In cosmology, a Hubble volume or Hubble sphere is a spherical region of the observable universe surrounding an observer beyond which objects recede from that observer at a rate greater than the speed of light due to the expansion of the Universe. The Hubble volume is approximately equal to 1031 cubic light years.
The proper 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. The surface of a Hubble sphere is called the microphysical horizon, the Hubble surface, or the Hubble limit.
More generally, the term "Hubble volume" can be applied to any region of space with a volume of order . However, the term is also frequently (but mistakenly) used as a synonym for the observable universe; the latter is larger than the Hubble volume.
Relationship to age of the universe
Hubble limit as an event horizon
For objects at the Hubble limit the space between us and the object of interest has an average expansion speed of c. So, in a universe with constant Hubble parameter, light emitted at the present time by objects outside the Hubble limit would never be seen by an observer on Earth. That is, the Hubble limit would coincide with a cosmological event horizon (a boundary separating events visible at some time and those that are never visible). See Hubble horizon for more details.
However, the Hubble parameter is not constant in various cosmological models so that the Hubble limit does not, in general, coincide with a cosmological event horizon. For example in a decelerating Friedmann universe the Hubble sphere expands with time, and its boundary overtakes light emitted by more distant galaxies so that light emitted at earlier times by objects outside the Hubble sphere still may eventually arrive inside the sphere and be seen by us. Conversely, in an accelerating universe, the Hubble sphere shrinks with time, and its boundary overtakes light emitted by nearer galaxies so that light emitted at earlier times by objects inside the Hubble sphere will eventually recede outside the sphere and will never be seen by us.
- Edward Robert Harrison (2003). Masks of the Universe. Cambridge University Press. p. 206. ISBN 0-521-77351-2.
- N. Carlevaro & G. Montani (2009). "Study of the Quasi-isotropic Solution near the Cosmological Singularity in Presence of Bulk-Viscosity". International Journal of Modern Physics D. 17: 881–896. arXiv:0711.1952. Bibcode:2008IJMPD..17..881C. doi:10.1142/S0218271808012553.
- For a discussion of why objects that are outside the Earth's Hubble sphere can be seen from Earth, see TM Davis & CH Linewater (2003). "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe". Publications of the Astronomical Society of Australia. 21: 97–109. arXiv:astro-ph/0310808. Bibcode:2004PASA...21...97D. doi:10.1071/AS03040.
- For an example of mistaken usage, see Max Tegmark (2004). "Parallel Universes". In Barrow, J. D.; Davies, J. D.; Harper, C. L. Science and Ultimate Reality: From Quantum to Cosmos. Cambridge University Press. pp. 459ff. ISBN 0-521-83113-X.
- Edward Robert Harrison (2000). Masks of the Universe. Cambridge University Press. p. 439. ISBN 0-521-66148-X.
- John L Tonry; et al. (2003). "Cosmological Results from High-z Supernovae". Astrophys J. 594: 1. arXiv:astro-ph/0305008. Bibcode:2003ApJ...594....1T. doi:10.1086/376865.