In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is uniformly isotropic and homogeneous when viewed on a large enough scale, since the forces are expected to act equally throughout the universe on a large scale, and should, therefore, produce no observable inequalities in the large-scale structuring over the course of evolution of the matter field that was initially laid down by the Big Bang.
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.'
Since the 1990s, observations assuming the cosmological principle have concluded that 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.
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.
[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.
[17] Some authors say that the universe around Earth is isotropic at high significance by studies of the cosmic microwave background temperature maps.
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.
The standard interpretation of the dipole is that it is due to the Doppler effect caused by the motion of the solar system with respect to the CMB rest-frame.
[31] Further claims of anisotropy along the CMB dipole axis have been made with respect to the Hubble diagram of type Ia supernovae[32] and quasars.
Alternatively, Planck data has been used to estimate the velocity with respect to the CMB independently of the dipole, by measuring the subtle aberrations and distortions of fluctuations caused by relativistic beaming[38] and separately using the Sunyaev-Zeldovich effect.