Our Life-Friendly Universe: Cosmic Fine-Tuning

The Big Bang theory of the origin and subsequent evolution of the universe is very well supported by the evidence, most especially the cosmic microwave background radiation, which is being studied in ever greater detail by successive satellite observations. One might also mention, besides the obvious evidence of expansion, the neat synthesis of light element production in the early universe and heavy element manufacture in stars. Nevertheless, the Big Bang presents us with some puzzles, not least the nature of the so-called dark matter and dark energy that compose 95% of the stuff of which the universe is made. The problem I wish to address in this article concerns the very special way in which the universe seems to be set up so that we can exist to observe it. Denoted by the term “fine-tuning,” this specialness is manifested in two areas:

1. The initial conditions, very near to the Big Bang itself, must be very tightly constrained if the universe is to be conducive to life arising within it at some stage.

2. The constants embedded in the laws of physics, which are not derived from theory but determined empirically, must lie in very narrow ranges for the universe to be life producing. These constants tell us (a) how strong the fundamental forces of nature are, i.e., the forces of gravity, electromagnetism, and the weak and strong nuclear interactions; and (b) how massive the fundamental particles are, such as the electron, proton, and neutron.

In the literature, the term “anthropic principle,” coined by pioneer in the subject Brandon Carter (1974), is widely used to denote these constraints on the laws of nature and the initial conditions at the Big Bang needed for our existence. The term has several variants and can be taken either as a tautology or a strong metaphysical claim, as helpfully discussed by Geraint Lewis and Luke Barnes (2016, 15–21). As a result, I shall generally use the term “fine-tuning” and use the term “anthropic” much more sparingly.

Examples of Fine-Tuning

Numerous examples of fine-tuning can be given, and I have chosen five to give the flavor of what we are talking about:

1. The parameter Ω is defined as the density of the universe divided by a so-called critical density that demarcates eternally expanding from re-collapsing universes. If Ω is even slightly less than one, the universe will expand forever; if it is even slightly greater than one, the universe will re-collapse under gravity. Martin Rees (1999, 88) informs us that, at one second from the Big Bang, Ω needs to be equal to unity to 1 part in 10¹⁵. If Ω lies outside this range, the universe will either expand or re-collapse much too quickly for galaxies and stars to form. In either case, the evolution of life will be impossible. John D. Barrow and Frank F. Tipler (1986, 410) take the calculation back to the Planck time, 10^-43 seconds from the Big Bang, when a quantum theory of gravity is needed to describe the universe. At that point, Ω needs to be equal to unity to the utterly remarkable accuracy of 1 part in 10⁵⁷. This is termed the “flatness problem” by cosmologists, since it implies that space-time is geometrically flat rather than positively or negatively curved.

   Today, Ω is still very close to unity, so close that we cannot easily distinguish what the ultimate fate of the universe will be. It is also interesting that ordinary matter that we understand only comprises 5% of what the universe is made of. Another 27% is so-called dark matter. We do not know what dark matter is, but it needs to be there, otherwise galaxies will fly apart and not be held together by gravity. The remaining 68% is sometimes called dark energy and is also very mysterious. I shall come back to that shortly.

