Dynamical analysis of $k$-essence cosmology in the light of Supernova Ia observations

Abstract

In this paper, we analyse the JLA data on Supernova observations in the context of $k-$essence dark energy model with Lagrangian $L=VF(X)$, with a constant potential $V$ and the dynamical term $X=(1/2){\nabla }_{\mu }\varphi {\nabla }_{\nu }\varphi ={\dot{\varphi }}^2/2$ for a homogeneous scalar field $\varphi (t)$, in a flat FRW spacetime background. Scaling relations are used to extract temporal behaviour of different cosmological quantities and the form of the function $F(X)$ from the data. We explore how the parameters of the model, viz. value of the constant potential $V$ and a constant $C$ appearing in the emergent scaling relation, control the dynamics of the model in the context of JLA data, by setting up and analysing an equivalent dynamical system described by a set of autonomous equations.

22 pages, 7 figures, 3 tables; Accepted for publication in European Physical Journal Plus

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