5.2 The Goldilocks universe
In the second half of the 20th century, a host of popular books and articles were written, investigating the claim that the universe seems “fine-tuned” for life. Broadly, the argument is that if some parameter (such as the ratio of gravitational to electromagnetic force, or the ratio of the strong force to electromagnetic force, or the mass difference between the two lightest quarks, or the strength of the weak force and so on) had not lain within a comparatively narrow range of values, then stars could not have formed, or they wouldn’t have lived long enough for life to form on their planets, or all of the hydrogen would have been “burned” in the early universe, or few elements beyond hydrogen could have been formed in stars, or protons and neutrons would have been unstable – the list goes on. In each case, chemistry – and life – would not have evolved in such a universe.
Tempting though it is to delve deeper into the scientific and philosophical questions raised by these conjectures, I won’t. The popular explanation for the “Goldilocks Universe” is rooted in the cosmological multiverse, which is the term sometimes given to the (possibly infinite) set of universes generated within the exponentially expanding inflaton field. According to the model, each universe is created when a quantum fluctuation in a localized region of the field dissipates its energy, which is instantly converted into the hot Big-Bang plasma of radiation and matter at the beginning of the universe. A universe created in this way is referred to as a bubble universe (or, sometimes, a pocket universe). Notice that the cosmological multiverse is quite distinct from the quantum multiverse of Many Discrete Worlds (MDW) and Many Worlds Interpretation (MWI), and, in particular, differs from the quantum multiverse in that its component universes may take completely different and widely varying values for the fundamental constants.
The idea, then, is that, with so many different universes with so many different permutations of fundamental constants, there are bound to be some universes with conditions that are just right for the formation of fundamental particles and atoms and stars and planets and molecules and life with sufficient self-awareness to see the implausibility of their own existence! Let us call this explanation the Many-Universes Explanation for Goldilocks – MUEG. This is the counter to those who explain our fortuitous arrangement of fundamental constants by appealing to a Cosmic Designer.
However, that scheme won’t work. Considering our universe as a mathematical (sub)structure, then the whole cosmological multiverse must also be a mathematical structure. If observed quantum outcomes are to satisfy the expected Born probabilities, then the universes which happen to have our fundamental constants would have to bubble up in inflaton space in frequences distributed according to the Born rule, just as they do in our quantum multiverse. Such a scenario lies outside the scope of any inflaton model, as, too, would one where complete quantum multiverses are created in the inflaton space.
So, instead of speculating on scenarios founded on inflaton space, let us pull back for a broader perspective. If we accept that our universe, and, therefore, our quantum multiverse, are purely mathematical structures, then MUEG is self-evident. That is because, if we assume that all logically permitted mathematical structures must exist, then that must include the mathematical structure which is our multiverse, which includes our particular universe. Within the infinitude of allowed mathematical structures lies an infinitude of multiverses and universes that are not quite fine-tuned enough to be the same as our own, but which allow us to accept that our own multiverse, while remarkable to us, is not remarkable at all, within the broader context of all possible mathematical structures. (Don’t confuse the finitude of our multiverse and universe with the infinite number of possible mathematical structures.) If a multiverse containing such a universe is a logically allowed mathematical structure, then our universe simply has to exist! We seem to have satisfied MUEG by showing that an infinite number of slightly different multiverses exist as mathematical structures alongside our own particular multiverse.
