Despite being an integral over time, this expression gives the correct distance that would be measured by a hypothetical tape measure at fixed time "t", i.e. the "proper distance" (as defined below) after accounting for the time-dependent "comoving speed of light" via the inverse scale factor term formula_2 in the integrand. By "comoving speed of light", we mean the velocity of light "through" comoving coordinates [formula_3] which is time-dependent even though "locally", at any point along the null geodesic of the light particles, an observer in an inertial frame always measures the speed of light as formula_4 in accordance with special relativity. For a derivation see "Appendix A: Standard general relativistic definitions of expansion and horizons" from Davis & Lineweaver 2004. In particular, see "eqs". 16-22 in the referenced 2004 paper in that paper the scale factor formula_5 is defined as a quantity with the dimension of distance while the radial coordinate formula_6 is dimensionless.