Supercomputers against strong coupling in gravity with curvature and torsion

TL;DR

This paper introduces HiGGS, a computational tool that automates Hamiltonian analysis of gravity theories with curvature and torsion, enabling large-scale surveys of strongly coupled modes in Poincaré gauge theories.

Contribution

The paper presents HiGGS, a novel Mathematica package that performs parallelized Hamiltonian constraint analysis for non-Riemannian gravity theories, facilitating exploration of their parameter space.

Findings

Surveyed the space of outlawed Poincaré gauge theories.

Identified configurations with potential to eliminate strong coupling.

Provided primary and secondary constraint brackets for future analysis.

Abstract

Many theories of gravity are spoiled by strongly coupled modes: the high computational cost of Hamiltonian analysis can obstruct the identification of these modes. A computer algebra implementation of the Hamiltonian constraint algorithm for curvature and torsion theories is presented. These non-Riemannian or Poincar\'e gauge theories suffer notoriously from strong coupling. The implementation forms a package (the `Hamiltonian Gauge Gravity Surveyor' - HiGGS) for the xAct tensor manipulation suite in Mathematica. Poisson brackets can be evaluated in parallel, meaning that Hamiltonian analysis can be done on silicon, and at scale. Accordingly HiGGS is designed to survey the whole Lagrangian space with high-performance computing resources (clusters and supercomputers). To demonstrate this, the space of `outlawed' Poincar\'e gauge theories is surveyed, in which a massive parity-even/odd vector or parity-odd tensor torsion particle accompanies the usual graviton. The survey spans possible configurations of teleparallel-style multiplier fields which might be used to kill-off the strongly coupled modes, with the results to be analysed in subsequent work. All brackets between the known primary and secondary constraints of all theories are made available for future study. Demonstrations are also given for using HiGGS - on a desktop computer - to run the Dirac-Bergmann algorithm on specific theories, such as Einstein-Cartan theory and its minimal extensions.