Unraveling particle dark matter with Physics-Informed Neural Networks

TL;DR

This paper employs Physics-Informed Neural Networks to solve Boltzmann equations for dark matter in alternative cosmologies, enabling the inference of physical parameters from relic density data with uncertainty quantification.

Contribution

It introduces a mesh-free PINN approach to model freeze-in dark matter in non-standard cosmologies and infers key physical parameters from limited observational data.

Findings

Distinct relationship between cosmology exponent and particle cross sections.

PINNs successfully solve inverse problems with minimal data.

Uncertainty quantification enhances confidence in parameter estimates.

Abstract

We parametrically solve the Boltzmann equations governing freeze-in dark matter (DM) in alternative cosmologies with Physics-Informed Neural Networks (PINNs), a mesh-free method. Through inverse PINNs, using a single DM experimental point -- observed relic density -- we determine the physical attributes of the theory, namely power-law cosmologies, inspired by braneworld scenarios, and particle interaction cross sections. The expansion of the Universe in such alternative cosmologies has been parameterized through a switch-like function reproducing the Hubble law at later times. Without loss of generality, we model more realistically this transition with a smooth function. We predict a distinct pair-wise relationship between power-law exponent and particle interactions: for a given cosmology with negative (positive) exponent, smaller (larger) cross sections are required to reproduce the data. Lastly, via Bayesian methods, we quantify the epistemic uncertainty of theoretical parameters found in inverse problems.