  We study the stability of Einstein static Universe, with FLRW metric, by
considering linear homogeneous perturbations in the kinetic coupled gravity. By
taking linear homogeneous perturbations, we find that the stability of Einstein
static Universe, in the kinetic coupled gravity with quadratic scalar field
potential, for closed ($K=1$) isotropic and homogeneous FLRW Universe depends
on the coupling parameters $\kappa$ and $\varepsilon$. Specifically, for
$\kappa=L_P^2$ and $\varepsilon=1$ we find that the stability condition imposes
the inequality $a_0>\sqrt{3}L_P$ on the initial size $a_0$ of the closed
Einstein static Universe before the inflation. Such inequality asserts that the
initial size of the Einstein static Universe must be greater than the Planck
length $L_P$, in consistency with the quantum gravity and quantum cosmology
requirements. In this way, we have determined the non-minimal coupling
parameter $\kappa$ in the context of Einstein static Universe. Such a very
small parameter is favored in the inflationary models constructed in the
kinetic coupled gravity. We have also studied the stability against the vector
and tensor perturbations and discussed on the acceptable values of the equation
of state parameter.
