The word “cosmology” is derived from the Greek κόσμος (“cosmos”) which means, roughly speaking, ”the world as considered as an orderly system”. The other side of the coin to “cosmos” is Χάος (“chaos”). In one world-view the Universe comprised two competing aspects: the orderly part that was governed by laws and which could (at least in principle) be predicted, and the “random” part which was disordered and unpredictable. To make progress in scientific cosmology we do need to assume that the Universe obeys laws. We also assume that these laws apply everywhere and for all time or, if they vary, then they vary in accordance with another law. This is the cosmos that makes cosmology possible. However, with the rise of quantum theory, and its applications to the theory of subatomic particles and their interactions, the field of cosmology has gradually ceded some of its territory to chaos.
In the early twentieth century, the first mathematical world models were constructed based on Einstein’s general theory of relativity. This is a classical theory, meaning that it describes a system that evolves smoothly with time. It is also entirely deterministic. Given sufficient information to specify the state of the Universe at a particular epoch, it is possible to calculate with certainty what its state will be at some point in the future. In a sense the entire evolutionary history described by these models is not a succession of events laid out in time, but an entity in itself. Every point along the space-time path of a particle is connected to past and future in an unbreakable chain. If ever the word cosmos applied to anything, this is it.
But as the field of relativistic cosmology matured it was realised that these simple classical models could not be regarded as complete, and consequently that the Universe was unlikely to be as predictable as was first thought. The Big Bang model gradually emerged as the favoured cosmological theory during the middle of the last century, between the 1940s and the 1960s. It was not until the 1960s, with the work of Hawking and Penrose, that it was realised that expanding world models based on general relativity inevitably involve a break-down of known physics at their very beginning. The so-called singularity theorems demonstrate that in any plausible version of the Big Bang model, all physical parameters describing the Universe (such as its density, pressure and temperature) all become infinite at the instant of the Big Bang. The existence of this “singularity” means that we do not know what laws if any apply at that instant. The Big Bang contains the seeds of its own destruction as a complete theory of the Universe. Although we might be able to explain how the Universe subsequently evolves, we have no idea how to describe the instant of its birth. This is a major embarrassment. Lacking any knowledge of the laws we don’t even have any rational basis to assign probabilities. We are marooned with a theory that lets in water.
The second important development was the rise of quantum theory and its incorporation into the description of the matter and energy contained within the Universe. Quantum mechanics (and its development into quantum field theory) entails elements of unpredictability. Although we do not know how to interpret this feature of the theory, it seems that any cosmological theory based on quantum theory must include things that can’t be predicted with certainty.
As particle physicists built ever more complete descriptions of the microscopic world using quantum field theory, they also realised that the approaches they had been using for other interactions just wouldn’t work for gravity. Mathematically speaking, general relativity and quantum field theory just don’t fit together. It might have been hoped that quantum gravity theory would help us plug the gap at the very beginning of the Universe, but that has not happened yet because there isn’t such a theory. What we can say about the origin of the Universe is correspondingly extremely limited and mostly speculative, but some of these speculations have had a powerful impact on the subject.
One thing that has changed radically since the early twentieth century is the possibility that our Universe may actually be part of a much larger “collection” of Universes. The potential for semantic confusion here is enormous. The Universe is, by definition, everything that exists. Obviously, therefore, there can only be one Universe. The name given to a Universe that consists of bits and pieces like this is the multiverse.
There are various ways a multiverse can be realised. In the “Many Worlds” interpretation of quantum mechanics there is supposed to be a plurality of versions of our Universe, but their ontological status is far from clear (at least to me). Do we really have to accept that each of the many worlds is “out there”, or can we get away with using them as inventions to help our calculations?
On the other hand, some plausible models based on quantum field theory do admit the possibility that our observable Universe is part of collection of mini-universes, each of which “really” exists. It’s hard to explain precisely what I mean by that, but I hope you get my drift. These mini-universes form a classical ensemble in different domains of a single-space time, which is not what happens in quantum multiverses.
