How is observable universe so big if the universe is so young? The diameter of observable universe is 93 billion light years but the age of universe is only estimated to be 14 billion years. So how does light have 46.5 billion years to travel from the boundary of observable universe to us? I mean if the radius is 46.5 billion light years then that should mean light took 46.4 billion years to go from there to here right?
 A: The farthest light we can see (the horizon) has been emited 13.8 billion years ago (minus opacity period during 300 000 first years, but that's not the point) by objects then (I mean, in CMB frame) at a distance of 13.8 billion light-years. The fact is that distance to those objects has continued to grow for 13.8 billion years, so they are now (in CMB frame) farther.
A: There are a few things to clarify:


*

*the age of the universe is for the whole universe, that might be infinite in size 

*It is a misunderstanding that the diameter of the observable universe corresponds to the 13.8 billion years
Still, there is a difference/contradiction between the age of the observable universe, and the diameter. 
You are saying that the diameter is around 90 billion lightyears, and the age is 13.8 billion years.
Now as I said, the age is for the whole universe (created at the big bang) but the diameter is obviously for the observable part. But let's disregard that, and just talk about the difference.
Now the difference is because in the voids of intergalactic space, space itself is expanding. At the edge of the observable universe, that is 46.5 billion lightyears away, it would take now 46.5 billion years for light to get here, but only if space would not expand.
Actually, these 46.5 billion years is a static view. Like a snapshot. Light was actually emitted 13.8 billion years ago (the earliest, again, disregarding the fact that this is just the observable universe), since everything that emits light from the edge of the observable universe, was created earliest 13.8 billion years ago.
But as those particles of matter were traveling, space was expanding. In 13.8 billion years of time, these particles of matter receded from us 46.5 billion lightyears away.
Now this is again a static view. Those particles of matter that are now 46.5 billion lightyears away, if they are emitting photons now, those photons will not reach us in 46.5 billion years. But much much later. Why?
Because again, they are traveling in expanding space. They are now 46.5 billion lightyears away. But if the photons are emitted from 46.5 billion (from the edge of the observable universe) lightyears now, they will travel for way longer then 46.5 billion years until they reach us here on Earth because space itself is expanding inbetween.
