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Beyond Schr\"{o}dinger-Poisson: Nonrelativistic Effective Field Theory for Scalar Dark Matter

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arxiv 2104.10128 v1 pith:YESCL4TQ submitted 2021-04-20 astro-ph.CO hep-th

Borna Salehian , Hong-Yi Zhang , Mustafa A. Amin , David I. Kaiser , Mohammad Hossein Namjoo This is my paper · ORCID
classification astro-ph.COhep-th
keywords equationsmatterrelativisticcorrectionsdarkscalarsystembeyond
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Massive scalar fields provide excellent dark matter candidates, whose dynamics are often explored analytically and numerically using nonrelativistic Schr\"{o}dinger-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.

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Cited by 5 Pith papers

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