  In the recent studies of four-dimensional Einstein-Hilbert action, quite a
few interesting results such as the Kawai-Lewellen-Tye (KLT) relations,
MHV-Lagrangian and quadratic forms have been reported. These results naturally
raise an important question: Whether these results are valid for the modified
theories of gravity in 4-dimensions? In this work, we consider $R+\alpha\,R^2$
gravity and derive the complete quartic interaction vertex in light-cone gauge.
We then discuss the implications of the results for KLT relations, and
computing MHV amplitudes.
