In this case the comoving coordinate distance r is related to χ χ by: χ χ = { | κ κ | − − 1 / 2 sinh − − 1 ⁡ ⁡ | κ κ | r , if κ κ < 0 (a negatively curved ‘hyperbolic’ universe) r , if κ κ = 0 (a spatially flat universe) | κ κ | − − 1 / 2 sin − − 1 ⁡ ⁡ | κ κ | r , if κ κ > 0 (a positively curved ‘spherical’ universe)