Marvin Pinkwart-Walker

• In the present work we examine the cosmological horizon problem from a quantum mechanical to effectively quantum gravitational perspective. Spacetime coarse graining is a basic property of many quantum gravitational theories. In this spirit, noncommutative and nonassociative models yield spacetime uncertainties. A small time uncertainty is enough to solve the horizon problem without adding a cosmological inflationary process, because this small time uncertainty induces an infinite spatial uncertainty on the initial hyperplane. We interpret this as maximal quantum entanglement of the cosmological quantum state. We analyze a non-local deformation of quantum field theory; the canonical equal time commutation relations of a scalar quantum field with its canonical momentum allow for an isotropic and homogeneous deformation which incorporates violation of microcausality. The physical core of this consideration can be traced back to a deformed dispersion relation in the Hamiltonian, which allows quantum correlations across the classical light cone. This explicitly Lorentz-violating model furthermore allows to calculate the deformation in the quantum fluctuation spectrum. In order to measure the initial entanglement it is necessary to consider a particle probe which propagates on (quantum) spacetime. The correct quantization of this probe including spin, interactions and gravity, needs a common mathematical framework for the classical theory. For this purpose, we consider graded Poisson brackets which are deformed via gauge interactions and gravity. We show that the bosonic string and the (spinning) relativistic particle can be coherently formulated via this approach. Ultimately, models have to be compatible with physical observations. In this work we describe two methods which are used to investigate the temperature fluctuations of the Cosmic Microwave Background for deviations from Gaussianity and Isotropy: multipole vectors and pseudo entropies.