ELENA: a software for fast and precise computation of first order phase transitions and gravitational waves production in particle physics models

We present ELENA (EvaLuator of tunnElliNg Actions), an open-source Python package designed to compute the full evolution of first-order phase transitions in the early Universe generated by particle physics models, taking into account several refinements that go beyond commonly assumed simplifications. The core of ELENA is based on a vectorized implementation of the tunnelling potential formalism, which allows for a fast computation of the finite-temperature tunnelling action. This, in turn, enables the sampling of the full range of temperatures where two phases coexist and the use of integral expressions that track the complete evolution of the transition, providing a comprehensive picture of it. In addition, ELENA provides all the tools to compute the resulting stochastic gravitational waves spectrum, allowing for the full chain of computations - from the Lagrangian parameter inputs to the final gravitational waves spectrum - in a fast and self-contained implementation.