Comoving and proper distances

Lore & Background

In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. Comoving distance factors out the expansion of the universe, giving a distance that does not change in time except due to local factors, such as the motion of a galaxy within a cluster. Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmic time, which can change over time due to the expansion of the universe. Comoving distance and proper distance are defined to be equal at the present time.

Reader's Guide

Comoving distance and proper distance are fundamental concepts in cosmology for understanding the large-scale structure and evolution of the universe. Comoving distance provides a constant coordinate distance between objects that move with the Hubble flow, allowing cosmologists to map the universe without the complication of expansion. Proper distance, on the other hand, gives the physical separation at a given cosmic time, which changes as the universe expands. The conversion factor between them is the scale factor. These measures are essential for interpreting observations of distant galaxies and the cosmic microwave background, as they underpin calculations of the size and age of the universe. The comoving distance formula involves an integral over time of the speed of light divided by the scale factor, reflecting the time-dependent comoving speed of light. Proper distance can be envisioned as the value one would measure with a very long ruler while the expansion of the universe was frozen.

Did You Know?

• Comoving distance and proper distance are defined to be equal at the present time.
• Comoving distance factors out the expansion of the universe, giving a distance that does not change in time except due to local factors.
• Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmic time.
• The conversion factor between comoving distance and physical distance is called the scale factor.