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Quantum backreactions in slow-roll and de Sitter spacetimes Losic, Bojan

Abstract

This thesis is comprised of three projects. In the first, I consider fluctuations in a perfect irrotational fluid coupled to gravity in an Einstein static universe background. I show that a linearization instability occurs in Einstein static spacetimes despite the presence of matter, and that this instability can only avoided by inducing spatially homogeneous perturbations of the spacetime. Since the first order homogeneous perturbations in this case are well known to be exponentially (dynamically) unstable, the tactic of neglecting these modes to create a long-lived, perturbed Einstein static universe does not work, even if all higher order (L > 1) modes are dynamically stable. The main conclusion is that Einstein static is unconditionally unstable at first order in perturbation theory despite the presence of a large class of neutrally stable, inhomogeneous, modes. In the second, I examine the importance of second order corrections to linearized cosmological perturbation theory in an inflationary background, taken to be a spatially flat FRW spacetime. The full second order problem is solved in the sense that I evaluate the effect of the superhorizon second order corrections on the inhomogeneous and homogeneous modes of the linearized flucuations. In order to quantify their physical significance I study their effective equation of state by looking at the perturbed energy density and isotropic pressure to second order. I define the energy density (isotropic pressure) in terms of the (averaged) eigenvalues associated with timelike (spacelike) eigenvectors of a total stress energy for the metric and matter fluctuations, and find that the second order contributions to the dispersion of these eigenvalues becomes of the same order or exceeds that of the linear contributions. This occurs for a wide range of initial conditions for slow-roll inflation and results in a constraint on the small slow-roll parameter of that model. The main conclusion is that the linearized approximation of a slowly rolling spacetime may, under reasonable circumstances, be intrinsically sick since higher order contributions are comparable to, or substantially larger than, the linear contributions. In the third and final project, backreactions are considered in a pure de Sitter space whose cosmological constant is generated by the potential of scalar field. The leading order effect of matter backreactions on the gravitational field is considered. The initial value problem for the perturbed Einstein equations is proven to generically possess linearization instabilites. I furthermore show that these linearization instabilities can be avoided by assuming strict de Sitter invariance of the quantum states of the linearized fluctuations. This invariance constraint applies to the entire spectrum of states, from the vacuum to the excited states, and is in that sense much stronger than the usual Poincare invariance of the Minkowski vaccum. Some sketches are presented on how to construct de Sitter invariant states. The main conclusion is that to leading order in their effect on the gravitational field, the quantum states of the matter and metric fluctuations must be de Sitter invariant.

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