Unified Treatment of the Luminosity Distance in Cosmology
  Comparing the luminosity distance measurements to its theoretical predictions
is one of the cornerstones in establishing the modern cosmology. However, as
shown in Biern & Yoo, its theoretical predictions in literature are often
plagued with infrared divergences and gauge-dependences. This trend calls into
question the sanity of the methods used to derive the luminosity distance. Here
we critically investigate four different methods --- the geometric approach,
the Sachs approach, the Jacobi mapping approach, and the geodesic light cone
(GLC) approach to modeling the luminosity distance, and we present a unified
treatment of such methods, facilitating the comparison among the methods and
checking their sanity. All of these four methods, if exercised properly, can be
used to reproduce the correct description of the luminosity distance.
