georges (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. A47 (5): 49–56. Bibcode:1927ASSB...47...49L. translated by A. S. Eddington: Lemaître, Georges (1931). "Expansion of the universe, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulæ". Monthly Notices of the Royal Astronomical Society. 91 (5): 483–490. Bibcode:1931MNRAS..91..483L. doi:10.1093/mnras/91.5.483.
13. ^ Helge Kragh: “The most philosophically of all the sciences”: Karl Popper and physical cosmology Archived 2013-07-20 at the Wayback Machine (2012)
14. ^ "Australian study backs major assumption of cosmology". 17 September 2012.
15. ^ "Simple but challenging: the Universe according to Planck". ESA Science & Technology. October 5, 2016 [March 21, 2013]. Retrieved October 29, 2016.
16. ^ Saadeh D, Feeney SM, Pontzen A, Peiris HV, McEwen, JD (2016). "How Isotropic is the Universe?". Physical Review Letters. 117 (13): 131302. arXiv:1605.07178. Bibcode:2016PhRvL.117m1302S. doi:10.1103/PhysRevLett.117.131302. PMID 27715088. S2CID 453412.
17. ^ Nathan J. Secrest; Sebastian von Hausegger; Mohamed Rameez; Roya Mohayaee; Subir Sarkar; Jacques Colin (February 25, 2021). "A Test of the Cosmological Principle with Quasars". The Astrophysical Journal Letters. 908 (2): L51. arXiv:2009.14826. doi:10.3847/2041-8213/abdd40. S2CID 222066749. Retrieved March 24, 2022.
18. ^ B. Javanmardi; C. Porciani; P. Kroupa; J. Pflamm-Altenburg (August 27, 2015). "Probing the Isotropy of Cosmic Acceleration Traced By Type Ia Supernovae". The Astrophysical Journal Letters. 810 (1): 47. arXiv:1507.07560. doi:10.1088/0004-637X/810/1/47. S2CID 54958680. Retrieved March 24, 2022.
19. ^ a b Yadav, Jaswant; J. S. Bagla; Nishikanta Khandai (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.
20. ^ 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.
21. ^ Horvath, I.; Hakkila, J.; Bagoly, Z. (2013). "The largest structure of the Universe, defined by Gamma-Ray Bursts". arXiv:1311.1104 [astro-ph.CO].
22. ^ Secrest, Nathan; von Hausegger, Sebastian; Rameez, Mohamed; Mohayaee, Roya; Sarkar, Subir; Colin, Jacques (2021-02-01). "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. ISSN 2041-8205. S2CID 222066749.
23. ^
24. ^ Nadathur, Seshadri (2013). "Seeing patterns in noise: gigaparsec-scale 'structures' that do not violate homogeneity". Monthly Notices of the Royal Astronomical Society. 434 (1): 398–406. arXiv:1306.1700. Bibcode:2013MNRAS.434..398N. doi:10.1093/mnras/stt1028. S2CID 119220579.
25. ^ Sylos-Labini F, Tekhanovich D, Baryshev Y (2014). "Spatial density fluctuations and selection effects in galaxy redshift surveys". Journal of Cosmology and Astroparticle Physics. 7 (13): 35. arXiv:1406.5899. Bibcode:2014JCAP...07..035S. doi:10.1088/1475-7516/2014/07/035. S2CID 118393719.
26. ^ Siewert, Thilo M.; Schmidt-Rubart, Matthias; Schwarz, Dominik J. (2021). "Cosmic radio dipole: Estimators and frequency dependence". Astronomy & Astrophysics. 653: A9. arXiv:2010.08366. Bibcode:2021A&A...653A...9S. doi:10.1051/0004-6361/202039840. S2CID 223953708.
27. ^ Secrest, Nathan; von Hausegger, Sebastian; Rameez, Mohamed; Mohayaee, Roya; Sarkar, Subir; Colin, Jacques (25 February 2021). "A Test of the Cosmological Principle with Quasars". The Astrophysical Journal. 908 (2): L51. arXiv:2009.14826. Bibcode:2021ApJ...908L..51S. doi:10.3847/2041-8213/abdd40. ISSN 2041-8213. S2CID 222066749.
28. ^ Singal, Ashok K. (22 June 2021). "Peculiar motion of Solar system from the Hubble diagram of supernovae Ia and its implications for cosmology". arXiv:2106.11968 [astro-ph.CO].
