Machine Learning Quintessence Dark Energy Potentials via Symbolic Regression and Bayesian Inference
Quintessence is a hypothesized scalar field forming a popular model for dark energy, the nonluminous energy density in the Universe responsible for the accelerated expansion of space. This field can change in time and henceforth solve difficulties arising in the ΛCDM standard model. The dynamics of the field are governed by its self-interaction potential. To infer the form of this potential by observational data, we construct a suitable potential using machine learning and derive the observable quantities then numerically. Symbolic regression is a form of supervised learning, with the aim of finding the most likely symbolic representations of mathematical models for a given data set.
We demonstrate how to build a symbolic regression machine learning pipeline, searching for self-interaction potentials of the quintessence scalar field Lagrangian. To construct this pipeline, we first implement a symbolic regression algorithm searching for classical Lagrangian potentials and discuss its ability to solve the problem for artificial data. For upgrading this algorithm to search for quintessence potentials, we assembly an automatic process of evaluating the individual potentials and comparing the resulting models to data of supernovae type Ia with Bayesian statistics. We discuss the difficulties of automatically assigning Bayesian measures due to the high complexity of the fitness process as well as limited computing strength. We conclude, that our symbolic regression pipeline is capable of finding suitable quintessence potentials under consideration of sufficiently diverse function populations.
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