Did spacetime start with the Big Bang? I mean, was there any presence of this spacetime we are experiencing now before big bang? And could there be a presence/existence of any other space-time before the big bang?

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A very naive question from a non-physics guy. I am here to learn. – Gulshan Feb 14 '11 at 9:52
By definition the big bang is start of everything! I doubt one can find even very popular decription, omitting that there is no sense in asking about "before" big bang. This does not mean that this is the one and only truth, but as long as one speaks about "big bang" question for "before" is free of meaning. – Georg Feb 14 '11 at 10:19
@Georg: how so? Big Bang doesn't imply anything else than the fact that universe collapsed into singularity at one point in the past. But we know this is unphysical and when quantum effects are added there are various models like Big Bounce, etc. They are of course quite speculative but I think this is a fine question. – Marek Feb 14 '11 at 10:30
edited edited edited – Georg Feb 14 '11 at 11:53

Gulshan,

The main theory which describes Space-Time and from which the prediction of the Big Bang comes is called General Relativity, from Einstein. This theory has several mathematical solutions and cosmologists worked to determine the most accurate. There are a class of alternatives but they all have the property that the equations which describe this solution have a singularity at T=0. Furthermore when this situation is examined physically it seems that there is a high density of all the Universe's matter there and then. So it is called the Big Bang.

The Singularity means that some terms become infinite and others unhelpfully become zero. So General Relativity has not been able to predict (or retrodict) what happens before, or how this process really began. The general assumption has been that it was some kind of giant Quantum Event. This assumption, when explained using a more complete theory of Quantum Gravity, may yet be correct.

However in the last few years, several mathematical cosmologists have taken seriously the idea that there was a Pre-Big Bang. Part of the reason for this may be because of the Cosmic Background Radiation data from satellites like WMAP. This data shows larger scale structure in the early universe than the older theories would have predicted.

In particular Roger Penrose has developed a view that the period since the Big Bang should be called an aeon, and that there were earlier aeons each infinitely long. This makes the Big Bang a kind of transition period between two aeons. The theory is speculative in several respects, but it is based on some mathematical constructions in General Relativity. This theory is called Conformal Cyclic Cosmology (CCC for short).

A recent short paper Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity gives the general idea. Although it is technical in places it demonstrates the kind of evidence that is motivating this theory. There are references in that paper to a book and other papers which describe that theory.

There are other theories around too, which suggest a pre-Big Bang model, perhaps other answers will mention those.

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 If there were something or some activity prior to Big Bang, does that imply those "things" or "activities" do not belong to our universe? – Gulshan Feb 14 '11 at 11:30 Well in this kind of model the term "universe" just gets extended. So what we think of as the universe just becomes the current aeon. Having said that those earlier events are Pre-Big Bang and so are not part of the universe/aeon we now inhabit. The point of the paper is that those events nevertheless left an imprint on our Universe/aeon. – Roy Simpson Feb 14 '11 at 11:35 It should also be pointed out that even without considering such Big Bang issues General Relativity allows for parts of our Universe to be separate from each other. The distinction there is between "Observable Universe" and "Universe" in the Cosmological sense. – Roy Simpson Feb 14 '11 at 11:43 Does the recently discovery, for which this year's(2011) physics noble prize is awarded, that the universe is expanding with an accilaration affects the pre-Big Bang model? – Gulshan Oct 14 '11 at 18:22 The Gurzadyan and Penrose paper was shown to be wrong shortly after it was published. CCC also has other serious problems, such as the inability to cook up the right particle physics to make the universe end up as 100% photons. I realize you were just giving it as an example, but wanted to point out that its status as of 2013 is not viable. – Ben Crowell Apr 23 at 4:39

Bear in mind that the real solution for the de Sitter spacetime is a scale factor $$a(t)~=~\sqrt{3/\Lambda}cosh(t\sqrt{\Lambda/3})$$ for $\Lambda$ the cosmological constant. $\Lambda$ was very large in the early universe, and it is not unreasonable to think that the universe was connected by the “throat” to the other half of the hyperboloid.

