The proper distance to the furthest observable point—the particle horizon— at time t is the horizon distance, sh(t).
So shor(t)=2ct in the radiation-dominated era and shor(t)=3ct in the matter-dominated era.
Notice that these distances are larger than ct, the distance travelled by a photon in time t..
Large Redshift and Look-Back Times
Note that the look-back times are approaching a constant value of 10 billion years for large redshift.
This is because the look-back time cannot be larger than the age of the Universe, which is 10 billion years for the assumptions used in the table..
Comoving distance and proper distance.
Comoving distance is the distance between two points measured along a path defined at the present cosmological time.
For objects moving with the Hubble flow, it is deemed to remain constant in time..
The comoving volume VC is the volume in which the number densities of non-evolving objects locked into the Hubble flow are constant with redshift.
It is the proper volume times three factors of the relative scale factor from the present epoch to the time at redshift z, or (1 + z)3..
Input one value each for H 0, Ω M, Ω vac to apply the same cosmology to all redshifts. © 1999-2012 Edward L.
Wright - Cite Wright (2006, PASP, 118, 1711).
Adapted at .Astronomy 4 and AAS 221 Hack Day.
A calculator that takes light travel time and computes the redshift .
There is also an advanced version of my Cosmology Calculator .
Cosmology is the study of the origin, current state, and future of our Universe.
This field has been revolutionized by many discoveries made during the past century.
This calculator allows one to input user-selected values of the Hubble constant, Omega (matter), Omega (vacuum) and the redshift z, and returns the current age of the Universe, the age, the co-moving radial distance (and volume) and the angular-size distance at the specified redshift, as well as the scale (kpc/arcsec) and the luminosity distance.
Cosmology is the study of the origin, current state, and future of our Universe.
This field has been revolutionized by many discoveries made during the past century.
My cosmology tutorial is an attempt to summarize these discoveries.
It will be "under construction" for the foreseeable future as new discoveries are made.
