Gauge-Invariance and Infrared Divergences in the Luminosity Distance
  Measurements of the luminosity distance have played a key role in discovering
the late-time cosmic acceleration. However, when accounting for inhomogeneities
in the Universe, its interpretation has been plagued with infrared divergences
in its theoretical predictions, which are in some cases used to explain the
cosmic acceleration without dark energy. The divergences in most calculations
are artificially removed by imposing an infrared cut-off scale. For the first
time, we show that a gauge-invariant calculation of the luminosity distance is
devoid of such divergences and consistent with the equivalence principle,
eliminating the need to impose a cut-off scale. We present proper numerical
calculations of the luminosity distance using the gauge-invariant expression
and demonstrate that the numerical results with an ad hoc cut-off scale in
previous calculations have negligible systematic errors as long as the cut-off
scale is larger than the horizon scale. We discuss the origin of infrared
divergences and their cancellation in the luminosity distance.
