  The existence of a small, non-zero cosmological constant is one of the major
puzzles in fundamental physics. Naively, quantum field theory arguments would
imply a cosmological constant which is up to 10$^{120}$ times larger than the
observed one. It is believed a comprehensive theory of quantum gravity would
resolve this enormous mismatch between theory and observation. In this work, we
study the ability of generalized uncertainty principle (GUP) models, which are
phenomenologically motivated models of quantum gravity, to address the
cosmological constant problem. In particular, we focus on how these GUP models
may change the phase space of QFT, and how this affects the momentum space
integration of the zero-point energies of normal modes of fields. We point out
several issues that make it unlikely that GUP models, in their current form,
would be able to adequately address the cosmological constant problem.
