The well-posedness of the Cauchy problem for self-interacting vector fields

Barausse, Enrico; Bezares, Miguel; Crisostomi, Marco; Lara Delgado, Jose Guillermo

doi:10.1088/1475-7516/2022/11/050

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The well-posedness of the Cauchy problem for self-interacting vector fields

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Lara Delgado, Jose Guillermo
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Barausse, E., Bezares, M., Crisostomi, M., & Lara Delgado, J. G. (2022). The well-posedness of the Cauchy problem for self-interacting vector fields. Journal of Cosmology and Astroparticle Physics, 2022(11): 050. doi:10.1088/1475-7516/2022/11/050.

Cite as: https://hdl.handle.net/21.11116/0000-000C-347A-1

Abstract

We point out that the initial-value (Cauchy) problem for self-interacting
vector fields presents the same well-posedness issues as for first-order
derivative self-interacting scalar fields (often referred to as $k$-essence).
For the latter, suitable strategies have been employed in the last few years to
successfully evolve the Cauchy problem at the level of the infrared theory,
without the need for an explicit ultraviolet completion. We argue that the very
same techniques can also be applied to self-interacting vector fields, avoiding
a number of issues and "pathologies" recently found in the literature.