Reconstruction of k-essence model

TL;DR

This paper presents a method to explicitly reconstruct k-essence models that can reproduce any arbitrary FRW cosmology, including special cases like quintessence and tachyon models, with stability considerations.

Contribution

The authors provide explicit formulas for reconstructing k-essence models for arbitrary cosmologies, including stability analysis and handling of redundant functions.

Findings

Reconstruction formulas for k-essence models are derived.

Exact $ ext{Lambda}$CDM reproduction is impossible with only kinetic terms.

Including potentials allows stable models matching desired cosmologies.

Abstract

We explicitly construct the k-essence models which reproduce the arbitrary FRW cosmology, that is, the arbitrary time-development of the scale factor or the Hubble rate. The k-essence model includes scalar quintessence model, tachyon dark energy model, ghost condensation model as special cases. Explicit formulas of the reconstruction are given. First we consider the case that the action only contains the kinetic term. In this case, we find that the model reproducing the development of the universe in the exact $\Lambda$CDM model cannot be constructed although there is a model which reproduces the development infinitely closing to $\Lambda$CDM model. We find, however, the solution is not stable. Another is more general case including potential etc., where we find that there appear infinite number of arbitrary functions of the scalar fields, which are redundant to the time development of the scale factor. By adjusting one of the redundant functions, however, we can obtain the model where any solution we need could be stable.