Corrections to the apparent value of the cosmological constant due to local inhomogeneities

TL;DR

This paper develops a theoretical framework to quantify how local inhomogeneities can systematically bias the observed value of the cosmological constant, emphasizing the importance of accounting for such effects in cosmological data analysis.

Contribution

It introduces a general method using $b5$ LTB solutions to calculate corrections to the apparent cosmological constant caused by local inhomogeneities, considering various profiles and degrees of smoothness.

Findings

Corrections to the cosmological constant are present for inhomogeneities of any size.

The approach accounts for different inhomogeneity profiles and smoothness conditions.

Local inhomogeneities can significantly affect the interpretation of cosmological data.

Abstract

Supernovae observations strongly support the presence of a cosmological constant, but its value, which we will call apparent, is normally determined assuming that the Universe can be accurately described by a homogeneous model. Even in the presence of a cosmological constant we cannot exclude nevertheless the presence of a small local inhomogeneity which could affect the apparent value of the cosmological constant. Neglecting the presence of the inhomogeneity can in fact introduce a systematic misinterpretation of cosmological data, leading to the distinction between an apparent and true value of the cosmological constant. We establish the theoretical framework to calculate the corrections to the apparent value of the cosmological constant by modeling the local inhomogeneity with a $\Lambda LTB$ solution. Our assumption to be at the center of a spherically symmetric inhomogeneous matter distribution correspond to effectively calculate the monopole contribution of the large scale inhomogeneities surrounding us, which we expect to be the dominant one, because of other observations supporting a high level of isotropy of the Universe around us. By performing a local Taylor expansion we analyze the number of independent degrees of freedom which determine the local shape of the inhomogeneity, and consider the issue of central smoothness, showing how the same correction can correspond to different inhomogeneity profiles. Contrary to previous attempts to fit data using large void models our approach is quite general. The correction to the apparent value of the cosmological constant is in fact present for local inhomogeneities of any size, and should always be taken appropriately into account both theoretically and observationally.