Relativistic Corrections and Structure Formation in Dark Matter Superfluidity

TL;DR

This paper extends the dark matter superfluidity model to include relativistic effects and analyzes how it influences structure formation, showing its potential to match cosmological observations while maintaining MOND-like behavior at galactic scales.

Contribution

It systematically incorporates relativistic corrections into the superfluid dark matter model and performs a linear perturbation analysis within FLRW spacetime.

Findings

Relativistic corrections are compatible with large-scale structure formation.

The model reproduces standard $ ext{Λ}$CDM behavior at the background level.

Parameter regimes are identified where the model aligns with observations.

Abstract

The theory of dark matter superfluidity has emerged as a compelling framework, in which the dynamics are governed by a non-relativistic $P(X)$ superfluid Lagrangian that naturally leads to Modified Newtonian Dynamics (MOND)-like behavior when coupled to baryons at galactic scales. Notably, at cosmological scales, this effective description reproduces the standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model at the background level, suggesting that cold dark matter may undergo Bose--Einstein condensation at galactic scales. In this work, we extend the non-relativistic formulation by systematically incorporating relativistic corrections within the Friedmann--Lema\^itre--Robertson--Walker (FLRW) spacetime. We further perform a linear perturbation analysis in this relativistic setting to investigate the evolution of matter density fluctuations. Our results clarify the viability of the superfluid dark matter scenario in explaining large-scale structure formation and identify the parameter regimes in which it remains consistent with current cosmological observations.