Why quantum fluctuation existed before big bang? I read somewhere that quantum fluctuation can give rise to a big bang and thus the creation of a universe which we know today, where do these quantum fluctuations come from if space is only created after big bang?
 A: The Big Bang is a purely classical concept. If we make a couple of assumptions about the distribution of matter in the universe then Einstein's equation tells us how the scale factor of the universe evolves with time. We can take our current universe and evolve it backwards in time, and if we do so we find the geometry becomes singular about 13.8 billion years ago. This is what we refer to as the Big Bang.
You'll hear statements like space was created at the Big Bang or time started at the Big Bang but these are at best imprecise and at worst meaningless. What the equations actually tell us is that we can't tell what happened at the Big Bang because the geometry was singular there. Therefore any statements about what happened at the Big Bang are not founded on known physics.
When we introduce quantum mechanics we get effects that mess up the nice simple classical picture. For example it's now widely believed that some quantum effect drastically changed the energy density around $10^{-33}$ seconds after the Big Bang and that caused cosmological inflation.
At earlier times it becomes unclear that we can usefully talk about a scale factor because spacetime may no longer be adequately described as a smooth manifold. This is typically the time at which people have suggested quantum fluctuations become important, and the idea that a quantum fluctuation may have been responsible for the entire visible universe has been around for a long time.
The point of all this is, well, there are two points:


*

*This is all based on speculation with no observational and precious little theoretical evidence that there is anything to the idea

*Assuming there is anything to the idea, spacetime still existed at this period but it was radically different to the smooth classical manifold we see today.
