An accelerated universe with negative equation of state parameter in Inhomogeneous Cosmology with $k$-essence scalar field

Abstract

We obtain a scaling relation for spherically symmetric k-essence scalar fields $\varphi (r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman- Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous cosmology when the LTB metric reduces to the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identifications of the metric functions. A k-essence lagrangian is set up and the Euler-Lagrangian equations solved assuming $\varphi (r,t)={\varphi }_1(r)+{\varphi }_2(t)$. The solutions enable the LBT metric functions to be related to the fields. The LTB inhomogeneous universe exhibits accelerated expansion i.e.cosmic acceleration driven by negative pressure.

7 pages, latex. arXiv admin note: substantial text overlap with arXiv:1602.01289