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Evolution of linear perturbations in Lemaître-Tolman-Bondi models and effects on light propagation

Meyer, Sven

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Spherical void models of Gpc-scale have widely been discussed in the literature as a possible alternative to the spatially homogeneous Friedmann models with dark energy. In this framework, the local universe is modeled by an exact solution of Einstein's field equations, the so-called Lemaitre-Tolman-Bondi (LTB) metric, which constitutes a spherically symmetric spacetime that is solely filled by pressureless dust. In extension to recent multi-probe analyses of void models in a cosmological context, we study the evolution of linear, gauge-invariant perturbations on top of LTB backgrounds starting from a full spectrum of Gaussian initial conditions. The relativistic framework of perturbation theory on radially inhomogeneous spacetimes is substantially more complicated than in standard homogeneous models of FLRW type, because the spacetime is intrinsically dynamical already at first order which causes gauge-invariant perturbations to couple. As shown by Clarkson et al. in 2009 (\cite{clarkson_perturbation_2009}), their evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme based on finite element methods to solve this equation system and generate appropriate scalar initial conditions in the homogeneous asymptotic limit of the LTB patch. In this context, we involve realisations of Gaussian random fields with an underlying power spectrum for the Bardeen potential. After spherical harmonic decomposition, the initial fluctuations are mapped to the corresponding LTB gauge-invariant variables and those evolved into the radially inhomogeneous LTB regime. Estimates of angular power spectra of each gauge-invariant quantity are computed as functions of redshift on the past null cone. This enables us 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. As a major complication, LTB gauge-invariant perturbations are abstract mathematical objects that, although in principle observable, cannot feasibly be transformed to physically meaningful quantities. We therefore adapt a relativistic framework of light propagation to perturbed LTB models that allows to map the combined contribution of gauge-invariant metric and matter perturbations to sources of the optical tidal matrix. The corresponding Sachs equation is derived for generically perturbed LTB spacetimes and numerically investigated in case of negligible perturbation coupling.

Item Type: Dissertation
Supervisor: Bartelmann, Prof. Dr. Matthias
Date of thesis defense: 15 June 2015
Date Deposited: 01 Jul 2015 10:19
Date: 2015
Faculties / Institutes: The Faculty of Physics and Astronomy > Dekanat der Fakultät für Physik und Astronomie
Subjects: 500 Natural sciences and mathematics
520 Astronomy and allied sciences
530 Physics
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