Non-relativistic effective theories for fields with general potentials and their implications for cosmology

TL;DR

This paper develops a systematic framework for deriving non-relativistic effective field theories from relativistic theories with general potentials, enabling better modeling of cosmological phenomena like ultra-light dark matter and solitons.

Contribution

It introduces a novel method to derive NREFTs for arbitrary potentials, including non-power-law and non-analytic forms, and extends the formalism to cosmological and astrophysical applications.

Findings

Derived NREFTs for generic self-interactions including non-analytic potentials.

Established an effective fluid description with key quantities like energy density and sound speed.

Applied the formalism to analyze solitons, boson stars, and dark matter halos.

Abstract

Non-relativistic effective field theories (NREFTs) play a crucial role in various areas of physics, from cold atom experiments to cosmology. In this paper, we present a systematic framework for deriving NREFTs from relativistic theories with generic self-interactions. Our approach allows for (but is not limited to) non-power-law potentials (such as those arising from dilatons or axions) or potentials that are non-analytic around the classical vacuum (such as those with logarithmic radiative corrections). These are of theoretical and phenomenological interest but have largely been unexplored in the non-relativistic regime. NREFTs are typically viewed as approximations for systems with low velocities, weak couplings, and small field amplitudes. The latter assumption is relaxed in our approach, as long as the mass term remains dominant (ensuring the validity of the non-relativistic limit). Additionally, we establish an effective fluid description for the non-relativistic scalar field, identifying key quantities such as energy density, pressure, and sound speed. To enable cosmological applications, we extend our formalism to account for the expanding universe, providing a reliable tool for investigating ultra-light dark matter models with arbitrary self-interactions. Finally, we demonstrate the applicability of our NREFT in analyzing solitons, which is also relevant to cosmology for studying celestial objects such as boson stars and the cores of dark matter halos.