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 – discuss]}). 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.

The cosmological principle is first clearly asserted in the Philosophiæ Naturalis Principia Mathematica (1687) of Isaac Newton.^{[dubious – discuss]} 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.

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.

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]

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 isotropyEdit

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 homogeneityEdit

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]

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]