Hubble’s law

Light from distant galaxies is generally redshifted: its observed wavelengths are longer than the wavelengths at which it was emitted. This redshift is interpreted as evidence that galaxies are receding from us as the universe expands.

Hubble’s law relates a galaxy’s recession speed to its distance:

Here, $$v$$ is recession speed, $$d$$ is distance, and $$H$$ is the Hubble constant: the present proportionality between recession speed and distance. The relationship means that more distant galaxies generally recede faster. For example, a galaxy twice as distant has twice the recession speed predicted by the law.

Hubble time

A simple estimate of the time since expansion began comes from imagining that a galaxy has always receded at its present speed. At constant speed, the time taken to reach its present distance would be distance divided by speed. Using Hubble’s law gives:

This estimate, $$1/H$$, is called the Hubble time. It uses the present value of $$H$$ as representative of the expansion. It is only an approximation: the expansion history need not match the assumption that the galaxy’s recession speed remained constant.

Big Bang theory and its evidence

The Big Bang theory describes a universe that was once much hotter and denser than it is today. As the universe expanded, it cooled. Two observations support this account: radiation left over from the early universe and the relative amounts of hydrogen and helium found today.

Cosmic microwave background radiation

In the early universe, matter was too hot for stable neutral atoms to form. Radiation repeatedly interacted with charged particles, so it could not travel freely over long distances.

As the universe expanded and cooled, electrons could combine with nuclei to form neutral atoms. Radiation could then travel freely through space. Continued expansion stretched its wavelengths until much of it became microwave radiation. This radiation is called the cosmic microwave background.

The cosmic microwave background is detected throughout space. Its presence is consistent with the universe having passed through an early hot, dense state.

Hydrogen and helium abundance

In the early hot universe, some hydrogen nuclei combined to form helium nuclei. As the universe expanded and cooled, conditions changed, leaving much of the matter as hydrogen and a substantial amount as helium.

Today, hydrogen is the most abundant element, with a substantial abundance of helium. These relative amounts are broadly consistent with predictions based on conditions in the early universe, providing further evidence for the Big Bang theory.