CosmoTransitions: Computing Cosmological Phase Transition Temperatures and Bubble Profiles with Multiple Fields

TL;DR

CosmoTransitions addresses the challenge of analyzing cosmological phase transitions driven by multiple scalar fields by providing a Python toolkit that computes the temperature-dependent phase structure, critical (degenerate) temperatures, and nucleation/bubble-wall profiles. The core innovation is a path-deformation algorithm that enables robust multi-field tunneling calculations, reducing the problem to a sequence of one-dimensional solves along a deformable path represented by splines. The package also incorporates one-loop finite-temperature corrections and a practical framework for implementing specific models via a generic_potential subclass, with demonstrations of multi-step transitions and thin- vs thick-walled bubbles. This work offers a practical, extensible toolset for exploring electroweak baryogenesis scenarios and gravitational-wave implications in beyond-Standard-Model theories. The methods enable rapid, accurate assessment of phase transition dynamics across multiple field dimensions and parameter choices.

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 super-cooling 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.

Figures (9)

• Figure 1: Overview of the CosmoTransitions package file structure. The files pathDeformation.py and tunneling1D.py find critical bubble profiles, transitionFinder.py finds the minima of finite temperature potentials as a function of temperature and analyzes phase transitions, and generic_potential.py defines an abstract class that can easily be subclassed to examine a specific model.
• Figure 2: The equations of motion for a field with a potential $V(\phi)$ can be thought of as the equations for a particle moving in an inverted potential $-V(\phi)$.
• Figure 3: A problematic potential with more than two minima. A tunneling solution from $\phi_A$ to $\phi_C$ is only guaranteed to exist for the topmost potential (blue line).
• Figure 4: Path deformation in two dimensions. The normal force exerted on the starting path (blue straight line) pushes it in the direction of the true tunneling solution (green curved line).
• Figure 5: Example of error correction in deformation. The normal force will push wiggles down towards the straight line solution. But if the stepsize is too large, the wiggles will get reversed and amplified instead.