On the metastability of the Standard Model vacuum
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False vacuum
Metastability
False vacuum decay is the first-order phase transition of fundamental fields. Vacuum instability plays a very important role in particle physics and cosmology. Theoretically, any consistent theory beyond the Standard Model must have a lifetime of the electroweak vacuum longer than the age of the Universe. Phenomenologically, first-order cosmological phase transitions can be relevant for baryogenesis and gravitational wave production. In this thesis, we give a detailed study on several aspects of false vacuum decay, including correspondence between thermal and quantum transitions of vacuum in flat or curved spacetime, radiative corrections to false vacuum decay and, the real-time formalism of vacuum transitions.
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QED vacuum
Quantum fluctuation
Arrow of time
Vacuum polarization
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It is generally considered as self evident that the lifetime of our vacuum in the landscape of string theory cannot be much shorter than the current age of the universe. Here I show why this lower limit is invalid. A certain type of "parallel universes" is a necessary consequence of the string-landscape dynamics and might well allow us to "survive" vacuum decay. As a consequence our stringy vacuum's lifetime is empirically unconstrained and could be very short. Based on this counterintuitive insight I propose a novel type of laboratory experiment that searches for an apparent violation of the quantum-mechanical Born rule by gravitational effects on vacuum decay. If the lifetime of our vacuum should turn out to be shorter than 6 ×10 -13 seconds such an experiment is sufficiently sensitive to determine its value with state-of-the-art equipment.
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If the universe is trapped and cooled in a metastable false vacuum state, that state will eventually decay by bubble nucleation and expansion. For example, many extensions of the standard model incorporate new scalar fields $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}$ whose potential has a local minimum at $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}=0$ but a global minimum elsewhere, to which the vacuum will eventually tunnel. I calculate the lifetime of the false vacuum, and the field profile of the bubble after tunneling, for any potential that is approximately a polynomial of degree $<~4$ near the false vacuum. Essentially exact results are given for a single field; for multiple fields a strict lower bound is placed on the tunneling rate.
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Metastability
Scalar potential
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Baryon asymmetry
False vacuum
Cosmic string
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Ultracold atomic gases can undergo phase transitions that mimic relativistic vacuum decay, allowing us to empirically test early-Universe physics in tabletop experiments. We investigate the physics of these analog systems, going beyond previous analyses of the classical equations of motion to study quantum fluctuations in the cold-atom false vacuum. We show that the fluctuation spectrum of this vacuum state agrees with the usual relativistic result in the regime where the classical analogy holds, providing further evidence for the suitability of these systems for studying vacuum decay. Using a suite of semiclassical lattice simulations, we simulate bubble nucleation from this analog vacuum state in a 1D homonuclear potassium-41 mixture, finding qualitative agreement with instanton predictions. We identify realistic parameters for this system that will allow us to study vacuum decay with current experimental capabilities, including a prescription for efficiently scanning over decay rates, and show that this setup will probe the quantum (rather than thermal) decay regime at temperatures $T\lesssim10\,\mathrm{nK}$. Our results help lay the groundwork for using upcoming cold-atom experiments as a new probe of nonperturbative early-Universe physics.
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Ultracold atom
QED vacuum
Quantum fluctuation
Penning trap
Instanton
Vacuum arc
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Functional renormalization group
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The false (unstable) vacuum is discussed from the point of view of the quantum theory of unstable states. Properties of the energy of the system in the unstable vacuum state are studied. Within the model considered, it is shown that at very late times, the energy of the system in the false vacuum state tends to the energy of the system in the true vacuum state as 1/t 2 .
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We use analytic estimates and numerical simulations to explore the stochastic approach to vacuum decay. According to this approach, the time derivative of a scalar field, which is in a local vacuum state, develops a large fluctuation and the field "flies over" a potential barrier to another vacuum. The probability distribution for the initial fluctuation is found quantum mechanically, while the subsequent nonlinear evolution is determined by classical dynamics. We find in a variety of cases that the rate of such flyover transitions has the same parametric form as that of tunneling transitions calculated using the instanton method, differing only by a numerical factor O(1) in the exponent. An important exception is an "upward" transition from a de Sitter vacuum to a higher-energy de Sitter vacuum state. The rate of flyover transitions in this case is parametrically different and can be many orders of magnitude higher than tunneling. This result is in conflict with the conventional picture of quantum de Sitter space as a thermal state. Our numerical simulations indicate that the dynamics of bubble nucleation in flyover transitions is rather different from the standard picture. The difference is especially strong for thin-wall bubbles in flat space, where the transition region oscillates between true and false vacuum until a true vacuum shell is formed which expands both inwards and outwards, and for upward de Sitter transitions, where the inflating new vacuum region is contained inside of a black hole.
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Instanton
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We study radiative corrections to the decay rate of false vacua, paying particular attention to the renormalization-scale dependence of the decay rate. The decay rate exponentially depends on the bounce action. The bounce action itself is renormalization-scale dependent. To make the decay rate scale-independent, radiative corrections, which are due to the field fluctuations around the bounce, have to be included. We show quantitatively that the inclusion of the fluctuations suppresses the scale dependence, and hence is important for the precise calculation of the decay rate. We also apply our analysis to a supersymmetric model and show that the radiative corrections are important for the Higgs-stau system with charge breaking minima.
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Maxima and minima
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Nothing
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