Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2011-02-17
Eur.Phys.J.C (2012) 72:1943
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
8 pages, 5 figures, Latex
Scientific paper
10.1140/epjc/s10052-012-1943-z
A $k$-essence scalar field model having (non canonical) Lagrangian of the form $L=-V(\phi)F(X)$ where $X=1/2g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi$ with constant $V(\phi)$ is shown to be consistent with luminosity distance-redshift data observed for type Ia Supernova. For constant $V(\phi)$, $F(X)$ 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 $\phi$. $H$ and $a$ are extracted from SNe Ia data and using the differential equation the time dependence of the field $\phi$ is found to be: $\phi(t) \sim \lambda_0 + \lambda_1 t + \lambda_2 t^2$. 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 $\phi$ is used to determine the $X$-dependence of the function $F(X)$.
Bandyopadhyay Abhijit
Gangopadhyay Debashis
Moulik Arka
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