False Vacuum Decay with Multiple Scalar Fields

Guada Escalona, Victor Francisco (author), Nemevšek, Miha (mentor)

As in boiling super-heated liquids, the decay of a false vacuum is a first-order phase transition. A local ground state decays to an energetically more favorable minimum of lower energy due to the thermal and quantum fluctuations of the fields. In this work, we present an efficient semi-analytic method that computes the decay rate of such a state for any number of scalar fields and space-time dimensions. It is based on the collection of an arbitrary number of linear segments that describe a potential with several minima. The exact evolution of the field for each segment to provide the complete description of the bounce field configuration, which provides the leading contribution of the decay rate. By increasing the number of segments, one obtains the bounce action up to the desired precision. The resulting matching equations are solved semi-analytically and the generalization to more fields is computed iteratively via linear analytic perturbations. Based on this construction, we provide a robust and user-friendly Mathematica package that implements our method, named FindBounce. As it preserves the semianalytic structure of the method, its computational time grows linearly with the number of fields and segments. We present several applications and comparisons with other tools, where typical running time is roughly less than 1 (2) seconds for 10 (20) fields with 0.5% accuracy of the action. Finally, we describe a procedure that computes subleading contributions of the decay rate for any smooth potentials and extend it to include potentials with discontinuous first derivatives. As a consequence, we exhibit an exact decay rate at one loop for a real and complex scalar field in a bi-quartic potential with two treelevel minima. We compute the product of eigenvalues, remove the translational zero modes and renormalize the divergences with the zeta function formalism. We end up with a complete decay rate in a closed-form.

• Language: English
• Keywords: Quantum tunneling, Instantons, False vacuum decay, Vacuum stability, Phase transitions, Cosmology, Baryogenesis, Gravitational waves.
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-125903
• COBISS.SI-ID: 59570947
• Publication date in RUL: 09.04.2021

Secondary language

• Language: Slovenian
• Title: Razpad lažnega vakuuma z več skalarnimi polji

Abstract

Kot pri vrenju pregretih tekočin, je razpad lažnega vakuuma fazni prehod prvega reda. Lokalno osnovno stanje preide v energetsko bolj ugoden nižji minimum energije, ki se zgodi zaradi termičnih in kvantnih fluktuacij polj. V tem delu predstavimo učinkovito semi-analitično metodo, ki izračuna razpadni čas takšnega stanja za poljubno število skalarnih polj in prostorsko-časovnih dimenzij. Osnovana je na naboru poljubnega števila linearnih segmentov, ki opišejo potencial z več minimi. Eksaktne rešitve razvoja polja za vse segmente so združene v popoln opis konfiguracije odbojnega polja, ki dá vodilni prispevek k razpadni širini. S povečevanjem števila segmentov, dobimo odbojno akcijo do željene natančnosti. Ujemane enačbe, ki se pri tem pojavijo, se reši analitično, posplošitev na več polj pa je izračunana iterativno s pomočjo linearnih analitičnih perturbacij. Na osnovi te konstrukcije smo ustvarili robusten in uporabniku prijazen Mathematica paket, imenovan FindBounce, ki implementira našo metodo. Zaradi semianalitične strukture, računska zahtevnost raste linearno s številom polj in segmentov. Predstavimo nekaj aplikacij in primerjav z drugimi orodji, pri katerih je izvajalni čas v grobem manj kot 1 (2) sekundi za 10 (20) polj z 0.5% natančnostjo akcije. Za konec opišemo postopek, ki izvrednoti prispevke višjega reda k razpadni širini za poljuben gladek potencial, in ga posplošimo tako, da zaobjame tudi potenciale z nezveznimi prvimi odvodi. Posledično dobimo točno razpadno širino na nivoju ene zanke za realno in kompleksno skalarno polje v dvojnem kvartičnem potencialu z dvema minima na drevesnem redu. Izračunamo produkt lastnih vrednosti, odstranimo translacijske ničelne načine in renormaliziramo divergence s formalizmom zeta funkcije. Ostane nam zaključena oblika celotne razpadne širine.

• Keywords: Kvantno tuneliranje, instantoni, razpad lažnega vakuuma, stabilnost vakuuma, fazni prehodi, kozmologija, bariogeneza, gravitacijski valovi.