# Ray tracing and Hubble diagrams in post-Newtonian cosmology

## Abstract

On small scales the observable Universe is highly inhomogeneous, with galaxies and clusters forming a complex web of voids and filaments. The optical properties of such configurations can be quite different from the perfectly smooth Friedmann-Lemaȋtre-Robertson-Walker (FLRW) solutions that are frequently used in cosmology, and must be well understood if we are to make precise inferences about fundamental physics from cosmological observations. We investigate this problem by calculating redshifts and luminosity distances within a class of cosmological models that are constructed explicitly in order to allow for large density contrasts on small scales. Our study of optics is then achieved by propagating one hundred thousand null geodesics through such space-times, with matter arranged in either compact opaque objects or diffuse transparent haloes. We find that in the absence of opaque objects, the mean of our ray tracing results faithfully reproduces the expectations from FLRW cosmology. When opaque objects with sizes similar to those of galactic bulges are introduced, however, we find that the mean of distance measures can be shifted up from FLRW predictions by as much as 10%. This bias is due to the viable photon trajectories being restricted by the presence of the opaque objects, which means thatmore »

- Authors:

- School of Physics and Astronomy, Queen Mary University of London, 327 Mile End Road, London E1 4NS (United Kingdom)
- Départment de Physique Théorique, Université de Genève, 24 quai Ernest-Ansermet, 1211 Genève 4 (Switzerland)

- Publication Date:

- OSTI Identifier:
- 22676098

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 07; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPUTERIZED SIMULATION; COSMOLOGICAL MODELS; COSMOLOGY; DENSITY; DISTANCE; FORECASTING; GALAXIES; LUMINOSITY; OPTICS; PHOTONS; RED SHIFT; SPACE-TIME; TRAJECTORIES; UNIVERSE

### Citation Formats

```
Sanghai, Viraj A.A., Clifton, Timothy, and Fleury, Pierre, E-mail: v.a.a.sanghai@qmul.ac.uk, E-mail: pierre.fleury@unige.ch, E-mail: t.clifton@qmul.ac.uk.
```*Ray tracing and Hubble diagrams in post-Newtonian cosmology*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/07/028.

```
Sanghai, Viraj A.A., Clifton, Timothy, & Fleury, Pierre, E-mail: v.a.a.sanghai@qmul.ac.uk, E-mail: pierre.fleury@unige.ch, E-mail: t.clifton@qmul.ac.uk.
```*Ray tracing and Hubble diagrams in post-Newtonian cosmology*. United States. doi:10.1088/1475-7516/2017/07/028.

```
Sanghai, Viraj A.A., Clifton, Timothy, and Fleury, Pierre, E-mail: v.a.a.sanghai@qmul.ac.uk, E-mail: pierre.fleury@unige.ch, E-mail: t.clifton@qmul.ac.uk. Sat .
"Ray tracing and Hubble diagrams in post-Newtonian cosmology". United States.
doi:10.1088/1475-7516/2017/07/028.
```

```
@article{osti_22676098,
```

title = {Ray tracing and Hubble diagrams in post-Newtonian cosmology},

author = {Sanghai, Viraj A.A. and Clifton, Timothy and Fleury, Pierre, E-mail: v.a.a.sanghai@qmul.ac.uk, E-mail: pierre.fleury@unige.ch, E-mail: t.clifton@qmul.ac.uk},

abstractNote = {On small scales the observable Universe is highly inhomogeneous, with galaxies and clusters forming a complex web of voids and filaments. The optical properties of such configurations can be quite different from the perfectly smooth Friedmann-Lemaȋtre-Robertson-Walker (FLRW) solutions that are frequently used in cosmology, and must be well understood if we are to make precise inferences about fundamental physics from cosmological observations. We investigate this problem by calculating redshifts and luminosity distances within a class of cosmological models that are constructed explicitly in order to allow for large density contrasts on small scales. Our study of optics is then achieved by propagating one hundred thousand null geodesics through such space-times, with matter arranged in either compact opaque objects or diffuse transparent haloes. We find that in the absence of opaque objects, the mean of our ray tracing results faithfully reproduces the expectations from FLRW cosmology. When opaque objects with sizes similar to those of galactic bulges are introduced, however, we find that the mean of distance measures can be shifted up from FLRW predictions by as much as 10%. This bias is due to the viable photon trajectories being restricted by the presence of the opaque objects, which means that they cannot probe the regions of space-time with the highest curvature. It corresponds to a positive bias of order 10% in the estimation of Ω{sub Λ} and highlights the important consequences that astronomical selection effects can have on cosmological observables.},

doi = {10.1088/1475-7516/2017/07/028},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 07,

volume = 2017,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}