How does the cosmic large-scale structure bias the Hubble diagram?

TL;DR

This paper investigates how cosmic large-scale structure biases the Hubble diagram through inhomogeneities, affecting cosmological parameter inference, especially dark energy evolution, by deriving the relevant average and calculating second-order biases.

Contribution

The authors derive the observationally relevant average for the Hubble diagram and compute its second-order bias, assessing impacts on cosmological parameter estimation.

Findings

Bias significantly impacts dark-energy equation of state estimates.

Errors in standard parameter inference are below observational uncertainties.

Using optimal distance indicators reduces bias to sub-percent levels.

Abstract

The Hubble diagram is one of the cornerstones of observational cosmology. It is usually analysed assuming that, on average, the underlying relation between magnitude and redshift matches the prediction of a Friedmann-Lema\^itre-Robertson-Walker model. However, the inhomogeneity of the Universe generically biases these observables, mainly due to peculiar velocities and gravitational lensing, in a way that depends on the notion of average used in theoretical calculations. In this article, we carefully derive the notion of average which corresponds to the observation of the Hubble diagram. We then calculate its bias at second-order in cosmological perturbations, and estimate the consequences on the inference of cosmological parameters, for various current and future surveys. We find that this bias deeply affects direct estimations of the evolution of the dark-energy equation of state. However, errors in the standard inference of cosmological parameters remain smaller than observational uncertainties, even though they reach percent level on some parameters; they reduce to sub-percent level if an optimal distance indicator is used.