CosmoTransitions: Computing cosmological phase transition temperatures and bubble profiles with multiple fields

Abstract

Abstract I present a numerical package (CosmoTransitions) for analyzing finite-temperature cosmological phase transitions driven by single or multiple scalar fields. The package analyzes the different vacua of a theory to determine their critical temperatures (where the vacuum energy levels are degenerate), their supercooling temperatures, and the bubble wall profiles which separate the phases and describe their tunneling dynamics. I introduce a new method of path deformation to find the profiles of both thin- and thick-walled bubbles. CosmoTransitions is freely available for public use. Program summary Program Title: CosmoTransitions Catalogue identifier: AEML_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEML_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 8775 No. of bytes in distributed program, including test data, etc.: 621096 Distribution format: tar.gz Programming language: Python. Computer: Developed on a 2009 MacBook Pro. No computer-specific optimization was performed. Operating system: Designed and tested on Mac OS X 10.6.8. Compatible with any OS with Python installed. RAM: Approximately 50 MB, mostly for loading plotting packages. Classification: 1.9, 11.1. External routines: SciPy, NumPy, matplotLib Nature of problem: I describe a program to analyze early-Universe finite-temperature phase transitions with multiple scalar fields. The goal is to analyze the phase structure of an input theory, determine the amount of supercooling at each phase transition, and find the bubble-wall profiles of the nucleated bubbles that drive the transitions. Solution method: To find the bubble-wall profile, the program assumes that tunneling happens along a fixed path in field space. This reduces the equations of motion to one dimension, which can then be solved using the overshoot/undershoot method. The path iteratively deforms in the direction opposite the forces perpendicular to the path until the perpendicular forces vanish (or become very small). To find the phase structure, the program finds and integrates the change in a phase’s minimum with respect to temperature. Running time: Approximately 1 minute for full analysis of the two-scalar-field test model on a 2.5 GHz CPU.