Abstract

In this thesis the consequences of the presence of a Schwarzschild black hole in de Sitter space are studied in the setting of non-perturbative quantum gravity and in inflationary cosmology. We first review the formalism of Causal Dynamical Triangulations (CDT) which implements a lattice regularization of the gravitational path integral
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and discuss the emergence of Euclidean de Sitter space in the four-dimensional pure gravity model. Coupling the model to matter in the form of a point-like mass, the question is posed whether the corresponding classical limit is also correct. On the classical level, this matter source generates a Schwarzschild-de Sitter background geometry for a universe with a positive cosmological constant. In order to test the classical limit of the matter-coupled model, we study the properties of an observable that is sensitive to the presence of the mass. More specifically, it is shown that the volume profile of the Euclidean Schwarzschild-de Sitter solution in the proper-time gauge deviates in a characteristic manner from the profile of Euclidean de Sitter space. The appearance of coordinate caustics puts an upper bound on the total mass for which the results are expected to be valid. We also discuss some of the implementation details for numerically measuring the expectation value of the volume profiles in the framework of CDT with the matter source. In the second part of the thesis the implications of the presence of black holes in inflationary cosmology are analyzed. This work is motivated by anomalies in the cosmic microwave background (CMB) which have so far not been explained. To this end, we first estimate the formation probability of small primordial black holes from Gaussian density fluctuations during a pre-inflationary matter dominated era. Then, the Keldysh propagator of a scalar field on Schwarzschild-de Sitter space is constructed perturbatively to first non-trivial order in a dimensionless mass parameter. Using this result we determine the correction from a black hole to the scale invariant power spectrum of a scalar field on de Sitter space. In the zero curvature gauge this correction is closely related to the correction to the spectrum of scalar cosmological perturbations on quasi de Sitter space. Numerical results are presented for different black hole masses and positions. They suggest that the effect is strong enough to be tested and possibly even ruled out by observations. The last chapter deals with the generalization to primordial magnetic monopoles. These heavy relics generate a background geometry which is well-approximated by the Reissner-Nordström-de Sitter solution away from the center but regular in the center. We evaluate the corrections to the Keldysh propagator from the mass and the charge of the monopole perturbatively in momentum space. Although the effect of a single monopole is smaller than that of a primordial black hole their number in our past light cone is expected to be significantly larger, thus possibly leaving an observable imprint on the CMB.
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