Beyond Schrödinger-Poisson: nonrelativistic effective field theory for scalar dark matter
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Author(s)
Salehian, Borna
Zhang, Hong-Yi
Amin, Mustafa A.
Kaiser, David I.
Namjoo, Mohammad H.
Date Issued
September 9, 2021
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2021 Sep 09;2021(9):50
Version
Final published version
Abstract
Abstract
Massive scalar fields provide excellent dark matter candidates, whose dynamics are often explored analytically and numerically using nonrelativistic Schrödinger-Poisson (SP) equations in a cosmological context. In this paper, starting from the nonlinear and fully relativistic Klein-Gordon-Einstein (KGE) equations in an expanding universe, we provide a systematic framework for deriving the SP equations, as well as relativistic corrections to them, by integrating out ‘fast modes’ and including nonlinear metric and matter contributions. We provide explicit equations for the leading-order relativistic corrections, which provide insight into deviations from the SP equations as the system approaches the relativistic regime. Upon including the leading-order corrections, our equations are applicable beyond the domain of validity of the SP system, and are simpler to use than the full KGE case in some contexts. As a concrete application, we calculate the mass-radius relationship of solitons in scalar dark matter and accurately capture the deviations of this relationship from the SP system towards the KGE one.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP09(2021)050
