Hawking is making a theological argument about the nature of creation. He is arguing against the idea that the universe was made by an intelligent being. In order to be clear, I will call this creator "the Demiurge", which Wikipedia tells me is the proper term.
Hawking and Pope
According to Hawking, the Pope says that the early universe history revealed by science is compatible with Christian creation myths, because science reveals that there is a creation in the past, and science gives no answer for what came before, or how the things came out of the big-bang.
This is completely true in pre-inflationary cosmology, where creation has indescribable elements, because you are producing an almost-but-not-quite symmetrical thing by fine-tuning the initial conditions of the matter in the universe. So, as Hawking has it, the Pope is saying that the Demiurge adjusted the stuff coming out of the Big-Bang to make it look like our universe.
Absent inflation, if you just look at pre-inflationary big-bang cosmology, the stuff coming out of the big-bang is so absurdly fine-tuned that you would actually need a very clever demiurge working very carefully to make all that stuff come out just right. But we know today that inflation has made this fine-tuning, so you don't need a Demiurge. This is not Hawking's argument (although it is related).
Hawking's argument is not based on a traditional singular big-bang, where all matter comes from a special region which is not part of space-time, but it is based more on Hawking's personal idea that the path integral for quantum gravity makes sense near the beginning of the universe, and that the geometry of space time turns into Euclidean geometry there, near the beginning, with a smooth cupping over of space-time so that the notion of time as separate from space, or of earlier and later, are meaningless for at least a few Planck-times after the big bang. Hawking believes that this type of thing will reproduce inflationary cosmology, perhaps through a Starobinsky type inflation, perhaps by kicking up a scalar field, perhaps by analytically linking a deSitter space to a sphere. I don't know, because I don't put much faith in pre-loop path-integral quantum gravity, because it has no well defined regulator, so I can't fully make sense of Hawking's ideas.
Hawking then argues that a theory of initial conditions, using a path integral, makes the notion of a creator superfluous--- since you have no time near the big-bang in this view. So there is no creation in time, nor is there a need to separate the notion of the initial state of the universe from its subsequent evolution.
Religious creation ideas
The major problem with such ideas, both Hawking's and the Pope's (at least as Hawking says it, I didn't read the Pope), is that modern day theologians do not usually think of the Demiurge creating the universe in a process which takes place in what we call time. They take the creator idea to mean that the Demiurge, acting outside of space and time, produced the whole enchilada--- space+time "all at once" from our point of view. This idea is total metaphysics, it has no bearing on our observable universe, and I see absolutely no point in discussing it further--- it is about as meaningful from a logical positivist point of view as saying that there is a lump of cheese with mold in the shape of Elvis orbiting a star on a galaxy beyond the cosmological horizon. You can't see this stuff, you can make up whatever crap you want and no one is going to prove you wrong.
But many people are always searching for meaning in the physical universe, so this type of discussion sells books. I don't think Hawking is motivated by any actual theological questions here. I think he just wants to sell books. Perhaps he also wishes to dismantle Christianity. I don't know.
If Hawking wants to dismantle monotheistic religion, attacking the Demiurge idea is just not going to work. The Demiurge notion is not really related in any significant way to the religious conceptions of a personal God. A creation story is just a political tool to get children, who naturally wonder "where did the universe come from?", motivated to study theology. The proper motivations generally require a certain amount of life experience which is not available to individuals at a young age. So religious doctrines hijack childrens' scientific instincts by telling just-so stories. The process is mostly stable, absent a Galileo, because as these children grow up to appreciate religious experience, they tend to see it as more important than telling the truth about the material universe, so that they repeat the same stories to their children. Since the stories are written down, they never change, so that they become more and more manifestly ridiculous with time.
The creation story in the Bible is so primitive, that anyone who actually believes it in a literal sense (not just claims to believe it, but actually believes it) is suffering from a serious psychosis and should seek professional help. But this creation story is not very useful for making sense of the rest of the Bible, it is just a pro-forma addition to what amounts to a narrative of tribal geneology which is mostly concerned with the relations of various Middle-Eastern tribes, and their ancient struggles for dominance in the region.
The notion of divinity is abstracted from these pseudo-historical literary narratives. They are probably based on composite narratives of great men and women who felt a connection to a larger entity than themselves, and tried to describe how this connection motivated their work. The narrative is designed to explain the relationship of individual human experience to the collectives which they form, which give this experience meaning, and to the limiting conceptions of the infinite future limit which determines which codes of ethics to follow. The idea is that codes of ethics, through the Darwinian struggle of tribes and ideas, of Gods and traditions, slowly approach an ideal ethics with time. This process can destroy entire empires, like the Egyptians and the Romans, and this destruction can often be directly linked to their moral failings, through the process of collective struggle against an oppressive state, which is never guaranteed to succeed over a short time scale, but which thanfully often does succeed, and always succeeds on a long enough time scale.
