Unified Treatment of the Luminosity Distance in Cosmology

TL;DR

This paper critically compares four methods for modeling luminosity distance in cosmology, unifying their treatment to ensure consistency and address issues like divergences and gauge dependence.

Contribution

It provides a unified framework for four different approaches to luminosity distance, enabling comparison and validation of their correctness in cosmological measurements.

Findings

All four methods can produce correct luminosity distance when properly exercised.

The unified treatment facilitates comparison and consistency checks among methods.

Addresses issues of infrared divergences and gauge dependence in theoretical predictions.

Abstract

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.