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Paper   IPM / Astronomy / 16831
School of Astronomy
  Title:   Beyond Schrödinger-Poisson: Nonrelativistic Effective Field Theory for Scalar Dark Matter
1.  Borna . Salehian
2.  Hong-Yi . Zhang
3.  Mustafa . A. Amin
4.  David . I. Kaiser
5.  Mohammad Hossein. Namjoo
  Status:   Published
  Journal: JHEP
  Year:  2021
  Supported by:            ipm IPM
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

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