Quantum Field Theory and Decoherence in the Early Universe

Abstract

Quantum field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, quantum processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion. Inspired by these considerations, this PhD thesis is concerned with two aspects of quantum field theory relevant to cosmology: quantum backreaction and decoherence. Quantum backreaction is a line of research where the impact of quantum fluctuations on the background spacetime geometry in perturbative quantum gravity is investigated. The cosmological constant problem and the process of quantum backreaction are intimately related: quantum backreaction might provide us with a dynamical mechanism to effectively make the cosmological constant almost vanish. We investigate the quantum backreaction of the trace anomaly and of fermions. We find that the trace anomaly does not dynamically influence the effective value of the cosmological constant. We furthermore evaluate the fermion propagator in FLRW spacetimes with constant deceleration. Although the dynamics resulting from the one-loop stress-energy tensor need yet to be investigated, we find that we certainly cannot exclude a significant effect due to the quantum backreaction on the Universe’s expansion. Decoherence is a quantum theory which addresses the quantum-to-classical transition of a particular system. The idea of the decoherence formalism is that a macroscopic system cannot be separated from its environment. The framework of decoherence is widely used, e.g. in quantum computing, black hole physics, inflationary perturbation theory, and in elementary particle physics, such as electroweak baryogenesis models. We formulate a novel “correlator approach” to decoherence: neglecting observationally inaccessible correlators gives rise to an increase in entropy of the system, as perceived by an observer. This is inspired by realising that higher order, non-Gaussian correlators are usually perturbatively suppressed. A quantum system with a large entropy corresponds to an effectively classical, stochastic system. To allow for a quantitative comparison between our correlator approach and the conventional approach to decoherence, we apply both formalisms to two simple quantum mechanical models. We find that the entropy in the conventional approach to decoherence quite generically reveals secular growth, indicating physically unacceptable behaviour. The conventional approach furthermore suffers from the fact that no well-established treatment to take perturbative corrections into account exists, nor has the framework of renormalisation ever been implemented. Our correlator approach to decoherence is taylored to applications in quantum field theory. We perform the first realistic study of decoherence in a renormalised quantum field theoretical setting. Using out-of-equilibrium field theory techniques, we extract two quantitative measures of decoherence in our model: the total amount of decoherence and the decoherence rate. The main finding in this part of the thesis is that, although a pure state remains pure under unitary evolution, an observer perceives this state over time as a mixed state with positive entropy as non-Gaussianities are dynamically generated. Alternatively, one could say that a realistic observer cannot probe all information about the system and thus discerns a loss of coherence of the pure state