The Szekeres Swiss Cheese model and the CMB observations

Abstract

This paper presents the application of the Szekeres Swiss Cheese model to the analysis of observations of the cosmic microwave background (CMB) radiation. The impact of inhomogeneous matter distribution on the CMB observations is in most cases studied within the linear perturbations of the Friedmann model. However, since the density contrast and the Weyl curvature within the cosmic structures are large, this issue is worth studying using another approach. The Szekeres model is an inhomogeneous, non-symmetrical and exact solution of the Einstein equations. In this model, light propagation and matter evolution can be exactly calculated, without such approximations as small amplitude of the density contrast. This allows to examine in more realistic manner the contribution of the light propagation effect to the measured CMB temperature fluctuations. The results of such analysis show that small-scale, non-linear inhomogeneities induce, via Rees-Sciama effect, temperature fluctuations of amplitude $10^{-7}-10^{-5}$ on angular scale $\theta <0.24^{\circ }$ ($\ell >750$). This is still much smaller than the measured temperature fluctuations on this angular scale.However, local and uncompensated inhomogeneities can induce temperature fluctuations of amplitude as large as $10^{-3}$, and thus can be responsible the low multipoles anomalies observed in the angular CMB power spectrum.

18 pages, 6 figures; new models added; discussion of the Weyl curvature added; improved description of models

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• Probing spatial homogeneity with LTB models: a detailed discussion
• Redshift drift in axially symmetric quasi-spherical Szekeres models
• Cosmic backreaction and the mean redshift drift from symbolic regression
• Modelling Inhomogeneity in Szekeres Spacetime
• Conceptual problems in detecting the evolution of dark energy when using distance measurements
• Frame Rotation in the Szekeres Spacetimes
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Hubble Diagrams in Statistically Homogeneous, Anisotropic Universes
• Quantum potentiality in Inhomogeneous Cosmology
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Post-Newtonian Gravity in Cosmology