But this is all still very new and tentative, and people still don't really know if either the approximation or the theory is valid.

[2] THE NO-BOUNDARY PROPOSAL

The Hartle-Hawking no-boundary proposal (http://prola.aps.org/abstract/PRD/v28/i12/p2960_1) tries to bypass this whole issue by eliminating the boundary. By going from real to imaginary time and hence from Lorentzian to Euclidean spacetime -- more precisely, by working in an approximation that is assumed to be dominated by Euclidean spactimes -- they find that they can write down a wavefunction that doesn't have a boundary in Euclidean spacetime. The singularity doesn't exist in the imaginary time solution, just in real time. (At least, I think it's still there in real time. It's probably more accurate to say that, much like Vilenkin's proposal, classical spacetime just doesn't make sense at the Big Bang, so there isn't a "singularity" in the sense of having a singular spacetime geometry in general relativity.)

The point is that we no longer need to specify initial data; the Euclidean solution can be determined without it, and then the "initial data" in real time is determined from that -- the real-time initial data isn't a separate thing that has to be fed in by hand, it's part of the solution. (All kinds of odd things happen in imaginary time, too; in a sense, the Big Bang and Big Crunch are the same thing.)

Resorting to imaginary time probably seems quite odd, to say the least, but there's precedent -- physicists do it all the time in quantum field theory, it seems necessary to do this to get the calculations to work out. (Otherwise the integrals aren't well-defined.) On the other hand, it's mathematically legitimate to do this; the Osterwalder-Schrader reconstruction theorem says that it's possible to take all your calculations in imaginary time, do them there, and then bring the answers back to real time in a unique way. But quantum field theory is based on flat background spacetimes -- not the case in gravity.

Now, this theorem can be extended to situations with curved, dynamical spacetimes (like in general relativity) -- see http://arXiv.org/abs/quant-ph/9904094 -- but it's quite touchy. Hawking has been a leading proponent of Euclidean quantum gravity. But that approach has gradually fallen out of favor, from what I can see. If I recall correctly, numerical evidence suggested that the theory would have a first order phase transition instead of the necessary second order transition, or something like that.

Also, some toy models in two dimensions suggest that Euclidean and Lorentzian quantum gravity are fundamentally different (http://arXiv.org/abs/hep-th/9912267). Interestingly, the way in which they differ is that the Euclidean theory allows "baby universes" to branch off, while the Lorentzian theory doesn't.) This doesn't mean that Euclidean theory is wrong, just that we can't pretend that the choice of Lorentzian or Euclidean doesn't matter. It's also interesting to note that in these models, the presence of these "baby universes" seems to lead to a sickness in the Euclidean theory, causing it to be dominated by degenerate "branched polymer" geometries that screw up the classical limit (I think this is essentially the phase transition issue I mentioned).

(Actually, there has been a fair amount of work on "baby universes", "third quantization", and "spatial topology change" that is probably relevant to this list of alternatives I'm making, but I don't know much about it.)

Anyway, for whatever reason, Euclidean quantum gravity isn't taken as seriously as it once was, so that throws the NBP in a different light. But it might still be good within the semi-classical context of quantum cosmology. (Also, as I said above, Bojowald's Lorenztian work also eliminates the need for initial data, though not in such an exotic way.)

More on the Hartle-Hawking wavefunction:

http://math.ucr.edu/home/baez/week138.html

[3] THE TUNNELING PROPOSAL

Vilenkin's proposal (http://prola.aps.org/abstract/PRD/v27/i12/p2848_1, http://prola.aps.org/abstract/PRD/v30/i2/p509_1) is what started off the whole "quantum creation of universes out of nothing" idea. (Well, Tryon and Fomin and others preceded him but didn't get much lasting popularity.) He has the universe tunneling out of the zero state in a manner somewhat analogous to ordinary quantum tunneling through a potential. Like the NBP and Bojowald's loop quantum cosmology, the solution eliminates the need for initial conditions, though it doesn't do so by eliminating the boundary in imaginary time. (I don't understand how it does do this, however.) It also lacks a Big Bang singularity; the "Big Bang" is a tunneling event to classical spacetime.