29. ^ Singal, Ashok K. (2022). "Solar system peculiar motion from the Hubble diagram of quasars and testing the cosmological principle". Monthly Notices of the Royal Astronomical Society. 511 (2): 1819–1829. arXiv:2107.09390. doi:10.1093/mnras/stac144.
30. ^ de Oliveira-Costa, Angelica; Tegmark, Max; Zaldarriaga, Matias; Hamilton, Andrew (25 March 2004). "The significance of the largest scale CMB fluctuations in WMAP". Physical Review D. 69 (6): 063516. arXiv:astro-ph/0307282. Bibcode:2004PhRvD..69f3516D. doi:10.1103/PhysRevD.69.063516. ISSN 1550-7998. S2CID 119463060.
31. ^ Land, Kate; Magueijo, Joao (28 November 2005). "Is the Universe odd?". Physical Review D. 72 (10): 101302. arXiv:astro-ph/0507289. Bibcode:2005PhRvD..72j1302L. doi:10.1103/PhysRevD.72.101302. ISSN 1550-7998. S2CID 119333704.
32. ^ Kim, Jaiseung; Naselsky, Pavel (10 May 2010). "Anomalous parity asymmetry of the Wilkinson Microwave Anisotropy Probe power spectrum data at low multipoles". The Astrophysical Journal. 714 (2): L265–L267. arXiv:1001.4613. Bibcode:2010ApJ...714L.265K. doi:10.1088/2041-8205/714/2/L265. ISSN 2041-8205. S2CID 24389919.
33. ^ Hutsemekers, D.; Cabanac, R.; Lamy, H.; Sluse, D. (October 2005). "Mapping extreme-scale alignments of quasar polarization vectors". Astronomy & Astrophysics. 441 (3): 915–930. arXiv:astro-ph/0507274. Bibcode:2005A&A...441..915H. doi:10.1051/0004-6361:20053337. ISSN 0004-6361. S2CID 14626666.
34. ^ Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (April 2020). "Probing cosmic isotropy with a new X-ray galaxy cluster sample through the ${\displaystyle L_{\text{X}}-T}$ scaling relation". Astronomy & Astrophysics. 636: A15. arXiv:2004.03305. Bibcode:2020A&A...636A..15M. doi:10.1051/0004-6361/201936602. ISSN 0004-6361. S2CID 215238834.
35. ^ Migkas, K.; Pacaud, F.; Schellenberger, G.; Erler, J.; Nguyen-Dang, N. T.; Reiprich, T. H.; Ramos-Ceja, M. E.; Lovisari, L. (May 2021). "Cosmological implications of the anisotropy of ten galaxy cluster scaling relations". Astronomy & Astrophysics. 649: A151. arXiv:2103.13904. Bibcode:2021A&A...649A.151M. doi:10.1051/0004-6361/202140296. ISSN 0004-6361. S2CID 232352604.
36. ^ Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (16 September 2021). "Does Hubble Tension Signal a Breakdown in FLRW Cosmology?". Classical and Quantum Gravity. 38 (18): 184001. arXiv:2105.09790. Bibcode:2021CQGra..38r4001K. doi:10.1088/1361-6382/ac1a81. ISSN 0264-9381. S2CID 234790314.
37. ^ Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (2022). "Hints of FLRW breakdown from supernovae". Physical Review D. 105 (6). arXiv:2106.02532. doi:10.1103/PhysRevD.105.063514. S2CID 235352881.
38. ^ Luongo, Orlando; Muccino, Marco; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (30 August 2021). "On Larger $H_0$ Values in the CMB Dipole Direction". arXiv:2108.13228 [astro-ph.CO].
39. ^ Aguirre, Anthony & Gratton, Steven (2003). "Inflation without a beginning: A null boundary proposal". Phys. Rev. D. 67 (8): 083515. arXiv:gr-qc/0301042. Bibcode:2003PhRvD..67h3515A. doi:10.1103/PhysRevD.67.083515. S2CID 37260723.
40. ^ Aguirre, Anthony & Gratton, Steven (2002). "Steady-State Eternal Inflation". Phys. Rev. D. 65 (8): 083507. arXiv:astro-ph/0111191. Bibcode:2002PhRvD..65h3507A. doi:10.1103/PhysRevD.65.083507. S2CID 118974302.
41. ^