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[en] We consider a polymer quantization of a free massless scalar field in a homogenous and isotropic classical cosmological spacetime. This quantization method assumes that field translations are fundamentally discrete, and is related to but distinct from that used in loop quantum gravity. The semiclassical Friedmann equation yields a universe that is nonsingular and nonbouncing, without quantum gravity. The model has an early nearly de Sitter inflationary phase with sufficient expansion to resolve the horizon and entropy problems, and a built-in mechanism for a graceful exit from inflation.