Comoves

Comoves is typically discussed in the context of comoving coordinates in cosmology. The verb form “to comove” (and its third-person form “comoves”) describes objects that share the cosmic expansion and thus move with the Hubble flow, having zero peculiar velocity relative to this expansion. The corresponding adjective is comoving, used to describe coordinates that expand with the universe as described by the scale factor a(t).

In cosmology, comoving coordinates are used within the Friedmann-Lemaître-Robertson-Walker framework. They provide a description where the positions of distant galaxies are fixed unless they have local motions, so the growth of their separations is attributed to the expansion of space rather than to motion through space itself. The comoving distance between two objects is a fixed coordinate separation, while the physical, or proper, distance Dp(t) evolves with time as Dp(t) = a(t) times the comoving separation.

Comoving distances are derived from redshift and the expansion history. In a flat universe, the comoving distance to redshift z is often written as D_C(z) = c ∫_0^z dz'/H(z'), where H(z) is the Hubble parameter. The present-day proper distance relates to this comoving distance by Dp(t0) = a(t0) D_C, and with the common normalization a(t0) = 1, Dp(t0) = D_C. For non-flat geometries, curvature modifies the relation through the appropriate distance–redshift formulas.

Observationally, comoving coordinates underpin surveys of large-scale structure, the cosmic web, and statistical measures like the comoving volume element. They separate the effects of universal expansion from local dynamics, though peculiar velocities and gravitational clustering introduce deviations from strict comovement.