Single-Field Inflation with the Standard Model Higgs

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http://urn.fi/URN:NBN:fi:hulib-202012074705
Title: Single-Field Inflation with the Standard Model Higgs
Author: Bracho Blok, Fernando Arturo
Contributor: University of Helsinki, Faculty of Science
Publisher: Helsingin yliopisto
Date: 2020
Language: eng
URI: http://urn.fi/URN:NBN:fi:hulib-202012074705
http://hdl.handle.net/10138/322422
Thesis level: master's thesis
Discipline: Teoreettinen fysiikka
Abstract: We study single scalar field inflation with the standard model Higgs boson as the inflaton. We first review the homogeneous and isotropic description of the universe given by the FLRW model as well as the inflation scenario. Then we study how this scenario can can be achieved by a single scalar field minimally coupled to gravity in the slow-roll approximation. Next we study linear perturbation theory around the FLRW background. Here the perturbations are decoupled into scalar, vector and tensor perturbations which allows to study them separately. The split of physical quantities into perturbations around a background introduces gauge degrees of freedom which we address by reviewing gauge transformation of the scalar and tensor perturbations (the latter which turns out to be gauge-independent). We then use the comoving gauge and define, for the scalar perturbations, the gauge-invariant quantity known as the comoving curvature perturbation. For scalar perturbations the Einstein Field equation yields the Mukhanov-Sasaki equation, which we solve to first order in the slow-roll approximation in terms of the Mukhanov variable. We then quantize this variable using canonical quantization and calculate the power spectrum from vacuum fluctuations. We also carry the same analysis for tensor perturbations. With the power spectra at hand we introduce the spectral parameters and discuss current observations and constraints on such parameters. In Higgs inflation the Standard Model Higgs boson takes the role of the inflaton. Here the Higgs field is also coupled to the Ricci scalar, giving us a non-minimal coupling to gravity. This coupling can be transformed away using a conformal transformation at the expense of a field re-definition. This enables us to use the results reviewed thus far. At tree level we find the inflationary predictions to be in excellent agreement with current observations. However, quantum corrections complicate this picture. We review the tree level unitarity of the model and examine arguments in favour and against it. We also study how quantum corrections can qualitatively change the shape of the potential and the viability of Higgs inflation in each scenario.
Subject: cosmology
inflation
Higgs field
non-minimal coupling
unitarity


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