The size and extent of the universe beyond the observable universe are topics that scientists continue to explore and study. It is currently unknown whether the universe is finite or infinite in size. However, I can provide information on how the estimation you mentioned is made.
The observable universe is the portion of the universe that we can potentially observe from Earth, given the constraints of the finite speed of light and the age of the universe. It extends about 93 billion light-years in diameter. This means that the light we observe from the most distant objects in the universe has traveled for approximately 13.8 billion years since the Big Bang.
Based on our current understanding of the universe, scientists propose different models to estimate the overall size of the universe beyond the observable universe. One concept is the idea of cosmic inflation, which suggests that the universe underwent a period of rapid expansion shortly after the Big Bang. According to this theory, inflation would have caused the universe to expand faster than the speed of light, allowing regions that are now beyond our observable universe to be brought into view.
The estimation of the universe being at least 250 billion times larger than the observable universe likely comes from calculations based on inflationary cosmology and the overall geometry of the universe. These estimates involve complex mathematical models and measurements of cosmic microwave background radiation, large-scale structures, and other cosmological observations.
It's important to note that our understanding of the universe is continually evolving as new data is gathered and analyzed. As scientific knowledge progresses, our understanding of the size and nature of the universe will continue to refine and expand.