The $k$-essence scalar field in the context of Supernova Ia Observations

Abstract

A $k$-essence scalar field model having (non canonical) Lagrangian of the form $L=-V(\varphi )F(X)$ where $X=1/2g^{\mu \nu }{\nabla }_{\mu }\varphi {\nabla }_{\nu }\varphi$ with constant $V(\varphi )$ is shown to be consistent with luminosity distance-redshift data observed for type Ia Supernova. For constant $V(\varphi )$, $F(X)$ satisfies a scaling relation which is used to set up a differential equation involving the Hubble parameter $H$, the scale factor $a$ and the $k$-essence field $\varphi$. $H$ and $a$ are extracted from SNe Ia data and using the differential equation the time dependence of the field $\varphi$ is found to be: $\varphi (t)\sim {\lambda }_0+{\lambda }_{1}t+{\lambda }_2{t}^2$. The constants ${\lambda }_i$ have been determined. The time dependence is similar to that of the quintessence scalar field (having canonical kinetic energy) responsible for homogeneous inflation. Furthermore, the scaling relation and the obtained time dependence of the field $\varphi$ is used to determine the $X$-dependence of the function $F(X)$.

8 pages, 5 figures, Latex

References in corpus (11)

• Cosmology and the Fate of Dilatation Symmetry
• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• Improved Dark Energy Constraints from ~100 New CfA Supernova Type Ia Light Curves
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Measuring the matter density using baryon oscillations in the SDSS
• Unifying inflation with dark energy in modified F(R) Horava-Lifshitz gravity
• Observational Constraints to Ricci Dark Energy Model by Using: SN, BAO, OHD, fgas Data Sets

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