Speed of light and current dimensions of the universe [duplicate]

I've seen several documentaries explaining that the diameter of the universe is currently estimated at over 90 billion light-years. And which that - in the face of the age of the universe being about 13.7 billion years - that doesn't contradict the "speed of light" limit, because in the very beginning "space - not matter - could expand faster than light".

What does it mean? All I can see is that we can actually visualize galaxies 13.5 billion light-years away from us in every direction (Isn't it?). Therefore 13.5 billion years ago they were up to 27 billion light-years apart from one another, having had "only" 0.2 billion years from big bang to reach those positions ... This is not "space" expanding, this is matter composing galaxies having travelled much faster than light! Moreover, they all keep saying that - in peering at galaxies 13.5 billion light-years away from us - we are close to looking at the "beginnings of the universe".

But if the Big Bang was 13.7 billion years ago, we (the matter now building up our planet) were together with them (the matter composing those far away galaxies) just 0.2 billion years before ... How can we see light coming from so far away from us, emitted by objects which were together with us "just a little while" before?

marked as duplicate by user10851, Kyle Kanos, Kyle Oman, ACuriousMind♦, Qmechanic♦Jul 23 '15 at 21:38

Okay, let's start with the basics. The Big Bang was not like an explosion in space from which spewed all matter in the universe. The Big Bang was a moment in time. We have this thing called a spacetime metric. I won't bore you with the details, but essentially it is the equation we use to describe all of the geometry in the universe. It includes all the dimensions and the dips and bumps and warpings that the gravity of massive objects imparts on them. In this metric, there is something called a scale factor, $a$, this scale factor is something that describes the expansion of the universe. It is multiplied by the spatial dimensions. In our metric, any spatial distance between two points is the distance that we would measure with a ruler today, in the present. To that end, we define $a=1$ in the present. Because space is expanding and the distance between two points grows as time goes on, we know that a distance we measure today would be smaller in the past. Therefore, in the past $a<1$. For example, today we might measure the distance between two points to be 1 meter, but back when $a$ was $0.5$, the distance between those same two points would have been measured as half a meter. Stick with me, I'm getting to the point. The Big Bang is defined as the moment of time when $a=0$. That means the distance between two points in space was zero. It does not mean that everything was all in the same point, it just means that a ruler would measure the physical separation between two distinct points in space as zero. So you see, the Big Bang was a moment in time (like yesterday), not an event that happened somewhere.