Gauge-Invariance and Infrared Divergences in the Luminosity Distance

TL;DR

This paper demonstrates that a gauge-invariant approach to calculating the luminosity distance removes infrared divergences, ensuring consistent and accurate predictions without arbitrary cut-offs, and aligns with the equivalence principle.

Contribution

It introduces a gauge-invariant method for luminosity distance calculation that eliminates infrared divergences and confirms previous results are robust against cut-off choices.

Findings

Gauge-invariant calculation is free of infrared divergences.

Numerical results with cut-offs larger than the horizon scale are accurate.

Infrared divergences are canceled when using proper gauge-invariant expressions.

Abstract

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.