Semiclassical polymer field with a cubic potential in cosmology

We study the semiclassical dynamics of a polymer quantized scalar field with a cubic potential in cosmology. The cosmological spacetime is chosen to be homogeneous and isotropic, and we work in the polymer quantization scheme where the field operator does not exist directly. The dynamics are studied in the `e-fold' time gauge, where a choice of time gauge fixing, in terms of the scale factor, is made at the classical level. The cubic potential is interesting to study because it is unbounded from below. We find that polymer quantization regularizes this potential, and leads to periods of slow-roll as well as exactly de-Sitter inflation.