I don't know much about it or its current status, but you can read Vilenkin's own (probably biased) comparison of it to other proposals (like NBP) at:

http://arXiv.org/abs/gr-qc/9812027

(He also mentions a solution by Linde that seems to be similar the the Hartle-Hawking NBP in principle but with the Euclidean time rotation performed oppositely.)

To be fair, here's an argument by Bousso and Hawking: http://arXiv.org/abs/gr-qc/9608009, and Garriga and Vilenkin's rebuttal, http://arXiv.org/abs/gr-qc/9609067. Hawking and Vilenkin have been picking at each other's theories (there are more examples of this than what I've cited). I really have no grounds for judging who's right on this issue.

I don't quite understand how Vilenkin's model relates to the Euclidean quantum gravity problems I mentioned with respect to the NBP. Vilenkin emphasizes that, unlike his own proposal, the NBP has a path integral sum over all (compact) _Euclidean_ spacetimes. Vilenkin says "... to find the under-barrier semiclasical wave function, one has to analytically continue to the integration over Euclidean ... then the path integral is dominated by the Euclidean solution of the classical field equations". Make of that what you will.

[4] ETERNAL INFLATION

This takes rather a different approach to describing the origins of our universe. I believe the idea is originally due to Linde. In inflationary theory, due to "decay of the false vacuum", the universe can rapidly expand at an exponential rate. This helps to explain some puzzles in standard cosmology. However, one implication of it is that this decay process can and must occur at random, continously and eternally. It leads to a picture of a "sea" of inflating "bubble" or "pocket" universes of all sizes and ages; we would live within one such bubble.

Note that this is different from true "baby universe" creation in quantum gravity where space actually splits off and changes topology; rather, in eternal inflation, what we think of as "our universe" is really a "bubble" region within the actual larger universe, with different physical characteristics than the surrounding "sea".

(On the other hand, there has been some talk that actual baby universes could inflate _within_ our "bubble" universe, shrouded behind event horizons, but this is a far less robust prediction -- it depends on whether quantum gravity permits baby universe creation -- and probably doesn't happen spontaneously if it's even possible. I mention it as an aside; the discussion of eternal inflation is independent of it.)

This idea of eternal inflation is a mixed blessing. It may be able to provide a description of the origins of our universe -- the "Big Bang" was not really a singularity, but rather the event at which the false vacuum randomly decayed and produced the inflation of a new bubble within spacetime. Indeed, if inflation is correct, eternal inflation seems to be an almost necessary consequence and thus we need to take this scenario seriously.

_However_, it also has a downside: it doesn't give any explanation for the origins of the actual universe containing all these bubbles. One can argue that this isn't much of a downside if the goal is to describe what we observe, because what goes on in the larger "sea" is fairly irrelevant to what goes on inside our bubble. But many will find it dissatisfying that it doesn't give the whole story. In fact, it suggests that we _can't know_ the whole story: inflation probably erases all information from prior to bubble nucleation, so we can't have observational evidence of what the "sea" universe was like before our Big Bang event.

This would be a serious blow for those interested in the larger "sea" universe and how it came to be, but it's not a _total_ loss. Quantum gravity may be able to predict what would happen in that circumstance. The problem is that we'd never be able to have _observational evidence_ supporting that prediction. On the surface that sounds fatal for a scientific theory, but as Guth argues (in a paper I cite below),

"The pocket universes other than our own are believed to be completely unobservable, so one can question whether it makes any scientific sense to talk about them. I would argue that it is valid science, because we are pursuing the consequences of a theory for which we already have other evidence. Of course the theory of inflation has to rest on the evidence that we observe, but once we are persuaded by these observations, then I think that we should also believe the other implications, even if they involve statements that cannot be directly tested."

In short, if we could come up with other tests of quantum gravity that make us fairly confident in one particular theory, then we should be inclined to believe what it would have to say about what happened in the "sea", even if we can't observe what happened there. Still, it's not a great situation for science to be in. But science never claimed that we would ever be able to have experimental evidence of everything that happened in our universe.

It is also worth mentioning that many have hoped that eternal inflation would eliminate the need for the beginning of a universe (which is problematic to account for if you don't appeal to things like spontaneous creation via tunneling). The picture is of a universe that has always existed, with new bubble universes being nucleated via quantum effects from time to time and us living in one of them.

