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Title A Covariant Natural Ultraviolet Cutoff in Inflationary Cosmology
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University/Publisher University of Waterloo
Abstract In the field of quantum gravity, it is widely expected that some form of a minimum length scale, or ultraviolet cutoff, exists in nature. Recently, a new natural ultraviolet cutoff that is fully covariant was proposed. In the literature, most studies of ultraviolet cutoffs are concerned with Lorentz-violating ultraviolet cutoffs. The difficulty in making a minimum length cutoff covariant is rooted in the fact that any given length scale can be further Lorentz contracted. It was shown that this problem is avoided by the proposed covariant cutoff by allowing field modes with arbitrarily small wavelengths to still exist, albeit with exceedingly small, covariantly-determined bandwidths. In other words, the degrees of freedom of sub-Planckian modes in time are highly suppressed. The effects of this covariant ultraviolet cutoff on the kinematics of a scalar quantum field are well understood. There is much to learn, however, about the effects on a field’s dynamics. These effects are of great interest, as their presence may have direct observational consequences in cosmology. As such, this covariant ultraviolet cutoff offers the tantalizing prospect of experimental access to physics at the Planck scale. In cosmology, the energy scales that are probed by measurements of cosmic microwave background (CMB) statistics are the closest that we can get to the Planck scale. In particular, the statistics of the CMB encodes information about the quantum fluctuations of the scalar inflaton field. A measure of the strength of a field’s quantum fluctuations is in turn given by the magnitude of the field’s Feynman propagator. To this end, in this thesis I study how this covariant ultraviolet cutoff modifies the Feynman propagator of a scalar quantum field. In this work, I first calculate the cutoff Feynman propagator for a scalar field in flat spacetime, and then I address the cutoff Feynman propagator of a scalar field in curved spacetime. My studies culminate with an explicit calculation for the case of a power-law Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. This last calculation is cosmologically significant, as power-law FLRW spacetime is a prototypical and realistic model for early-universe inflation. In preparation for studying the covariant cutoff on curved spacetime, I will review the necessary back- ground material as well as the kinematic influence of the covariant cutoff. I will also discuss several side results that I have obtained on scalar quantum field theories in spacetimes which possess a finite start time.
Subjects/Keywords theoretical physics; mathematical physics; cosmology; quantum field theory; quantum gravity; Planck scale effects; trans-Planckian; UV cutoff
Language en
Country of Publication ca
Record ID handle:10012/7759
Repository waterloo
Date Retrieved
Date Indexed 2020-08-12

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Planck scale [1]. Consider, for instance, the following heuristic argument. Suppose one wishes to resolve some very fine physical feature or to make a very precise distance measurement. Doing so, Heisenberg’s Uncertainty Principle implies that…

…experimental access to physics at the Planck scale. 1 In cosmology, the energy scales that are probed by measurements of cosmic microwave background (CMB) statistics are the closest that we can get to the Planck scale. In particular, the statistics…

…be that Planck scale effects could be observed in the CMB at only five to six orders of magnitude below the baseline. Such precision may be within the reach of conceivable experiments assuming that the cosmic foreground can be subtracted with…

…standard inner product on a Hilbert space. x Chapter 1 Introduction In the field of quantum gravity, it is widely expected that some form of a minimum length scale, or natural ultraviolet (UV) cutoff, exists in nature at the order of the…

…must know how spacetime curves, however, in order to measure distance. Therefore, the uncertainty in curvature causes uncertainty in the original distance measurement. One thus concludes that there should be a smallest length scale, presumably at the…

…order of a Planck length, beyond which smaller distances cannot be resolved. Any attempts to resolve finer lengths are undone by curvature uncertainties. In the literature, most studies of natural UV cutoffs have been concerned with cutoffs that break…

…local Lorentz symmetry. The difficulty in making a minimum length cutoff covariant is rooted in the fact that any given length scale can be further Lorentz contracted. Put simply, length is not a covariant quantity. Nevertheless, it is possible to…

…inflation. In most models of inflation, the Planck length and the Hubble length – the two relevant characteristic length scales of this epoch – are thought to have been separated by only five to six orders of magnitude [11, 12]. Therefore, it may…

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