Many textbooks use the symbol χ χ for the comoving distance. However, this χ χ must be distinguished from the coordinate distance r in the commonly used comoving coordinate system for a FLRW universe where the metric takes the form (in reduced-circumference polar coordinates, which only works half-way around a spherical universe): d s 2 = − − c 2 d τ τ 2 = − − c 2 d t 2 + a ( t ) 2 ( d r 2 1 − − κ κ r 2 + r 2 ( d θ θ 2 + sin 2 ⁡ ⁡ θ θ d ϕ ϕ 2 ) ) .