However, Borde and Vilenkin have demonstrated that eternal inflation might better be named "future-eternal inflation", since there appears to still be a need for an initial singularity -- the "sea" had a true Big Bang singularity, though _our_ Big Bang wasn't a true singularity. On the other hand, I don't think this is a really strong result, because it's a classical argument. (I think people hoped that the inflationary fields would let you evade some of the _classical_ singularity results in general relativity -- probably by avoiding the energy conditions -- but they don't.) We don't know whether quantum gravity removes singularities. Guth seems to think that it probably doesn't, but I think the issue is far less clear-cut, particularly in light of preliminary work like Bojowald's.

All of these issues are summarized in Guth's outstanding summary talk,

http://arXiv.org/abs/astro-ph/0101507

The important thing to note here is that eternal inflation could have happened in almost any scenario, regardless of what theory of quantum gravity is correct, or whether Big Bang singularities can happen, etc. It is largely independent of all the other proposals I mention (though it's possible that some of them may rule out this kind of inflation).

[5] STRING/M-THEORY COSMOLOGY

String theory (and its "successor", M theory) is what many would say is the leading candidate for a true theory of quantum gravity. I don't think theory has an agreed-upon picture of the origins of our universe, though I'm sure there are millions of speculations floating around. (String theory is very flexible -- a virtue in that it can explain a lot of things, a curse in that it can explain too many things unless data and better understanding of the dynamics can constrain the possibilities.) Banks has a discussion (http://arXiv.org/abs/hep-th/9911067) of M-theory quantum cosmology, but the theory doesn't seem to be worked out enough to make predictions about the origin of the universe. (Nobody even knows what M theory really is right now.)

Some old predictions from string theory (by Brandenberger and Vafa) are that the universe started out with all of its dimensions curled up, and then three of them uncurled and expanded. However, that doesn't really explain the Big Bang, only what happened after.

Here is a survey of string cosmology by Brandenberger:

http://arXiv.org/abs/hep-th/0103156

The most concrete (and perhaps most popular, though hotly debated) proposal for string cosmology I've seen (though hardly the official position of the string community, so listed separately) that tries to account for the Big Bang is pre-Big Bang cosmology. There is also the recent ekpyrotic universe, but it's so new and speculative that no one knows if it's plausible or will catch on.

Brandenberger also mentions other alternative string cosmologies, such as heterotic M-theory cosmology (http://arXiv.org/abs/hep-th/0003256), brane gas approaches, and brane-world scenarios. I won't say anything about them because I've never read anything about them.

[6] PRE-BIG BANG STRING COSMOLOGY

This scenario, due to Veneziano and Gasperini, assumes that the universe was originally cold and simple and empty and flat, and naturally evolved into a highly curved state culminating in a singularity-free hot "Big Bang" leading to our current universe. (This is different from quantum creation of universes, where universes arise from "nothing" or the zero state; rather, an initially flat vacuum state starts to "curl up" and produce matter due to quantum effects and creates a Big Bang.)

I think this scenario has an eternal universe that spends "forever" reaching the Big Bang transition, but I may be misunderstanding things. It sounds odd for a universe to spend an infinite amount of time before suddenly this big change (the Big Bang) happens, but it's really no stranger -- and no less possible -- than a time reversal of a universe that has a big change (the Big Bang) and then expands eternally. You have an infinite past, something happens at some point, and you have an infinite future (or not?). The further you go back in the past, the emptier and flatter the universe looks; the further you go in the future, the more the universe looks like the classical prediction of whatever the fate of our universe is (possibly eternal expansion, but maybe collapse).

I think there are some phenomenlogical problems with the PBB scenario (can it account for observations properly?); whether they can be solved is currently unknown. Also, people have objected to the condition of "asympotic past triviality" (i.e., the universe becoming flatter and simpler as you go back in time past the Big Bang); it's arguably the simplest assumption, but that doesn't mean that it actually happened -- it's still an assumption.

However, the PBB scenario is arguably one of the most _conservative_ approaches to string cosmology, with the most minimal assumptions.

