Mean comoving distance reached at fixed time, ⟨r(η)⟩, compared to its background counterpart . The difference combines the wiggly-ray and Shapiro time-delay effects. The x-axis indicates instead of η for better readability. Dots indicate numerical results and error bars are computed according to Appendix D.4. The dashed line indicates the unconstrained theoretical prediction (71), while the solid line shows the prediction (72) that accounts for our knowledge of the gravitational potential ϕ₀ at the observer.