A Scaling Relation in Inhomogeneous Cosmology with k-essence scalar
  fields
  We obtain a scaling relation for spherically symmetric k-essence scalar
fields $\phi(r,t)$ 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 $\phi(r,t)=\phi_{1}(r) +
\phi_{2}(t)$. The solutions enable the LBT metric functions to be related to
the fields. The LTB inhomogeneous universe exhibits late time accelerated
expansion i.e.cosmic acceleration driven by negative pressure.
