The principle of unitarity in quantum theory states that the total probability of all possible outcomes of a physical system must add up to 1. It ensures that information is conserved and that the evolution of quantum systems is reversible. While unitarity is a crucial principle in quantum theory, it does not necessarily imply that the universe must be infinite in time.
The question of whether the universe is finite or infinite in time is a subject of ongoing scientific investigation and philosophical debate. Currently, our understanding of the universe's origins is described by the Big Bang theory, which suggests that the universe had a hot and dense state approximately 13.8 billion years ago. However, the exact nature of what occurred at or before the Big Bang is still an active area of research.
In some cosmological models, such as certain inflationary models or cyclic universe scenarios, the universe can be considered to have existed before the Big Bang or to have cycles of expansion and contraction. These models attempt to address the question of the universe's beginning and whether it is finite or infinite in time.
It's important to note that our understanding of the universe is constantly evolving, and scientific theories continue to be refined and developed. At present, it is challenging to definitively determine whether the universe is finite or infinite in time based solely on the principle of unitarity. It requires a deeper understanding of the fundamental nature of space, time, and the laws of physics, which are still areas of active investigation and exploration.