The statement that the universe is 150 billion light-years across is a common source of confusion. It's important to understand that the expansion of the universe plays a significant role in this apparent discrepancy.
When we say that the universe is 13.8 billion years old, we are referring to the time since the Big Bang. This age is based on our best estimates using various cosmological measurements. However, during this time, the universe has been expanding. The expansion of space itself causes distant objects to move away from us, and the farther away they are, the faster they appear to be receding due to the expansion.
The concept of the observable universe comes into play here. The observable universe is the portion of the universe that we can potentially see given the finite speed of light and the age of the universe. Light from distant objects takes time to reach us, so we can only observe objects within a certain distance from us based on the age of the universe.
However, since the universe has been expanding over time, the light from some objects that were originally closer to us has had time to reach us despite the expansion. This means that the current distance to those objects is greater than what we would calculate based solely on the time since the Big Bang.
The value of 150 billion light-years refers to the comoving distance, which takes into account the expansion of the universe over time. It represents the current distance between us and the objects that emitted the light we currently observe, accounting for the expansion that has occurred since the light was emitted.
It's worth noting that the concept of distance in an expanding universe is more complex than simply measuring the current positions of objects. The expansion of space itself makes the calculation of distances more intricate. The 150 billion light-year figure is an estimation based on current cosmological models and measurements, which account for the expansion of the universe over time.