Optimal Inflationary Potentials

TL;DR

This paper introduces a novel symbolic regression method to generate and evaluate inflationary potentials, aiming to identify models that best balance simplicity and data fit, thereby advancing understanding of the early Universe.

Contribution

It presents a new approach combining symbolic regression and information theory to systematically generate and assess inflationary potentials based on current cosmological data.

Findings

Identified potentials that optimally balance simplicity and data explanation.

Demonstrated the use of information-theoretic metrics in model selection.

Provided a framework for extracting fundamental physics from observational data.

Abstract

Inflation is a highly favoured theory for the early Universe. It is compatible with current observations of the cosmic microwave background and large scale structure and is a driver in the quest to detect primordial gravitational waves. It is also, given the current quality of the data, highly under-determined with a large number of candidate implementations. We use a new method in symbolic regression to generate all possible simple scalar field potentials for one of two possible basis sets of operators. Treating these as single-field, slow-roll inflationary models we then score them with an information-theoretic metric ("minimum description length") that quantifies their efficiency in compressing the information in current data. We explore two possible priors on the parameter space of potentials, one related to the functions' structural complexity and one that uses a Katz back-off language model to prefer functions that may be theoretically motivated. This enables us to identify the inflaton potentials that optimally balance simplicity with accuracy at explaining current data, which may subsequently find theoretical motivation. Our exploratory study opens the door to extraction of fundamental physics directly from data, and may be augmented with more refined theoretical priors in the quest for a complete understanding of the early Universe.