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Bridging superfluid and nonminimally coupled BEC dark matter through relativistic aquadratic Lagrangian theory

Stefano Liberati*, Valentin Pomakov†, and Samuele Silveravalle‡

  • *Contact author: liberati@sissa.it
  • †Contact author: vpomakov@sissa.it
  • ‡Contact author: ssilvera@sissa.it
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Phys. Rev. D 114, 104036 – Published 10 November, 2026

DOI: https://doi.org/10.1103/14wc-dmgf

Abstract

Motivated by their common condensed-matter inspiration and their shared aim of reconciling MOND-like phenomenology on galactic scales with particle dark matter on larger scales, we investigate the relation between Superfluid Dark Matter (SFDM) and Bose-Einstein Condensate Dark Matter (BECDM). Since SFDM is formulated in the Newtonian regime whereas BECDM is fully relativistic, we first show that the MONDian formulation of SFDM arises as the Newtonian, low-acceleration limit of a RAQUAL theory in the Einstein frame. We then transform its covariant interaction sector to the Jordan frame and compare it with BECDM. The phonon–baryon interaction of SFDM maps onto the BECDM derivative coupling to the Einstein tensor, supplemented by a small nonminimal coupling to the Ricci scalar. The interaction sectors are therefore equivalent up to a linear perturbation of the Einstein–Hilbert term. Their kinetic sectors, however, remain inequivalent: the standard quadratic kinetic term of BECDM cannot be mapped onto the nonanalytic kinetic term required by SFDM. The two models are consequently related but not dynamically equivalent. This mapping provides a covariant interpretation of the SFDM interaction and clarifies which theoretical properties can be transferred between the two frameworks.

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Outline

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Phys. Rev. D 114, 104036– Published 10 November, 2026
  • Received 8 August 2026
  • Accepted 9 October 2026
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