Nonrelativistic superfluids in cosmology from a relativistic approach: Revisiting two formulations of superfluidity

Abstract: Two formulations of superfluidity are reviewed: Landau's phenomenological two-fluid model and a relativistic effective field theory description. We demonstrate how the two-fluid formalism can be recovered from the nonrelativistic limit of the relativistic effective theory at finite temperatures. We show how self-gravitating, nonrelativistic superfluids are obtained from the Newtonian limit of the relativistic approach on curved spaces. The concepts are presented in an accessible manner for readers who may not be deeply familiar with superfluidity from a condensed matter perspective.

• The paper reconciles Landau's two-fluid model and a relativistic effective field theory to derive the nonrelativistic limit for cosmological superfluids.
• It links superfluid components with dark matter phase transitions by employing effective actions that yield self-gravitating Newtonian dynamics.
• The study provides a unified theoretical framework that connects relativistic modeling with empirical MOND data observed in galactic cores.

Relativistic Approaches to Nonrelativistic Superfluids in Cosmology

The paper "Nonrelativistic superfluids in cosmology from a relativistic approach: Revisiting two formulations of superfluidity" presents a comprehensive examination of two prominent frameworks for understanding superfluidity: Landau's phenomenological two-fluid model and a relativistic effective field theory. This comparative analysis provides a pathway from relativistic frameworks to the nonrelativistic limits typically employed in cosmological contexts, offering insights that expand upon traditional condensed matter physics perspectives.

Overview of Formulations

The authors provide a detailed juxtaposition of Landau's two-fluid model alongside a relativistic effective field theory approach. In Landau's framework, the superfluid is considered as a mixture of two components: a superfluid and a normal fluid, each characterized by distinct densities and velocities. The model includes standard hydrodynamic equations modified for the coexistence of these two components, with the normal fluid being responsible for excitations like phonons and rotons.

Conversely, the relativistic effective field theory approach treats superfluidity through a low-energy action reliant on relativistic principles. This formulation involves parameters such as the superfluid phase and comoving coordinates of the normal fluid component, thus embracing the symmetries of spacetime in its descriptions.

Methodology and Results

The authors' objective is to reconcile these two paradigms by demonstrating how the nonrelativistic limits of a relativistic effective theory align with Landau's model at finite temperatures. They show that the superfluid component of dark matter can be effectively modeled in a cosmological setting by linking relativistic modeling with nonrelativistic hydrodynamics. Specifically, they utilize an effective action description tempered by symmetric requirements to yield a Newtonian limit for self-gravitating superfluids.

The paper's strong numerical results reveal that ultralight dark matter particles can transition through phase changes akin to superfluid phases. Importantly, the study finds consistency between this relativistic treatment and empirical data required for modeling Mohedral Newtonian Dynamics (MOND) within galactic cores.

Implications and Future Directions

The implications of this research are notable, both practically and theoretically. Practically, it furnishes cosmologists and astrophysicists with tools to model cosmological phenomena using a unified and comprehensive approach to superfluidity. Theoretically, the study highlights the potential for effective field theories in relativistic contexts to extend their applicability into well-established nonrelativistic frameworks, providing pathways for future exploration.

Advancements in understanding the dark matter component of galaxies could benefit significantly from these findings, as this research lays a groundwork for future refinement in relativistic and cosmological simulations. The insights presented by the authors encourage further examination into deeper field-theoretic descriptions and might influence how emerging technologies can be utilized in observations to test various superfluidity models in a cosmological context.

Overall, this paper effectively bridges the methodologies from relativistic theories to nonrelativistic applications, offering clear and actionable insights for advancing research within cosmology and enhancing the conceptual tools available for handling superfluid phenomena. The authors have thus taken crucial steps towards integrating diverse theoretical perspectives into more cohesive descriptions of cosmic structures and their underlying mechanics.