Comoving distance remains constant with cosmic expansion for objects sharing the Hubble flow, whereas proper distance scales directly with the scale factor, making their divergence a foundational principle of standard cosmology.
The claim is a standard definition in physical cosmology regarding how coordinate distances and physical proper distances behave as space expands. While textbook common knowledge in astronomy, papers such as [3] and [10] touch upon the definitions and dynamics of comoving and proper distances in expanding spacetimes.