Some references:

http://www.to.infn.it/~gasperin/ http://arXiv.org/abs/hep-th/0002094

(By the way, ignore the usual boastful string theory claims in that paper that "the only candidate for a consistent synthesis of general relativity (GR) and quantum mechanics (QM) is superstring theory" -- many if not most string theorists have a parochial and outdated picture of the status of quantum gravity. There are certainly other candidates that seem promising -- such as loop quantum gravity -- though it remains to be seen which is more accurate.)

[7] MISCELLANY

There are lots of ideas out there! I've just mentioned some of the better known ones (or at least the ones I've heard of). Here are a couple more speculative ones.

[7a] Cosmological Natural Selection.

Smolin has proposed (http://arXiv.org/abs/gr-qc/9404011; _The Life of the Cosmos_) "cosmological natural selection", in which Big Bangs are the result of universes forming from the creation of black hole singularities in previous "universes".

This proposal currently has no real theoretical basis -- it's almost pure speculation -- but it's an interesting way to avoid the anthropic principle. Why are the fundamental constants of the universe the way they are? Smolin suggests it's because they evolve with time, and if universes are the products of black holes, they should evolve in such a way to produce a lot of black holes -- and thus, perhaps to produce stars and life.

Even if this particular idea is wrong, the idea of dynamical "self-organization" may persist in other theories -- like string theory -- to explain how the universe got to be the way it is, even if we don't know much about how (or if) the universe started out.

Changing subjects: very recently a new proposal has appeared, the "ekpyrotic universe" (http://arXiv.org/abs/hep-th/0103239), inspired by the Randall-Sundrum "brane world" picture (http://arXiv.org/abs/hep-th/9810155, http://arXiv.org/abs/hep-ph/9905221, http://arXiv.org/abs/hep-th/9906064) -- or rather its subsequent incorporation within heterotic M theory by Horava and Witten (http://arXiv.org/abs/hep-th/9510209, http://arXiv.org/abs/hep-th/9603142, http://arXiv.org/abs/hep-th/9711197, http://arXiv.org/abs/hep-th/9803235).

In the R-S picture, our 4-dimensional universe is a "brane" (or surface) living within a higher-dimensional spacetime. (Rather, all the matter and gauge fields are stuck on this brane; the only thing that can leave the brane is gravity. This is natural within the D-brane physics of string theory.) This differs from traditional string theory, in which we are not confined to any lower-dimensional surface of the higher-dimensional spacetime -- our universe appears 4D not because we're stuck on a 4D subsurface, but because some of the spatial dimensions are "curled up small" (compactified). I won't go into the Horava-Witten picture that the ekpyrotic scenario is most directly founded on, since I don't understand it.

Brane worlds are an alternative to compactification for explaining why we only see four dimensions. But it it should be noted that brane world scenarios can easily be accomodated within string theory (where most of the brane-world work is going on); you just assume that fewer dimensions are compactified, and R-S/H-W is invokved to explain why we don't see the other non-compactified dimensions.

In the ekpyrotic universe, spacetime is (ignoring the compactified dimensions) 5-dimensional and is bounded on two sides by a pair of flat 4-dimensional branes. What we perceive as our universe is one of those branes; the other one is "hidden" because nothing can travel between the branes other than gravitational effects, so we can't see it directly. (This has led to some discussion of "shadow universes" in the media.) This hidden brane is standard in R-S models; it's used to solve the hierarchy problem and other issues.

The ekpyrotic theory introduces a third 4-dimensional brane -- for simplicity, I think; there could be more -- in between the boundary branes, that can move around "in the bulk" (in the full "5-dimensional" spacetime). (Alternatively, you might be able to do without it; it's possible that a bulk brane may "peel off" from the hidden brane.) Eventually it smacks into our brane, fusing with it, and triggers (what we perceive in our universe to be) a "Big Bang".

To me, the ekpyrotic scenario sounds kind of artificial -- we don't know that our universe should look like this; nothing in string theory suggests that this initial condition should be likely. (Though if it _did_ look like this, the scenario described can happen if string theory is correct.) At this point it's really just a "proof of concept", trying to show that other alternatives are possible.

In addition, a paper that appeared not long after this original proposal (http://arXiv.org/abs/hep-th/0104073) claims that the ekpyrotic scenario has severe fine-tuning problems. So it could just be one of the numerous short-lived clever ideas that only looks interesting now because there hasn't been time for it to have been completely refuted.

