Cosmology Calculations

Ever see an astronomy press release that trumpets the discovery of a galaxy at redshift 5.6? Ever wonder what "redshift 5.6" means? Ever get confused by the correspondence of redshift, time, and various other cosmology parameters?

If so, then this is the web page for you.

The equations that relate time, redshift, and the other cosmological parameters are complicated enough that one has to use a computer to solve all but the most trivial cases. Fortunately, computers have gotten fast enough that one can implement these equations over the web.

Below you will find a simple 3-step procedure for obtaining the basic parameters of several popular cosmological models (or one of your own choosing) at most any point in time or redshift.

Step 1: Choose the Cosmological Model

Model Name Present Day Matter Density Parameter [Omega_Matter] Present Day Vacuum Energy Parameter [Omega_Lambda] Present Day Hubble Parameter (km/s/Mpc) Present Age of Universe (Gyr)

Lambda Model, t=14 Gyr
0.3 0.7 67.335 14

Lambda Model, t=13 Gyr
0.34 0.66 70 13

Flat Model
1.0 0.0 50 13.037

Open Model
0.3 0.0 60.833 13

Custom Model
TBD

Notes

Model Name	Present Day Matter Density Parameter [Omega_Matter]	Present Day Vacuum Energy Parameter [Omega_Lambda]	Present Day Hubble Parameter (km/s/Mpc)	Present Age of Universe (Gyr)
Lambda Model, t=14 Gyr	0.3	0.7	67.335	14
Lambda Model, t=13 Gyr	0.34	0.66	70	13
Flat Model	1.0	0.0	50	13.037
Open Model	0.3	0.0	60.833	13
Custom Model				TBD

The Lambda Model with t=14 Gyr is probably the most popular cosmological model today.
The Flat Model was the most popular model of the late 1980's and early 1990's. While it has some significant problems, it still serves as a useful baseline comparison.
The Open Model solves some of the problems with the Flat Model, but not as many as the Lambda Models.
The calculation code only handles models where either Omega_Lambda = 0 or Omega_Matter + Omega_Lambda = 1.
TBD means "to be determined". For Custom Models, the Age of the Universe will be calculated from the other inputs.
Gyr means "giga-years" = billion years.

Step 2: Choose the Type of Calculation

Specific Time Calculation - Time (Gyr) = [must be greater than 0.0005]

Specific Redshift Calculation - Redshift = [must be less than 5000.0]

Table

Number of Rows (max 100) =

Evenly spaced in Time

or Redshift with starting redshift = [must be less than 5000.0]

Notes

To convert a time to a redshift, click "Specific Time Calculation" and enter the time in the box.
To convert a redshift to a time, click "Specific Redshift Calculation" and enter the redshift in the box.
Table output will cover the entire range of time/redshift in the universe. For time, that will be from t=0 to the present day. For redshift, that will be from a specified starting redshift to z=0 (present day).
Table output evenly spaced in redshift must specify a starting redshift because redshift becomes infinite at the earliest times. A large starting redshift is not particularly useful.

Step 3: Press the Button

Page last updated on: June 5, 2002

Evenly spaced in	Time
or	Redshift with starting redshift = [must be less than 5000.0]