Size of the Universe before the Big Bang I can't understand how all the matter contained in the Universe, was contained in an area the size of a grapefruit before the Big Bang ? How could so much matter have been compressed in such a tiny space ?
Nobody knows what the big bang was, but using the laws of physics as we understand them, and using what has been observed studying quantum mechanics and very high energy collisions, a lot of what's defined as moments after the big bang are basically working backwards and deduction.  Quantum physics models explain very accurately why we have the hydrogen/helium ratio that we see and why the cosmic background radiation formed.

The simple answer to how it was possible to get all that stuff into such a small space is two fold.   One, when it's that dense, it's no longer matter, but energy, and two, it was that small for an incredibly short period of time - too short for gravity to win, which, when you have that much mass in that small a space, you'd think gravity would win, but the primordial grapefruit expanded faster than the speed of light and gravity is limited by the speed of light, and perhaps limited in other ways by quantum gravity, but we don't know how to study that yet.

So you can have that a universe amount of mass in a grapefruit or watermelon size if it's that small for a very very short time, close to impossibly hot and faster than light expanding. 

Somewhat different explanations could be that the Universe is infinite, or curved in on itself, in which case the gravity, if the young universe is uniform, balances out to zero everywhere until the uniformity breaks.   This is similar to the gravity at the center of the Earth.  With equal mass in every direction, gravity becomes zero.    

The cosmic background radiation suggests that the young universe was very close to uniform and that, plus rapid expansion circumvents the "why didn't it become a black hole" problem.   Various shapes of the universe don't change the rapid expansion model, which is the most popular model today.

There are also models that involve additional dimensions which explain the big bang, but I think those have fallen out of favor, perhaps because extra dimensions have never been observed at CERN and because I've not read about that model recently, though if memory serves, Stephen Hawking put the 5 dimensional big bang idea in one of his books that he marketed to the general public.    Extra dimensions make all kinds of things possible, like putting all that mass in a small space.