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Scientific paper
Oct 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt.......109r&link_type=abstract
Thesis (PhD). CORNELL UNIVERSITY, Source DAI-B 58/08, p. 4295, Feb 1998, 190 pages.
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Scientific paper
This dissertation is concerned with non-perturbative aspects of field theories in the setting of the early Universe. The work consists of two main areas of research. In chapter 1 the existence and nature of so- called inverse phase transitions is investigated. It has long been known that according to the loop expansion many theories contain portions of parameter space for which spontaneously broken symmetries are not restored at high temperature. We investigate this phenomenon of symmetry non-restoration (and the closely related phenomenon of inverse symmetry breaking, where a symmetry that is good at low temperature is broken at high temperature) with the aid of non-perturbative renormalization group techniques based on the Wilsonian effective action. These techniques allow us to prove the existence of inverse phase transitions in a more rigorous framework since the renormalization group approach does not suffer from the infrared divergences that plague the loop expansion near the critical temperature. We are also able to establish that the transitions are second order and that the broken phase persists to arbitrarily high temperature. The second problem being investigated is the evolution of the Universe after inflation, in particular the process of reheating. It was only recently realized that for a large class of inflationary models the theory of reheating based on perturbative decay of the inflaton is inadequate. Instead a non-perturbative resonance mechanism dominates the energy transfer from the inflaton to other fields. In chapter 2 this phenomenon is investigated using lattice simulations for a simple two scalar field model in Minkowski space. Analytic estimates for the decay time and the maximum variances at resonance shutoff are derived. Chapter 3 treats in detail the more realistic case of scalar fields in the expanding Universe. A general analytic criterion for the resonance shutoff is obtained and verified by lattice simulations. Of particular interest is the case when the coupling between the inflaton and a second scalar field is negative. In this case the production of very heavy particles, such as the X-bosons required for GUT baryogenesis, becomes possible. The resulting baryon asymmetry is calculated analytically in a simple toy model.
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