Reconstruction of a kinetic k--essence Lagrangian from a modified of dark energy equation of state

TL;DR

This paper reconstructs the Lagrangian density of a purely kinetic k-essence dark energy model from four parameterized equations of state, using a numerical method and observational supernova data to constrain the models.

Contribution

It introduces a numerical reconstruction method for the k-essence Lagrangian from various dark energy equations of state and applies observational constraints using supernova data.

Findings

Reconstructed k-essence Lagrangians for multiple EoS parameterizations.

Numerical solutions relate Lagrangian density to given EoS.

Constraints on models based on 586 supernovae data points.

Abstract

In this paper the Lagrangian density of a purely kinetic k--essence that models the behavior of dark energy described by four parameterized equations of state proposed by Cooray \& Huterer (Astrophys. J. {\bf 513} L95, 1999), Zhang \& Wu (Mod. Phys. Lett. A {\bf 27} 1250030, 2012), Linder (Phys. Rev. Lett. {\bf 90} 091301, 2003), Efstathiou (Mon. Not. Roy. Astron. Soc. {\bf 310} 842, 2000), and Feng \& Lu (J. Cosmol. Astropart. Phys. {\bf 1111} 034, 2011) has been reconstructed. This reconstruction is performed using the method outlined by de Putter \& Linder (Astropart.\ Phys.\ {\bf 28} 263, 2007), which makes it possible to solve the equations that relate the Lagrangian density of the k--essence with the given equation of state (EoS) numerically. Finally, we discuss the observational constraints for the models based on 586 SNIa data points from the LOSS data set compiled by Ganeshalingam et al. (Mon. Not Roy. Astron. Soc. {\bf 433} 2240, 2013).