The art of simulating the early universe. Part I. Integration techniques and canonical cases

@article{Figueroa2020TheAO,
  title={The art of simulating the early universe. Part I. Integration techniques and canonical cases},
  author={Daniel G. Figueroa and Adrien Florio and Francisco Torrenti and Wessel Valkenburg},
  journal={Journal of Cosmology and Astroparticle Physics},
  year={2020},
  volume={2021}
}
We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of 𝒪(δ t2) accuracy like staggered leapfrog and… 

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