Perturbations and observables in inhomogeneous cosmologies
Final Report Abstract
This project dealt with radially inhomogeneous solutions of general relativity and its application to cosmology. As a first attempt, it has been examined whether an inhomogeneous cosmological model can be set up that is compatible with the standard model of cosmology on the level of the most recent observational probes available, but does not have to be augmented by an exotic fluid component like dark energy. Since, according to general relativity, the local expansion of underdense regions (voids) decelerates less fast with respect to the background, a large Gigaparsec-scale inhomogeneity can mimic effects of an accelerated expansion on the backward lightcone. Assuming that our galaxy is very close to the center of this underdense region, we modelled the local universe by a Lemaître-Tolman-Bondi (LTB) solution of general relativity. We constructed a very flexible spline interpolation scheme for the density profile of the void region and constrained the nodal values of this spline on based on a combined set of observable probes. Those include measurements of the local Hubble rate, distance-redshift relations to Type IA supernovae, essential features of the temperature fluctuation power spectrum of the Cosmic Microwave background (CMB) and upper limits on the kinetic Sunyaev-Zeldovic effect. This resulted in the most up-to-date and flexible analysis of LTB void models so far. We found that despite this flexibility, no fit to this combined set of observations comparable to the cosmological standard model can be obtained in a matter-dominated setup. The standard spatially homogeneous ΛCDM model performs way better than any matter-dominated (even asymptotically curved) LTB void model. Regarding this most advanced confirmation of previous findings, we can therefore rule out spherical void models for the description of the local universe on a firm scientific basis. As a follow-up, we augmented the the LTB solution by a cosmological constant Λ and take it as an additional fit parameter. The resulting test of the Copernican Principle included the same observational probes. Remarkably, only very small, %-level deviations from a homogeneous and isotropic density profile of the universe have been found. Observables considered so far do not include any information from linear structure formation on top of the (Λ)LTB geometry, because linear perturbation theory in spherically symmetric dust models suffers from two main difficulties: (1) Perturbation variables are dynamically coupled at first order and (2) no trivial physical interpretation of gauge-invariant variables exists as they reduce to complicated mixings of scalar-vector-tensor expressions in the spatially homogeneous limit. We first set up a numerical scheme that evolves the master- and constraint equations of linear perturbations forward in time and takes the full dynamical coupling effects into account. In addition, we implemented cosmologically viable initial conditions on a spatial hypersurface of constant time. The resulting harmonic power spectra of the perturbation variables allowed to quantify coupling effects for different angular scales and redshifts for the best fit models obtained in the first part of the project. It turned out that coupling effects are marginal in case of ΛLTB and very prominent on LTB void models which can be expected in both cases. In matter-dominated spherical void models the coupled evolution can deviate by almost 60% from the uncoupled evolution that has been used in the literature up to that point. We finally predicted effects of the gauge-invariant variables on observable signatures on the backward lightcone. Using a relativistic formalism of light propagation, we computed a cosmic shear signal and temperature fluctuation amplitudes caused by the integrated Sachs-Wolfe- and linear kinetic Sunyaev-Zeldovic effect. In this context, clear distinctions of these signatures between the matter- and Λ-dominated models have been found and compared to corresponding quantities in the standard ΛCDM model.
Publications
- Probing spatial homogeneity with LTB models: a detailed discussion. Astronomy and Astrophysics, 570:A63, October 2014
M. Redlich, K. Bolejko, S. Meyer, G. F. Lewis, and M. Bartelmann
(See online at https://doi.org/10.1051/0004-6361/201424553) - Evolution of linear perturbations in Lemaître-Tolman-Bondi void models. Journal of Cosmology and Astro-Particle Physics, 03:053, March 2015
Sven Meyer, Matthias Redlich, and Matthias Bartelmann
(See online at https://doi.org/10.1088/1475-7516/2015/03/053) - Light propagation in linearly perturbed LambdaLTB models. Journal of Cosmology and Astro-Particle Physics, 11:037, November 2017
Sven Meyer and Matthias Bartelmann
(See online at https://doi.org/10.1088/1475-7516/2017/11/037) - Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant. Journal of Cosmology and Astro-Particle Physics, 12:025, December 2017
Sven Meyer and Matthias Bartelmann
(See online at https://doi.org/10.1088/1475-7516/2017/12/025)
