  We construct and study a simple noncommutative scheme (theta-deformation) for
the effective Loop Quantum Cosmology of the flat
Friedmann-Lema\^itre-Robertson-Walker model in the presence of a homogeneous
scalar field $\phi$ with a potential $\mathcal{V}(\phi)=\frac{1}{2}m^2\phi^2$.
We first conduct a simple analysis from the corresponding Hamilton equations of
motion considering a generic term $\mathcal V(\phi)$. It is observed that the
characteristic Big Bounce of Loop Quantum Cosmology is preserved under such
noncommutative extension. When specializing to the quadratic case, numerical
solutions to the corresponding Hamilton equations exhibiting an early
inflationary epoch with a sufficiently large number of e-foldings are found. It
is concluded that, in this noncommutative setup, solutions exist which are in
the overall compatible with the early universe predicted by standard
(effective) Loop Quantum Cosmology (i.e. a bouncing and inflationary early
universe). The issue of the genericness of a sufficiently long inflationary
period on the space of solutions in this noncommutative construct remains to be
addressed.
