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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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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
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@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
    
@dimension10 Actually this is a good question, so long as "Big Bang" is construed as the beginning of the universe as we know it rather than simply "the singularity in an FRW universe." In fact, this question is at the heart of eternal inflation and cyclic universe theories, both being studied in various forms by quite a few reputable cosmologists. –  Chris White Jul 6 '13 at 19:29
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5 Answers

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 '13 at 4:39
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The only well tested theory of gravity we have right now is general relativity (GR). In models based on GR, time and space only exist for $t>0$.

This raises the question of what caused the big bang. In relativity, we use the term "event" to mean a certain position in space at a certain time. The big bang is not an event, because there is no time $t=0$. If you want to find a cause for some event happening at a given time $t>0$, there is always some earlier $t'$, with $0<t'<t$, that can supply that cause. So in this sense, the big bang doesn't require a cause, because only events require causes, and GR doesn't describe the big bang as an event.

We also have fundamental reasons to believe that GR is inaccurate under the very dense and hot conditions at $t < ~ 10^{-43}$ s (known as the Planck time), because of quantum-mechanical effects. If we had a theory of quantum gravity that worked under those conditions, then it might turn out that the singularity at $t=0$ was not real, and events at $t>0$ could be explained in terms of causes at $t<0$. This is what seems to happen, for example, in loop quantum cosmology. However, nobody has a theory of quantum gravity that works and has been tested against experiment, so we don't really know.

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I'm not a cosmologist either, which at least means I can speak in simple terms that don't assume you are deeply familiar with every mathematical permutation of the subject. As I understand it, the universe is expanding, not just in the sense of the material in it spreading out, but in the sense that space-time itself is expanding. If we run the clock backwards, then, everything comes together at a point, including space and time. Of course, physicists can't really model the point itself, but they can model the properties of the universe as we get close to the point and amazingly, the predictions seem to generally agree with what we see. Hence the idea of the Big Bang. But the human mind evolved in space time, so inevitably people picture this as a void in which there's nothing for awhile and then the universe explodes into being. This has to be wrong, though. What exactly is the void in this picture, since space does not yet exist? How can there be "awhile" before the big bang if time didn't exist "yet"? (Here the grammatical structure of our language works against us, since it assumes we are talking about something happening in space-time.) The simple way to keep your thought pictures honest is to remember that we can't see the universe FROM THE OUTSIDE, so don't try to picture it this way. The Big Bang can only be honestly pictured from inside the universe, so there's no meaning to the question of what happened "before" the Big Bang - it's a non sequitur. Similarly with the question "What was there before the Big Bang?" There "was" (time) no "there" (space) for there to be anything in. It sounds like you've already thought of this, which I take it is why you're asking the question. I don't think it is unreasonable to suspect that the earliest moments of the universe are not well modeled by the mathematics of infinities and infinitesimals, and that we don't really have a good grasp on this yet despite the agreement with the empirical data we have so far. But don't get sidetracked by physicists who get so caught up in the math that they forget that the model is not the thing modeled.

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I seriously doubt that. There are quite a few theories trying to discuss "the beginning of the universe", and not all of them agree with having a "beginning" to the universe.

I don't have concrete facts to support what I'm about to say so consider it as "just another idea."

"Our whole universe was in a hot dense place, then fourteen billion years ago expansion started." So there was a big explosion, and everything tried to get away from every other thing. This process has been going on for about fourteen billion years, and it will eventually stop. Because a big portion of the attracting/repelling forces (electromagnetic force which can attract and repel) will have been neutralized (like a stone which does have electrons and protons but doesn't attract or repel), and the attracting forces (gravity) will take over. The universe starts to get smaller and denser, and collapse into a small hot dense place, and in "hot places", the repelling forces will eventually take over, and so another bang happens, and it will create a universe much like of our own.

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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
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What is the down-vote for? Seriously. –  user346 Feb 14 '11 at 15:04
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@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
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@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
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Also the traditional definition of an instanton is that of a self-dual or anti-self-dual solution of Yang-Mills. When GR is cast in connection variables (nothing to do with the Ashtekar variables yet) its phase space is exactly that of Yang-Mills. And deSitter is precisely the self-dual solution of the GR Hamiltonian in first-order form. So instanton seems like a suitable term. There is also a book on "gravitational instantons" but I forget the exact title. –  user346 Feb 14 '11 at 15:53
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