iCosmos › Lookback time calculator
Lookback time calculator
How long ago the light we see from redshift z set off: tL = t0 − t(z).
The interactive calculator loads here: change the redshift and the cosmological parameters (Ωm, ΩΛ, Ωr, w0, wa, H0) and the result and plot update instantly.
What it is
The lookback time tL is the time the light has been travelling: the age of the universe today minus its age when the light was emitted. When astronomers say a galaxy is seen “as it was 8 billion years ago”, they mean its lookback time.
Multiplied by the speed of light it gives the light-travel distance, which is why lookback time in billions of years equals the light-travel distance in billions of light-years.
Formula
- tL(z) = (1 / H0) ∫0z dz′ / [(1 + z′) E(z′)]
- tL = t0 − t(z)
Worked example
In the classic model (Ωm = 0.3, ΩΛ = 0.7, H0 = 70 km s−1 Mpc−1), light from z = 1 left 7.7153 billion years ago, when the universe was 5.752 billion years old (it is 13.467 billion years old today).
From z = 2 the lookback time is 10.24 Gyr, and from z = 10 it is 13.00 Gyr.
Common questions
Is lookback time the same as distance?
Lookback time × c is the light-travel distance, which is one way of describing distance. It is smaller than the comoving distance because space expanded while the light travelled.
Why does lookback time approach the age of the universe at high redshift?
Most of cosmic history lies at low redshift. By z = 10 the universe was less than half a billion years old, so the lookback time is already within a few percent of the total age.
Related calculators
- Age of the universe calculator
- Comoving distance calculator
- Redshift to distance calculator
- Hubble parameter H(z) calculator
- The full iCosmos cosmology calculator
About iCosmos
iCosmos was created by Mihran Vardanyan. Mihran Vardanyan is a cosmologist who earned his DPhil in cosmology at the University of Oxford, supervised by Joseph Silk and Roberto Trotta. He developed iCosmos during his research years at Oxford Astrophysics, where his work applied Bayesian model selection to the curvature and size of the Universe.
How to cite: Vardanyan, Mihran. iCosmos V4: Cosmology Calculator. https://icosmos.co.uk/. Include your access date, model parameters and exported data when reporting calculations.