This is similar to the problem of the white hole, which is the other half of the Schwarzschild metric. We generally ignore that, and so too most often the de Sitter spacetime is physically considered to be an exponentially expanding space where $cosh(x)~\simeq~e^x$ for large $x$. So we start with the FLRW energy equation $$\Big(\frac{\dot a}{a}\Big))^2~=~{8\pi G\rho}{3}~–~\frac{k}{a^2}$$ Here "dot" means time derivative. This equation can be derived using Newton's laws, or the energy of a projectile moving in a gravity field.

The other half of the hyperboloid might physically involve an instanton state, or tunneling state. The Schrodinger equation for a particle moving in one dimension with some potential $V$ is $$i\hbar\frac{\partial\phi}{\partial t}~=~-\frac{\hbar^2}{2m}\frac{\partial^2\psi}{\partial x^2}~-~V(x)\psi$$ If we consider a stationary case with a phase $\psi(x,t)~=~\psi(x)e^{-iEt/\hbar}$ the left had term just becomes $E\psi$, where $E$ is the energy of the particle. Now let us rearrange things so that $$\frac{\hbar^2}{2m}\frac{\partial^2\psi}{\partial x^2}~=~(E~-~V(x))\psi$$ For a particle moving in space we set $\psi(x)~\sim~exp(ikx)$, do the two derivatives and cancel out the ψ(x). $$k^2~=~(2m/\hbar^2)(E~–~V).$$ The funny thing is that for $V~>~E$ we have an imaginary $k$. This means that the kinetic energy is in a funny sense negative, which is not something you expect in classical mechanics. For a system of this sort it is in a classically forbidden region, and in more general systems there may be some dispersion $\omega~=~\omega(k)~=~vk~+~\dots$, which leads to an imaginary frequency. The phase for the system is $exp(i\phi)~=~exp(i\omega t)$. The imaginary quantity associated with the angular frequency ω may be reassigned to the time $t$, that is a mathematical triviality. So in some of these problems it is useful to use this and work with imaginary time, or what is sometimes called Euclideanized time.

So the other half of the hyperboloid might be physically modeled to be a tunneling of a cosmology across a potential boundary. This might then be an instanton due to a “blob” of vacuum energy which quantum escapes from another spacetime. So from that setting if may be seen that the universe has some sort of precursor. or is quantum mechanically tied to another spacetime. This might then be seen in the setting of a multi-cosmological universe or within what is called the multiverse.

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Awesome answer +1. Needs some editing though. – user346 Feb 14 '11 at 14:11
Interesting theory that the matter quantum tunnelled in from another (presumably collapsed?) space-time. Presumably also the $\Lambda$ was broadly similar in these space-times? – Roy Simpson Feb 14 '11 at 14:24
What is the down-vote for? Seriously. – user346 Feb 14 '11 at 15:04
@space_cadet -I did not downvote it, but look at Gulshan's comment under the question--"A very naive question from a non-physics guy. I am here to learn." Do you think he could possibly follow that explanation? Mixing instantons and DeSitter spacetime with no explanation, then explaining that a dot means time derivative, which is obvious... otherwise, I agree the answer is very interesting speculation. +1 for the post, but not really at the level of the question asked. – Gordon Feb 14 '11 at 15:34
@Gordon I don't think level should be relevant because there are people of all levels here. The questioner is not obliged to care about the most technical reply, but a well-crafted response is immensely helpful to a full-time physicist, given that the question also has more than just superficial relevance to theoretical physics. I suppose @Lawrence's answer might suit a question such "what is the Hartle-Hawking state" and "how does tunneling of false vacuum lead to the creation of a spacetime", but as Rumsfeld said we answer the questions we have not the questions we wish we had. ;) – user346 Feb 14 '11 at 15:46