If, by “end,” you mean that time will stop and the cosmos will cease to exist, then no, the universe will not end. After a very long time, though, the universe will reach a stage at which literally nothing will happen. All the matter will be formless and disorderly, and all the energy will be so sparsely distributed that there will be no significant interactions of any kind, subatomic or otherwise. So, in a sense, that also would be an “end” to the universe—not a fiery or definitive end, but an infinitely long period of cold, dark nothingness.