Boundary terms in cosmology

TL;DR

This paper explores an alternative boundary term treatment in cosmology using Lagrange multipliers, predicting a stiff matter component that decays as the sixth power of the scale factor, relevant to early universe models.

Contribution

It introduces a novel method for handling boundary terms in cosmology, linking them to a decaying stiff matter fluid via Lagrange multipliers.

Findings

Predicts a stiff matter fluid component in the universe.

Shows the boundary term can be enforced to vanish during cosmic evolution.

Connects boundary term treatment to early universe scalar fields.

Abstract

In the derivation of the Einstein field equations via Hamilton's principle, the inclusion of a boundary term is essential to render the variational problem well-posed, as it addresses variations that do not vanish at the boundary of the spacetime manifold. Typically, this term is chosen as the Gibbons-Hawking-York boundary term. In this work, we propose an alternative treatment of the boundary term within a cosmological framework by employing the Lagrange multiplier method. This approach enforces the vanishing of the boundary term throughout the evolution of the Universe, leading to the prediction of a fluid component that decays as the sixth power of the scale factor. This type of fluid has been studied in the context of the early universe under the name of stiff matter, and it can be related to a scalar field known as kination.