Quantum Fields in Curved Spacetime with Cosmological and Gravitational Wave Implications

Abstract

A range of novel ideas, covering both general relativity and quantum field theory are introduced and explored. An analytic procedure for theories that modify the stress-energy-tensor in general relativity is examined which compares predicted deviations in the gravitational wave radiation from binary black hole mergers to the observed waveform from recent detections, i.e GW150914. This is applied directly to the theory of non-commutative spacetimes, which ultimately constrains the scale of non-commutative spacetime up to the Planck scale, some 15 orders of magnitude improvement on previous bounds. The stochastic background of gravitational wave radiation from first order electroweak phase transitions in the early universe is also examined. This is done in the context of the non-linearly realised electroweak sector of the Standard Model, which allows for a direct relation between coupling constants of the model and parameters of the expected stochastic gravitational wave background. For this particular model, a range of values are shown to not only produce gravitational waves detectable by future space-based detectors, such as eLISA, but can potentially create low-frequency radiation detectable by pulsar timing array experiments, such as the future SKA. Finally, non-inertial effects in the context of quantum fields in curved spacetimes are examined for a number of metrics. An oscillatory motion in the velocity expectation of a single fermionic particle is shown to exist in cosmological/expanding spacetimes, but not for accelerating or rotating spacetimes. In the rotating case, a new quantisation scheme is introduced along with the Bogoliubov coefficients enabling general calculations in rotating spaces to be computed with respect to defined non-rotating fermionic particle states.