# CMB seen through random Swiss Cheese

## Abstract

We consider a Swiss Cheese model with a random arrangement of Lemaȋtre-Tolman-Bondi holes in ΛCDM cheese. We study two kinds of holes with radius r{sub b}=50 h{sup −1} Mpc, with either an underdense or an overdense centre, called the open and closed case, respectively. We calculate the effect of the holes on the temperature, angular diameter distance and, for the first time in Swiss Cheese models, shear of the CMB . We quantify the systematic shift of the mean and the statistical scatter, and calculate the power spectra. In the open case, the temperature power spectrum is three orders of magnitude below the linear ISW spectrum. It is sensitive to the details of the hole, in the closed case the amplitude is two orders of magnitude smaller. In contrast, the power spectra of the distance and shear are more robust, and agree with perturbation theory and previous Swiss Cheese results. We do not find a statistically significant mean shift in the sky average of the angular diameter distance, and obtain the 95% limit |Δ D{sub A}/ D-bar {sub A}|∼< 10{sup −4}. We consider the argument that areas of spherical surfaces are nearly unaffected by perturbations, which is often invoked in light propagation calculations. Themore »

- Authors:

- Physics Department, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FIN-00014, University of Helsinki (Finland)

- Publication Date:

- OSTI Identifier:
- 22525221

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2015; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; COSMOLOGICAL CONSTANT; COSMOLOGICAL MODELS; DISTANCE; DISTURBANCES; ENERGY SPECTRA; LIGHT TRANSMISSION; NONLUMINOUS MATTER; PERTURBATION THEORY; PROBABILITY; RANDOMNESS; SHEAR; SKY; SPHERICAL CONFIGURATION

### Citation Formats

```
Lavinto, Mikko, and Räsänen, Syksy, E-mail: mikko.lavinto@helsinki.fi, E-mail: syksy.rasanen@iki.fi.
```*CMB seen through random Swiss Cheese*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/10/057.

```
Lavinto, Mikko, & Räsänen, Syksy, E-mail: mikko.lavinto@helsinki.fi, E-mail: syksy.rasanen@iki.fi.
```*CMB seen through random Swiss Cheese*. United States. doi:10.1088/1475-7516/2015/10/057.

```
Lavinto, Mikko, and Räsänen, Syksy, E-mail: mikko.lavinto@helsinki.fi, E-mail: syksy.rasanen@iki.fi. Thu .
"CMB seen through random Swiss Cheese". United States. doi:10.1088/1475-7516/2015/10/057.
```

```
@article{osti_22525221,
```

title = {CMB seen through random Swiss Cheese},

author = {Lavinto, Mikko and Räsänen, Syksy, E-mail: mikko.lavinto@helsinki.fi, E-mail: syksy.rasanen@iki.fi},

abstractNote = {We consider a Swiss Cheese model with a random arrangement of Lemaȋtre-Tolman-Bondi holes in ΛCDM cheese. We study two kinds of holes with radius r{sub b}=50 h{sup −1} Mpc, with either an underdense or an overdense centre, called the open and closed case, respectively. We calculate the effect of the holes on the temperature, angular diameter distance and, for the first time in Swiss Cheese models, shear of the CMB . We quantify the systematic shift of the mean and the statistical scatter, and calculate the power spectra. In the open case, the temperature power spectrum is three orders of magnitude below the linear ISW spectrum. It is sensitive to the details of the hole, in the closed case the amplitude is two orders of magnitude smaller. In contrast, the power spectra of the distance and shear are more robust, and agree with perturbation theory and previous Swiss Cheese results. We do not find a statistically significant mean shift in the sky average of the angular diameter distance, and obtain the 95% limit |Δ D{sub A}/ D-bar {sub A}|∼< 10{sup −4}. We consider the argument that areas of spherical surfaces are nearly unaffected by perturbations, which is often invoked in light propagation calculations. The closed case is consistent with this at 1σ, whereas in the open case the probability is only 1.4%.},

doi = {10.1088/1475-7516/2015/10/057},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 10,

volume = 2015,

place = {United States},

year = {2015},

month = {10}

}