Salehian, BornaZhang, Hong-YiAmin, Mustafa A.Kaiser, David I.Namjoo, Mohammad Hossein2021-09-232021-09-232021Salehian, Borna, Zhang, Hong-Yi, Amin, Mustafa A., et al.. "Beyond Schrödinger-Poisson: nonrelativistic effective field theory for scalar dark matter." <i>Journal of High Energy Physics,</i> 2021, (2021) Springer Nature: 50. https://doi.org/10.1007/JHEP09(2021)050.https://hdl.handle.net/1911/111401Massive 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.engThis article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.Journal articleSalehian2021https://doi.org/10.1007/JHEP09(2021)050