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

## 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-Lemaître-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.

- Authors:

- Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town 7701 (South Africa)
- Department of Physics and Astronomy, University of the Western Cape, Cape Town 7535 (South Africa)

- Publication Date:

- OSTI Identifier:
- 22679942

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 03; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGY; DISTANCE; DISTURBANCES; EQUATIONS OF STATE; ERRORS; GRAVITATIONAL LENSES; NONLUMINOUS MATTER; PERTURBATION THEORY; RED SHIFT; SIMULATION; UNCERTAINTY PRINCIPLE; UNIVERSE; VELOCITY

### Citation Formats

```
Fleury, Pierre, Clarkson, Chris, and Maartens, Roy, E-mail: pierre.fleury@uct.ac.za, E-mail: chris.clarkson@qmul.ac.uk, E-mail: roy.maartens@gmail.com.
```*How does the cosmic large-scale structure bias the Hubble diagram?*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/03/062.

```
Fleury, Pierre, Clarkson, Chris, & Maartens, Roy, E-mail: pierre.fleury@uct.ac.za, E-mail: chris.clarkson@qmul.ac.uk, E-mail: roy.maartens@gmail.com.
```*How does the cosmic large-scale structure bias the Hubble diagram?*. United States. doi:10.1088/1475-7516/2017/03/062.

```
Fleury, Pierre, Clarkson, Chris, and Maartens, Roy, E-mail: pierre.fleury@uct.ac.za, E-mail: chris.clarkson@qmul.ac.uk, E-mail: roy.maartens@gmail.com. Wed .
"How does the cosmic large-scale structure bias the Hubble diagram?". United States.
doi:10.1088/1475-7516/2017/03/062.
```

```
@article{osti_22679942,
```

title = {How does the cosmic large-scale structure bias the Hubble diagram?},

author = {Fleury, Pierre and Clarkson, Chris and Maartens, Roy, E-mail: pierre.fleury@uct.ac.za, E-mail: chris.clarkson@qmul.ac.uk, E-mail: roy.maartens@gmail.com},

abstractNote = {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-Lemaître-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.},

doi = {10.1088/1475-7516/2017/03/062},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2017,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}