Friedmann–Lemaître–Robertson–Walker metric in the context of "BKL singularity"

The discovery of cosmic microwave background radiation constitutes a major development in modern physical cosmology. In 1964, American physicist Arno Allan Penzias and radio-astronomer Robert Woodrow Wilson discovered the cosmic microwave background (CMB), estimating its temperature as 3.5 K, as they experimented with the Holmdel Horn Antenna. The new measurements were accepted as important evidence for a hot early Universe (Big Bang theory) and as evidence against the rival steady state theory as theoretical work around 1950 showed the need for a CMB for consistency with the simplest relativistic universe models. In 1978, Penzias and Wilson were awarded the Nobel Prize for Physics for their joint measurement. There had been a prior measurement of the cosmic background radiation (CMB) by Andrew McKellar in 1941 at an effective temperature of 2.3 K using CN stellar absorption lines observed by W. S. Adams. Although no reference to the CMB is made by McKellar, it was not until much later after the Penzias and Wilson measurements, that the significance of this earlier measurement was understood.

Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry. Curved spaces can generally be described by Riemannian geometry, though some simple cases can be described in other ways.

Curved spaces play an essential role in general relativity, where gravity is often visualized as curved spacetime. The Friedmann–Lemaître–Robertson–Walker metric is a curved metric which forms the current foundation for the description of the expansion of the universe and the shape of the universe. The fact that photons have no mass yet are distorted by gravity, means that the explanation would have to be something besides photonic mass. Hence, the belief that large bodies curve space and so light, traveling on the curved space will, appear as being subject to gravity. It is not, but it is subject to the curvature of space.

The Friedmann equations, also known as the Friedmann–Lemaître (FL) equations, are a set of equations in physical cosmology that govern cosmic expansion in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann in 1922 from Einstein's field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect fluid with a given mass density ρ and pressure p. The equations for negative spatial curvature were given by Friedmann in 1924.The physical models built on the Friedmann equations are called FRW or FLRW models and form the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.

Distance measures are used in physical cosmology to generalize the concept of distance between two objects or events in an expanding universe. They may be used to tie some observable quantity (such as the luminosity of a distant quasar, the redshift of a distant galaxy, or the angular size of the acoustic peaks in the cosmic microwave background (CMB) power spectrum) to another quantity that is not directly observable, but is more convenient for calculations (such as the comoving coordinates of the quasar, galaxy, etc.). The distance measures discussed here all reduce to the common notion of Euclidean distance at low redshift.

In accord with our present understanding of cosmology, these measures are calculated within the context of general relativity, where the Friedmann–Lemaître–Robertson–Walker solution is used to describe the universe.