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In summary: most of the proposals about the origin of the universe either eliminate the Big Bang singularity as "the origin of the universe", or they make it irrelevant. Generally, either there was something before the universe and (for one reason or another) quantum gravity effects began to dominate and produced a "Big Bang", and/or quantum effects at the "Big Bang" mean that the phrase "before the Big Bang" doesn't really make sense (it assumes classical notions of space and time). Or possibly there was something before the Big Bang, and pure quantum gravity spacetime effects weren't responsible for the Big Bang; it might have been an inflation event or brane collision or something, and what happened in the universe before that may have no relevance to making predictions about the observable universe.

The proposals vary in their use of knowledge of quantum gravity, from inflation (little to none) to standard quantum cosmology (some) to loop quantum cosmology (heavy) to string theory (it depends on where you draw the line between "quantum gravity" and "everything else" in a unified field theory, but I'd say "some" to "heavy"). I'd say that we can't definitively say anything about the origins of the "true" universe -- meaning models where our universe is just a subset of something else, as well as ones in which it's the whole deal -- without a solid theory of quantum gravity, though it not be necessary to account for "the observable universe" and what we perceive as "the Big Bang".

Most of these proposals seem pretty exotic, but this is not surprising; when you mix quantum uncertainty with notions of space, time, and causality, highly non-intuitive things are likely to happen. It should be noted that most of them were not ad-hoc "cooked up" to have the properties they do (like eliminating the need for initial data, or eliminating the singularity, or whatever) -- they are consequences of natural and often conservative extensions of known physics (albeit often within uncertain approximations).

It should also be noted, however, that there is a pretty good chance that direct observational evidence of what, if anything, happened before the Big Bang will either be very difficult or fundamentally impossible to obtain -- at least not in the near future. (Indirect evidence may be coming, but I'm not holding my breath for direct evidence.)

Now for a bit of non-physics relevant to talk.origins -- I'm sure this is where theists are waiting to jump in, pointing to a "failure of science", so I will just say:

(1) Like Guth, I don't regard it as a failure of science that we can't observe something, as long as we can _predict_ that we shouldn't be able to observe that thing, and as long as our theories have other tested predictions. There is no requirement in science or of nature that human experiments must be capable of revealing everything about the universe, or that human minds are even capable of understanding the laws of physics, or of finding them if they are understandable. (Nor does this imply that religion _can_ offer these things.) If we can understand the universe and obtain evidence about its origins, we may simply be lucky that we live in a univese whose laws permit that.

(2) It's a false dichotomy to think that if a given scientific theory can't explain something or be verified, then that implies that a theistic explanation is more likely. The default assumption is not "if science can't explain it, [insert religion here] explains it". The default assumption is "we don't know how it happened", and you have to provide evidence *for* something (and hopefully but not necessarily also *against* competing alternatives) in order for it to have merit.

Example: witness history littered with unexplained things that people originally proposed theistic solutions for, e.g. the weather, origins of life, formation of the Earth, nature of astronomical objects and "the heavens", etc. Theistic explanations have ultimately tended not to last as accounts of observed phenomena, even when there was no competing explanation (scientific or otherwise) for hundreds or thousands of years. Most of them have been replaced by scientific explanations, and even if not all of them are replaced, that in no way suggests that the remaining theistic explanations are likely to be right.

This relates to a common creationist misconception that the "godless evolutionists" adhere to their theories out of some desire to "avoid God". Aside from the fact that most "evolutionists" (and possibly most cosmologists) are probably Christian, I think that if you asked most of the atheists, they'd say that their scientific beliefs are independent of their religious ones.

That is, even if every known scientific theory were suddenly falsified tomorrow, that wouldn't mean that atheist scientists would suddenly become religious, because their atheism has to do with a *lack* of specific evidence for theism rather than the *presence* of a competing scientific explanation; falsifying a scientific explanation does not suddenly produce new evidence favoring a theistic explanation. In the absence of either scientific or theistic evidence, the atheist would revert to the default assumption of "I don't know", rather than switch to a theistic explanation. It would take new evidence specifically in favor of a theistic explanation -- and a particular, predictive one at that, not a generic "the gods created the universe" -- to do that.