  Most of the phenomenology of loop quantum gravity in the cosmological sector
is based on the so-called holonomy correction to the Hamiltonian constraint. It
straightforwardly modifies the Friedmann equations. In this work, we
investigate the influence of corrections generalizing the one usually used in
loop quantum cosmology. We find that a long enough inflation phase can be
generated by purely quantum geometrical effects but we also underline the
limitations of this scenario. In addition, we study the effects of generalized
holonomy corrections on an inflationary phase generated by a massive scalar
field. At the level of perturbations, we investigate in details the
consequences on the primordial scalar power spectrum.
