Comoving and proper distances
Two distance measures used in standard cosmology.
Comoving distance and proper distance are fundamental measures in standard cosmology, distinguished by how they account for the expansion of the universe. Comoving distance is defined to factor out this expansion, yielding a value that remains constant over time, changing only due to local influences such as the peculiar motion of a galaxy within a cluster. Proper distance, by contrast, corresponds to the physical separation between objects at a single, specific moment of cosmic time; because the universe expands, this distance changes over time. At the present cosmic epoch, the two distances are equal. The relationship between them is governed by the scale factor, which converts comoving distance into the physical distance that would have been smaller in the past and will become larger in the future.
These distances are naturally expressed using comoving coordinates, a coordinate system in which each galaxy is assigned a fixed spatial label that moves with the Hubble flow. Observers who perceive the universe as isotropic—including the cosmic microwave background radiation—are called comoving observers, and their reference frame defines the comoving frame. An object’s velocity relative to this local frame is its peculiar velocity; for a photon, this peculiar velocity is always the speed of light. Most galaxies are nearly comoving, as their peculiar velocities, caused mainly by gravitational attraction, are small compared to their Hubble-flow velocities. The comoving distance between two galaxies, measured by their coordinate labels, remains constant, while the physical distance changes with the scale factor. Proper distance can be envisioned as the length one would measure with a very long ruler if the expansion were frozen at a given instant. The comoving distance is computed via an integral over time that accounts for the time-dependent comoving speed of light, ensuring it yields the correct proper distance at a fixed time.
- field
- Cosmology
- known_for
- Defining distances in an expanding universe
- concept_1
- Comoving distance
- concept_2
- Proper distance
- related
- Scale factor
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.
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