# Evolution of linear perturbations in Lemaítre-Tolman-Bondi void models

## Abstract

We study the evolution of linear perturbations in a Lemaítre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations couple at first order. As shown by Clarkson et al. (2009) [1], the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme using finite element methods to solve this equation system and generate scalar initial conditions based on Gaussian random fields with an underlying power spectrum for the Bardeen potential. After spherical harmonic decomposition, the initial fluctuations are propagated in time and estimates of angular power spectra of each gauge invariant variable are computed as functions of redshift. This allows to analyse the coupling strength in a statistical way. We find significant couplings up to 25% for large and deep voids of Gpc scale as required to fit the distance redshift relations of SNe.

- Authors:

- Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg (Germany)

- Publication Date:

- OSTI Identifier:
- 22525916

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; 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; COSMOLOGICAL MODELS; DECOMPOSITION; DISTANCE; DISTURBANCES; ENERGY SPECTRA; FINITE ELEMENT METHOD; FLUCTUATIONS; GAUGE INVARIANCE; PARTIAL DIFFERENTIAL EQUATIONS; POTENTIALS; RANDOMNESS; RED SHIFT; SCALARS; SPHERICAL CONFIGURATION; UNIVERSE; VOIDS

### Citation Formats

```
Meyer, Sven, Redlich, Matthias, and Bartelmann, Matthias, E-mail: sven.meyer@uni-heidelberg.de, E-mail: matthias.redlich@stud.uni-heidelberg.de, E-mail: bartelmann@uni-heidelberg.de.
```*Evolution of linear perturbations in Lemaítre-Tolman-Bondi void models*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/03/053.

```
Meyer, Sven, Redlich, Matthias, & Bartelmann, Matthias, E-mail: sven.meyer@uni-heidelberg.de, E-mail: matthias.redlich@stud.uni-heidelberg.de, E-mail: bartelmann@uni-heidelberg.de.
```*Evolution of linear perturbations in Lemaítre-Tolman-Bondi void models*. United States. doi:10.1088/1475-7516/2015/03/053.

```
Meyer, Sven, Redlich, Matthias, and Bartelmann, Matthias, E-mail: sven.meyer@uni-heidelberg.de, E-mail: matthias.redlich@stud.uni-heidelberg.de, E-mail: bartelmann@uni-heidelberg.de. Sun .
"Evolution of linear perturbations in Lemaítre-Tolman-Bondi void models". United States.
doi:10.1088/1475-7516/2015/03/053.
```

```
@article{osti_22525916,
```

title = {Evolution of linear perturbations in Lemaítre-Tolman-Bondi void models},

author = {Meyer, Sven and Redlich, Matthias and Bartelmann, Matthias, E-mail: sven.meyer@uni-heidelberg.de, E-mail: matthias.redlich@stud.uni-heidelberg.de, E-mail: bartelmann@uni-heidelberg.de},

abstractNote = {We study the evolution of linear perturbations in a Lemaítre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations couple at first order. As shown by Clarkson et al. (2009) [1], the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme using finite element methods to solve this equation system and generate scalar initial conditions based on Gaussian random fields with an underlying power spectrum for the Bardeen potential. After spherical harmonic decomposition, the initial fluctuations are propagated in time and estimates of angular power spectra of each gauge invariant variable are computed as functions of redshift. This allows to analyse the coupling strength in a statistical way. We find significant couplings up to 25% for large and deep voids of Gpc scale as required to fit the distance redshift relations of SNe.},

doi = {10.1088/1475-7516/2015/03/053},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2015,

place = {United States},

year = {Sun Mar 01 00:00:00 EST 2015},

month = {Sun Mar 01 00:00:00 EST 2015}

}