Hubble Time Calculator

The Hubble constant has units of inverse time once the megaparsec is cancelled against the kilometre, so its reciprocal is immediately a timescale. At H0 = 70 km/s/Mpc the conversion gives 2.268 x 10^-18 per second, and the Hubble time is 13.97 billion years. That figure is the age the universe would have if expansion had always proceeded at today's rate. The true age is smaller because gravity slowed the early expansion, and recovering it means integrating the expansion history: the age equals the Hubble time multiplied by the integral of dz divided by (1+z) times E(z), where E(z) is the square root of Omega_M times (1+z) cubed plus Omega_Lambda for a flat model. For the standard parameters Omega_M = 0.315 and Omega_Lambda = 0.685 this correction factor is close to 0.96. The companion quantities follow from the same constant. The Hubble distance c/H0 is about 4,283 Mpc, or 14.0 billion light-years, and marks where the recession velocity formally equals c - not the edge of the observable universe, which lies near 46.5 billion light-years in comoving terms. The critical density 3 H0 squared over 8 pi G works out near 9.2 x 10^-27 kg per cubic metre, about five and a half hydrogen atoms per cubic metre. Two limitations apply here. The model assumes flatness and a cosmological constant with fixed equation of state, and it omits the radiation density Omega_r of roughly 9 x 10^-5, which is negligible today but matters at redshifts above a few thousand.

Vesto Slipher at the Lowell Observatory began measuring the radial velocities of spiral nebulae in 1912 and found most of them receding, though the distances were unknown. Georges Lemaitre combined redshift and distance data in a 1927 paper in the Annales de la Societe Scientifique de Bruxelles, deriving an expanding solution and an expansion rate of roughly 600 km/s/Mpc, but publishing in French in a journal few read. Edwin Hubble's 1929 paper in the Proceedings of the National Academy of Sciences, using Cepheid distances from the 100-inch Hooker telescope at Mount Wilson together with velocities largely measured by Milton Humason, put the linear distance-velocity relation in front of the whole field, with H0 near 500 km/s/Mpc. That value was far too high because the Cepheid calibration conflated two distinct populations of variable stars. Walter Baade's 1952 recognition of the error roughly halved the constant, and Allan Sandage's decades of work brought it into the 50 to 100 range, where it stubbornly remained. The Hubble Space Telescope Key Project reported 72 plus or minus 8 in 2001. The situation since has been a standoff: cosmic microwave background fits from the Planck satellite give about 67.4 km/s/Mpc, while the SH0ES distance-ladder programme gives about 73.0, a disagreement of several sigma now known as the Hubble tension. In 2018 the International Astronomical Union voted to rename the relation the Hubble-Lemaitre law.