https://doi.org/10.1140/epjc/s10052-025-14258-y
Regular Article - Theoretical Physics
PhaseTracer2: from the effective potential to gravitational waves
1
School of Physics, Henan Normal University, 453007, Xinxiang, People’s Republic of China
2
Institute of Theoretical Physics and Institute of Physics Frontiers and Interdisciplinary Sciences, Nanjing Normal University, Wenyuan Road, 210023, Nanjing, Jiangsu, China
3
Nanjing Key Laboratory of Particle Physics and Astrophysics, 210023, Nanjing, China
4
School of Physics and Astronomy, Monash University, 3800, Melbourne, VIC, Australia
5
Department of Physics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, 215123, Suzhou, China
6
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China
7
School of Physical Sciences, 100049, Beijing, China
8
School of Physics, Zhengzhou University, 450001, Zhengzhou, China
Received:
18
December
2024
Accepted:
3
May
2025
Published online:
21
May
2025
In recent years, the prospect of detecting gravitational waves sourced from a strongly first-order cosmological phase transition has emerged as one of the most exciting frontiers of gravitational wave astronomy. Cosmological phase transitions are an essential ingredient in the Standard Model of particle cosmology, and help explain the mechanism for creation of matter in the early Universe, provide insights into fundamental theories of physics, and shed light on the nature of dark matter. This underscores the significance of developing robust end-to-end tools for determining the resulting gravitational waves from these phase transitions. In this article we present PhaseTracer2, an improved version of the C++ software package PhaseTracer, designed for mapping cosmological phases and transitions in Standard Model extensions of multiple scalar fields. Building on the robust framework of its predecessor, PhaseTracer2 extends its capabilities by including new features crucial for a more comprehensive analysis of cosmological phase transitions. It can calculate more complex properties, such as the bounce action through the path deformation method or an interface with BubbleProfiler, thermodynamic parameters, and gravitational wave spectra. Its applicability has also been broadened via incorporating the dimensionally reduced effective potential for models obtained from DRalgo, as well as calculations in the 
and OS-like renormalisation schemes. This modular, flexible, and practical upgrade retains the speed and stability of the original PhaseTracer, while significantly expanding its utility.
© The Author(s) 2025
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