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Nonminimal fluid Lagrangian couplings

Christian G Böhmer1,2,*, Erik Jensko1,†, and Eissa Al-Nasrallah1,3,‡

  • 1Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
  • 2Astrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa
  • 3Department of Physics, College of Science, Kuwait University, Sabah Al Salem University City, P.O. Box 5969, Safat 13060, Shadadiya, Kuwait

  • *Contact author: c.boehmer@ucl.ac.uk
  • †Contact author: erik.jensko@ucl.ac.uk
  • ‡Contact author: eissa.alnasrallah.24@ucl.ac.uk
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Phys. Rev. D 114, 044080 – Published 24 August, 2026

DOI: https://doi.org/10.1103/55rx-yrrj

Abstract

Gravitational models with nonminimal couplings involving functions of the matter Lagrangian and curvature have become popular in recent decades. By coupling the matter Lagrangian directly to the gravitational Lagrangian, one hopes to construct theories that can explain dark energy or dark matter without introducing additional sources. When this matter Lagrangian describes a perfect fluid, some technicalities are involved in its variational formulation. We present a careful derivation of the gravitational field equations together with the complete set of fluid equations using two approaches: Schutz’s velocity potential and Brown’s Lagrange multipliers. We find that with nonminimal couplings, the energy-momentum conservation equations give rise to a nonvanishing contribution which acts in a different direction depending on the approach. This also leads to the emergence of different effective thermodynamic quantities such as the number density, chemical potential, free energy, and temperature. We demonstrate the nonequivalence of the Lagrangian formulations of Schutz and Brown for these types of models and provide a detailed interpretation of our results.

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Phys. Rev. D 114, 044080– Published 24 August, 2026
  • Received 19 May 2026
  • Accepted 23 July 2026
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