The gravitating perfect fluid-scalar field equations: quintessence and tachyonic

TL;DR

This paper analyzes the coupled equations of a self-gravitating perfect fluid with scalar fields, specifically quintessence and tachyonic types, exploring their mathematical properties, initial value problem, and providing a numerical example.

Contribution

It offers a detailed mathematical study of the gravitating perfect fluid-scalar field system, including the Cauchy problem and a numerical scheme for quintessence and tachyonic fields.

Findings

Mathematical properties and identities of the system are established.

The initial constraint equations for the system are derived.

A Taylor series-based numerical evolution scheme is demonstrated.

Abstract

The system consisting of a self gravitating perfect fluid and scalar field is considered in detail. The scalar fields considered are the quintessence and ``tachyonic'' forms which have important application in cosmology. Mathematical properties of the general system of equations are studied including the algebraic and differential identities as well as the eigenvalue structure. The Cauchy problem for both quintessence and the tachyon is presented. We discuss the initial constraint equations which must be satisfied by the initial data. A Cauchy evolution scheme is presented in the form of a Taylor series about the Cauchy surface. Finally, a simple numerical example is provided to illustrate this scheme.