The idea of the multiverse is that there exist multiple universes, and that what we perceive as being the Universe is only a small part of total reality.
There are various different kinds of possible multiversity.
This is the multiverse of Max Tegmark. In effect, it subsumes all other forms of multiverse, by definition. But for the purposes of this discussion I will assume more limited forms of multiversity.
It is possible that the laws of physics ultimately depend on some finite set of free parameters, consisting of dimensionless constants for which there is no further explanation – they just happen to have whatever values they have. We can imagine the existence of different universes with different values for these parameters. We can imagine the existence of universes for all possible sets of parameter values. If there are N free parameters, this is an N-dimensional space of universes.
In this version of the multiverse, the multiple universes all have exactly the same basic laws of physics. The only difference is the specific position and momentum of the basic objects (i.e. particles) within each universe. As it happens, quantum mechanics virtually requires such a multiverse, where the universal wave function can be regarded, at least to some approximation, as a superposition of an ever-increasing number of approximately classical wave functions, each such component wave function constituting a separate "universe".
If quantum mechanics gives us non-parametrized multiversity whether we like it or not, then parametrized multiversity gives a multiplicity of quantum wave functions, with each wave function constituting a multiplicity of universes. In effect the parametrized multiverse is actually a multi-multiverse.
Necessarily we exist in a universe in which the origin, evolution and on-going survival of life is possible.
But what can we say about the probabilities of origination and evolution?
If there are free parameters in the laws of physics, then these parameters are going to affect both probabilities, i.e. the probability of life originating, and the probability of it evolving (especially evolving to a point where intelligent life appears).
Empirically we can observe that the survival and evolution of life is something that occurs with reasonably high probability, at least once life has started. Our planet has a history of thousands of millions of years in which millions of species have evolved, some of them into ever-more complex forms.
However, the origin of life appears to be something that occurs with a very low probability. It has only ever been observed to occur once, since all existing life forms appear to be related to each other. And there is no evidence of the existence of alien life out in space. If the origin of life was at all common, we would expect to see physical evidence of at least some alien civilisations, even if the expected self-destruction rate of such civilisations was as high as 99.99%.
Given that the quantum multiverse probably exists, our own existence does not tell us anything at all about the probability of the origin of life. A lower bound on the probability is determined by probability of atoms spontaneously forming into the simplest possible life-form (while in some environment where reproduction can take place once the initial life form exists). As low as this probability might be, the number of universes within the quantum multiverse is much greater. So if it is at all possible for life to exist, life will exist.
In other words, the only requirement for the values of free parameters in the laws of physics is that those values must allow life to survive and evolve.
However, it is possible to apply a probabilistic argument to distinguish between a parametrized multi-multiverse and a non-parametrized multiverse in which a specific set of values for the free parameters has been chosen.
These two choices can be described in terms of a "God" who has created the multiverse, and what we might be able to deduce about why this God has created it.
If there is only one multiverse with one specific set of free parameter values, then this implies that God has chosen that particular set of values for some purpose. And if the values are chosen from some very small set of values which allow the development of intelligent life, then it is a reasonable conclusion that allowing the development of intelligent life is the very reason why those values where chosen.
On the other hand, if God has chosen to create the full set multiverses for all possible sets of free parameter values, then we can no longer deduce from our own existence anything about why God might have create such a multi-multiverse. In particular, it might be something happening in some other part of the multi-multiverse which explains the true purpose of God creating it.
To apply a probabilistic argument to the parametrized multi-multiverse, it is necessary to determine an a priori probability distribution over the N-dimensional space of free parameter values. If we consider that the sub-space where life is possible is actually a very small region (as implied by the fine-tuning argument), then it is plausible that the probability distribution, whatever it might be, is approximately uniform over this sub-space.
A secondary assumption is that the probability of the on-going survival and evolution of life is relatively insensitive to the free parameter values within that region in which the origin of life is most probable. This is plausible on the assumption that the two probabilities are largely determined by different factors. (A crude analogy is betweeen the probability of a fire starting, and the probability of a fire continuing to burn, which in many circumstances are determined by completely separate variables. For example, in the wild, the probability of a fire continuing to burn depends on the amount of dead plant material, and the general level of dryness, whereas the probability of a fire starting depends mainly on how often lightning strikes the area in question. Factors that strongly influence the occurrence of lighting storms might have little or no effect on the general accumulation of combustible material.)
Assuming an approximately uniform distribution, and assuming a parametrized multi-multiverse, we have to conclude that the most probable set of free parameter values must be whichever set of parameter values has the maximum probability of the origin of life.
Whereas, assuming only a multiverse with a fixed set of parameter values, we can only deduce that the parameter values must allow life to originate.
Now if God happens to choose a fixed set of values, but those happen to be the values which maximize the probability of life originating, then from within our own universe, we cannot distinguish this from the parametrized multi-multiverse.
But if God chooses a fixed set of values which allow life to originate, but for which the probability of life originating is much, much lower than the maximum possible value, then we can effectively reject the null hypothesis that we live in a parametrized multi-multiverse, and we can deduce that someone or something (i.e. "God"), has chosen the particular set of values that we observe in our universe.
Furthermore, if we could calculate the effect that varying the free parameters by small amounts would have on the nature of the universe we live on, we could work out what it is that the chosen parameters do optimise, and therefore the nature of God's true purpose in creating a non-parametrized quantum multiverse with the particular set of free parameter values that it happens to have.
Of course all these conclusions depend on various assumptions that I have made. These assumptions are plausible, but to verify them we would have to determine the laws of physics with much more precision than we have done so far. The day may yet come when we know that much physics, and when our ability to compute the consequences of the laws of physics and variations thereof is sufficient to calculate the probabilities of the origin and evolution of life as functions of those variations. When that day comes, we may truly be able to calculate whether or not our universe has been created for some special purpose, and what relation that purpose may have to our own existence.
Figure 1: Log probabilities of origin of life and evolution of intelligent life as a function of a free parameter X (here N, the number of free parameters, has been chosen to be 1). The probability of the origin of life is very sensitive to the parameter X, whereas the probability of the evolution of intelligent life (given the origin of life) is relatively insensitive to X. (SVG)
