  One of the qualitatively distinct and robust implication of Loop Quantum
Gravity (LQG) is the underlying discrete structure. In the cosmological context
elucidated by Loop Quantum Cosmology (LQC), this is manifested by the
Hamiltonian constraint equation being a (partial) difference equation. One
obtains an effective Hamiltonian framework by making the continuum
approximation followed by a WKB approximation. In the large volume regime,
these lead to the usual classical Einstein equation which is independent of
both the Barbero-Immirzi parameter $\gamma$ as well as $\hbar$. In this work we
present an alternative derivation of the effective Hamiltonian by-passing the
continuum approximation step. As a result, the effective Hamiltonian is
obtained as a close form expression in $\gamma$. These corrections to the
Einstein equation can be thought of as corrections due to the underlying
discrete (spatial) geometry with $\gamma$ controlling the size of these
corrections. These corrections imply a bound on the rate of change of the
volume of the isotropic universe. In most cases these are perturbative in
nature but for cosmological constant dominated isotropic universe, there are
significant deviations.
