Cosmological models with Lagrange Multiplier Field

TL;DR

This paper explores how Lagrange multiplier fields influence cosmological models, showing they can stabilize energy densities and potentially explain dark energy and dark matter phenomena.

Contribution

It introduces the role of Lagrange multiplier fields in modifying energy density evolution in Einstein-aether and quintessence models, offering new insights into dark energy and dark matter origins.

Findings

Einstein-aether energy density remains nearly constant over cosmic history.

Quintessence energy density can be nearly constant or phantom-like.

Lagrange multiplier fields enable scalar fields to mimic cold dark matter.

Abstract

We first consider the Einstein-aether theory with a gravitational coupling and a Lagrange multiplier field, and then consider the non-minimally coupled quintessence field theory with Lagrange multiplier field. We study the influence of the Lagrange multiplier field on these models. We show that the energy density evolution of the Einstein-aether field and the quintessence field are significantly modified. The energy density of the Einstein-aether is nearly a constant during the entire history of the Universe. The energy density of the quintessence field can also be kept nearly constant in the matter dominated Universe, or even exhibit a phantom-like behavior for some models. This suggests a possible dynamical origin of the cosmological constant or dark energy. Further more, for the canonical quintessence in the absence of gravitational coupling, we find that the quintessence scalar field can play the role of cold dark matter with the introduction of a Lagrange multiplier field. We conclude that the Lagrange multiplier field could play a very interesting and important role in the construction of cosmological models.