This is the main idea of religion, and it cannot be contradicted by physics, both because it has nothing to do with physics, and because it seems to be true.
Attributing the creation of the physical universe to such a complex epiphenomenon is to my mind completely out of place. To say that "God created the universe" makes about as much sense as saying "liberty (the concept) created the statue (of liberty)". It's not totally preposterous, because the concept of liberty did play a role in leading the revolutionary folks to build the statue, but it is not mechanistically useful if you want to know what the statue is made of. Likewise, the concept of God, as guiding human actions, can be thought of as a teleological reason for human existence, and therefore the statement "God created our perception of the universe" might be considered accurate (but only in a retro-causal teleological sense, like "housing Barack Obama is why the White House was built"). It's true, but only in a back-in-time, outside-space-and-time notion of causality that has nothing to do with physics. This is the idea of "final cause", the cause of something complex can be in the future, if something is planning for a future, which is found in Aristotle's writings. (I hate citing Aristotle, considering his awful stupidity regarding almost everything, but who knows who identified the notion of "final cause" first. Aristotle wrote about it.)
The notion of final cause is different from the notion of material cause, which is the kicking around of material things that leads things to happen. The idea that the two types of causes should be the same is the basic motivation for equating God and Demiurge. But this idea is ultimately useless, and it can be discarded. But you don't have to thw the God out with the Demiurge.
The paper you are talking about is describing one of several pre-big-bang scenarios that consider the big-bang to have complex dynamics. These models are generally speculative, and many of them are based on large-extra dimensions ideas which are experimentally ruled out, and are not to be taken seriously.
Large extra dimensions allow you to have complex stuff outside the non-gravitationally observable universe, like parallel sheets which house different universe which can only see each other gravitationally. These sheets can collide and these collisions have been (wrongly) argued to be similar to a big bang. The result of these sheet-collisions big-bangs can leave imprints on the cosmological scale, in the form of the light emitted during the cooling off period of the big-bang, which we see today as the microwave background radiation. The paper you cite is claiming that the details of the microwave background can be construed as compatible with one or another of these banging-brane scenarios.
These ideas are totally wrong for several reasons:
- Large extra dimensions (in any form) are experimentally ruled out: even before the LHC probed the TeV scale directly, neutrino masses, proton decay, strong CP, absence of electroweak and other non-renormalizable corrections placed the scale for new physics safely at the traditional GUT scale (this is most obvious for neutrino masses, which immediately and quantitatively reveal the scale). It is grossly incompetent to claim that large extra dimensions are possible, and the demoralizing effect of many people doing so has been a disaster for string theory, driving many people away from the field. The process has been something of a collective fraud, since it motivates grant money based on the false expectation that one can see string physics at colliders.
- Inflation means initial conditions are simple: The nature of a deSitter space, which is the initial condition for our universe in inflation theory, is such that it does not allow a high-entropy state. The entropy is maximal when the space is deSitter and Hawking thermal (filled with fluctuations and the Hawking temperature of the cosmological horizon). That such conditions (along with a slow-roll) agree with observations leave no room for complicated dances during the inflation period--- there is too little entropy, and we know it is correct to assume the universe is at maximum entropy (given the cosmological constant) at that time.
- The calculations are bogus: All the calculations of the microwave background signals from such crazy big-bang scenarios generally produce small corrections to what is observed. This is not what these scenarios actually predict. Since they have dynamics in the deSitter phase, they are not deSitter initial conditions, and so they predict some wild non-deSitter stuff, which is difficult to adjust to be a small perturbation. The predictions of such theory are not from a detailed quantitative model like the Starobinsky-Guth-Mukhanov-Linde-etc inflationary stuff, but from qualitative guesses.
While brane-world coupled with large-extra dimensions is a laughable idea, the idea of Branes in a compactification is not. You can try to mock up inflation as a process of brane-anti-brane annihilation, and this is an attractive idea, associated with Henry Tye. The inflation is the separation of branes and anti-branes, and the inflation is the two slowly driven toward each other to annihilate. This can produce a cosmological inflation with internal dynamics, but it is generally difficult to squeeze enough e-foldings out of the inflation, just because of rule-of-thumb bounds. But it is not inconcievable that this is what happened in the early universe, and that we will find evidence of this with time.