As the Hubble radius grows in the expanding Universe, it encompasses larger and larger perturbations.

Vigier: Gravitation and cosmology: from the Hubble radius to the Planck scale.

The total number of nucleons in the observable universe of roughly the Hubble radius is the Eddington number, currently estimated at 10.

The Friedmann equation relates the energy density of the Universe to the Hubble parameter, and shows that the Hubble radius is continually increasing.

The Hubble radius is defined as formula; and j l (x)are the Legendre polynomial and spherical Bessel functions of order l, respectively.

An extremely important concept in the theory of structure formation is the notion of the Hubble radius, often called simply the horizon as it is closely related to the particle horizon.

This is because the Hubble radius in a radiation or matter-dominated universe expands much more quickly than physical lengths and so points that are out of communication are coming into communication.

This paradox is resolved by cosmic inflation, which suggests that there was a phase of very rapid expansion in the early Universe in which the Hubble radius was very nearly constant.

The comoving radius of a Hubble sphere (known as the Hubble radius or the Hubble length) is , where is the speed of light and is the Hubble constant.

Any such model requires that the Hubble radius of the observable universe is equal to its Schwarzschild radius, that is, the product of its mass and the Schwarzschild proportionality constant.

The Hubble radius, which is related to the Hubble parameter as , where is the speed of light, defines, roughly speaking, the volume of the nearby universe that has recently (in the last expansion time) been in causal contact with an observer.

At recombination these scales were larger than the Hubble radius, and because microphysical processes can act only on scales less than the Hubble radius, these fluctuations must have been produced by the Sachs-Wolfe effect.

This is because, in an ordinary Friedmann-Lemaitre-Robertson-Walker cosmology, the Hubble radius increases more rapidly than space expands, so perturbations are only ever entering the Hubble radius, and they are not being pushed out by the expansion of space.