The luminosity distance in perturbed FLRW space-times

We derive an expression for the luminosity distance in Friedman-Lemaître—Robertson—Walker space—times affected by scalar perturbations. Our expression is complete to linear order and is expressed entirely in terms of standard cosmological parameters and observational quantities. We illustrate the result by calculating the rms scatter in the usual luminosity distance in flat (Ωm, ΩΛ)=(1.0, 0.0) and (0.3, 0.7) cosmologies. In both cases the scatter is appreciable at high redshifts, and rises above 11 per cent at z= 2, it may be the dominant noise term in the Hubble diagram based on Type Ia supernovae.