According to the Big Bang model, the Universe (or at least the part of it we know about) began about fourteen billion years ago. We do not know whether the Universe is finite or infinite, but we do know that if it has only existed for a finite time we can only observe a finite part of it. We can’t possibly see light from further away than fourteen billion light years because any light signal travelling further than this distance would have to have set out before the Universe began. Roughly speaking, this defines our “horizon”: the maximum distance we are in principle able to see. But the fact that we can’t observe anything beyond our horizon does not mean that such remote things do not exist at all. Our observable “patch” of the Universe might be a tiny part of a colossal structure that extends much further than we can ever hope to see. And this structure might be not at all homogeneous: distant parts of the Universe might be very different from ours, even if our local piece is well described by the Cosmological Principle.
Some astronomers regard this idea as pure metaphysics, but it is motivated by plausible physical theories. The key idea was provided by the theory of cosmic inflation, which I have blogged about already. In the simplest versions of inflation the Universe expands by an enormous factor, perhaps 1060, in a tiny fraction of a second. This may seem ridiculous, but the energy available to drive this expansion is inconceivably large. Given this phenomenal energy reservoir, it is straightforward to show that such a boost is not at all unreasonable. With inflation, our entire observable Universe could thus have grown from a truly microscopic pre-inflationary region. It is sobering to think that everything galaxy, star, and planet we can see might from a seed that was smaller than an atom. But the point I am trying to make is that the idea of inflation opens up ones mind to the idea that the Universe as a whole may be a landscape of unimaginably immense proportions within which our little world may be little more than a pebble. If this is the case then we might plausibly imagine that this landscape varies haphazardly from place to place, producing what may amount to an ensemble of mini-universes. I say “may” because there is yet no theory that tells us precisely what determines the properties of each hill and valley or the relative probabilities of the different types of terrain.
Many theorists believe that such an ensemble is required if we are to understand how to deal probabilistically with the fundamentally uncertain aspects of modern cosmology. I don’t think this is the case. It is, at least in principle, perfectly possible to apply probabilistic arguments to unique events like the Big Bang using Bayesian inference. If there is an ensemble, of course, then we can discuss proportions within it, and relate these to probabilities too. Bayesians can use frequencies if they are available but do not require them. It is one of the greatest fallacies in science that probabilities need to be interpreted as frequencies.
At the crux of many related arguments is the question of why the Universe appears to be so well suited to our existence within it. This fine-tuning appears surprising based on what (little) we know about the origin of the Universe and the many other ways it might apparently have turned out. Does this suggest that it was designed to be so or do we just happen to live in a bit of the multiverse nice enough for us to have evolved and survived in?
Views on this issue are often boiled down into a choice between a theistic argument and some form of anthropic selection. A while ago I gave a talk at a meeting in Cambridge called God or Multiverse? that was an attempt to construct a dialogue between theologians and cosmologists. I found it interesting, but it didn’t alter my view that science and religion don’t really overlap very much at all on this, in the sense that if you believe in God it doesn’t mean you have to reject the multiverse, or vice-versa. If God can create a Universe, he could create a multiverse to0. As it happens, I’m agnostic about both.
So having, I hope, opened up your mind to the possibility that the Universe may be amenable to a frequentist interpretation, I should confess that I think one can actually get along quite nicely without it. In any case, you will probably have worked out that I don’t really like the multiverse. One reason I don’t like it is that it accepts that some things have no fundamental explanation. We just happen to live in a domain where that’s the way things are. Of course, the Universe may turn out to be like that - there definitely will be some point at which our puny monkey brains can’t learn anything more – but if we accept that then we certainly won’t find out if there is really a better answer, i.e. an explanation that isn’t accompanied by an infinite amount of untestable metaphysical baggage. My other objection is that I think it’s cheating to introduce an infinite thing to provide an explanation of fine tuning. Infinity is bad."