Size of the Universe before the Big Bang

Question

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 ?

Answer 1

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.

Answer 2

The diameter of the "observable universe" (the entire universe may well be considerably bigger, or even infinite) is about 90 billion light years. It only makes sense to talk about how big this volume was as a function of cosmic time, since for instance an infinite universe was always infinite, right back to and including the big bang.

There is complicated maths that can be done to solve the Friedman equation to give the universe scale factor as a function of time, but here is a simple argument.

In the "matter dominated era", where the density of the universe is dominated by the matter within it (ignoring the complication of dark energy for the moment), the scale factor $a$ depends on time as $t^{2/3}$.

The universe is currently 13.7 billion years old, but the time when radiation and matter contributed equally to the density of the universe was about 50,000 years after the big bang. Using the scaling above, that means the current observable universe had a diameter of 21.3 million light years at that age.

Prior to that, the universe was dominated by the radiation energy density and $a$ varied as $t^{1/2}$. That means that after 1 second post-big bang, our current observable was universe was still 17 light years in diameter. The density of the universe at this point would be slightly bigger than that of water (1500 kg/m$^3$), so nothing exotic.

In order to get to the size of a "grapefruit" (say 30 cm diameter) requires us to go way back (in logarithmic terms) to $3\times 10^{-24}$ seconds, assuming that the Friedman equation holds that far back towards the big bang. The density here would be the equivalent of $\sim 10^{56}$ kg/m$^3$.

At the same time, the temperature of the universe would have been much, much hotter, something like $10^{18}$ Kelvin, and this is far too hot for anything resembling matter in the current universe to exist. i.e. No protons, neutrons, or even electrons could exist at these temperatures (or at least not in the form with mass that we see today).

Epochs less than about $10^{-12}$ s after the big bang are firmly in the realm of theoretical speculation rather than comfirmed empirical measurement.

So the basic answer to your question is that the contents of the universe existed in the form of energy, or in the form of ephemeral, point-like particles that annihilate with each other. There is no real upper limit on the density that such material can have.