Unified treatment of the luminosity distance in cosmology

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.

Light-cone observables and gauge-invariance in the geodesic light-cone formalism

“…This result also perfectly matches the luminosity distance calculated with other approaches but with specific choice of gauge conditions (see [18]). By taking the gauge transformation of the various terms we obtain…”

“…Indeed, as we showed in [18], the geometric approach, the Sachs approach, the Jacobi mapping approach and the GLC approach reproduce the same correct prediction in the conformal Newtonian gauge.…”

Cosmological information contents on the light-cone

“…The perturbation δD is a diffeomorphism invariant scalar, and it is gauge-invariant at the linear order [36]. For example, the perturbation δD for the luminosity distance as an observable quantity D has been computed (see, e.g., [37][38][39][40][41][42]), and it involves the Doppler effects and subtle relativistic effects associated with the light propagation. Here, we leave it general as the detailed expressions are less important for our current discussion.…”

Geometric optics in relativistic cosmology: New formulation and a new observable

“…In the literature different methods are proposed for various observables, and for some observable more than one method has been used (see e.g. [11] for a comparison of four different approaches for the calculation of the luminosity distance in the cosmological context). On the other hand the main result of the new formulation of * Corresponding author: villa@cft.edu.pl [1] emphasizes the advantage of having a unified framework: all the observables -the parallax, the magnification, the position drift, the angular diameter distance etc.…”