2. The philosopher Robin Collins (2012, 176–77; a slight update on 2003, 189–90) argues that the probability that intelligent life (what he calls “embodied conscious agents,” ECAs) could arise in the universe would be reduced to zero if the strength of gravity were more than about 10⁹ times the actual value it takes in our universe. That sounds a large factor, but by comparison, the range that permits a universe at all is something like 0 to 10³⁸ times the actual value (the latter would make gravity equal in strength to the strong nuclear force, the strongest of nature’s four forces). An increase in the strength of gravity by a factor of a billion would imply that any land animal the size of humans would be crushed; even insects would require thick legs to support them, and no animals could grow much bigger. To reduce the planet’s size so that its gravity were only a thousand times that of Earth—still marginal for the possibility of organisms with brain size comparable to ours—would imply a planetary diameter of about forty feet, utterly insufficient to sustain the appropriate ecological environment. If gravity were multiplied by a factor of 3,000, then planets could not last for more than a billion years, dramatically reducing the time for ECAs to evolve. Even a factor of 100 would have serious consequences for what ECAs could do technologically. Dividing 10⁹, the absolute maximum value for ECAs to be viable at all, by the possible maximum value of 10³⁸ yields a tiny probability of 10^-29 for gravity to be fine-tuned (utilizing the “principle of indifference,” admittedly philosophically controversial but adopted for reasons of simplicity in the absence of further information—see a justification for this in Richard Swinburne (2001, 115–19)). Within the narrow, fine-tuned range of values for observers to exist at all, we as humans find a surprising bonus: extra fine-tuning that enables scientific discovery and technology—one of a number of such bonuses identified by Collins (2018, 89–107).

3. The chemical elements from which the planets and we ourselves are made are manufactured in the intensely hot interiors of stars by nuclear reactions. Foremost in this seminal work on stellar nucleosynthesis was the atheist Cambridge astrophysicist Sir Fred Hoyle. It was Hoyle who coined the term “Big Bang,” not necessarily as a pejorative description, although he was strongly opposed to it. Indeed, he was one of a group of three Cambridge astrophysicists who produced the steady-state theory, describing an eternal unchanging universe, as an alternative to the Big Bang. Yet, Hoyle noted what he saw as very surprising connections between the origin of life, the building up of chemical elements in stars, and the laws of nuclear physics. According to Hoyle (1959, 64), these connections are either “random quirks” or signs of a super-intellect behind the universe.

   Hoyle discovered the particular “coincidences” required for carbon, vital for life, to be made in stars through the so-called triple-alpha reaction: the crashing together of three helium nuclei (alpha particles) to form a carbon nucleus. Because the intermediate element beryllium is extremely short-lived, Hoyle realized there had to be a particular energy level (a resonance) in the carbon atom for the reaction to work. His prediction of this energy level was verified by colleagues William Fowler and others in the United States. Hoyle also realized that energy levels in the oxygen atom need to be nonresonant so that oxygen can be formed by the addition of a further helium nucleus without destroying all the carbon in the process. These seeming coincidences can be related to the fine-tuning of the strong nuclear force, which is responsible for binding the particles in atomic nuclei, to within about 0.5% (see Oberhummer et al. 2000).

   Hoyle’s (1981, 12) discoveries led him to remark that “a superintellect had monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.” He said further:

   If this were a purely scientific question and not one that touched on the religious problem, I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside the stars. If this is so, then my apparently random quirks become part of a deep laid scheme. If not, then we are back again to a monstrous sequence of accidents. (Hoyle 1959, 64)

   Note that Hoyle (1950, 115) had formerly regarded religion as blind escapism.

There are numerous examples of fine-tuning that I shall not discuss in detail. Lewis and Barnes discuss many of them, e.g., delving deeper into atomic structure and asking what would happen if the up and down quark masses were different from their actual values. They cite Craig Hogan on this theme, in particular a plot of the down quark mass minus the up quark mass against the electron mass given a constant value of the sum of the quark masses. Only a tiny region of the parameter space allows for chemistry; outside this region, one has either a proton or neutron universe (Lewis and Barnes 2016, 46–53; Hogan 2007, 224–26). I shall mention some further highly significant examples later.

Cosmologist Paul Davies (2006, 3) expresses it thus: “Like the porridge in the tale of Goldilocks and the three bears, the universe seems to be ‘just right’ for life, in so many intriguing ways.”

Is There Really Anything to Explain?

Some philosophers and physicists have argued along the following lines. We inhabit this particular universe with the apparently fine-tuned features described. If these features were not as they are, we would not be here to observe them. This is the “observer selection effect.” We can only observe a universe that gives rise to our own existence. It follows that we should not be surprised to observe fine-tuned parameters that necessarily have to be as they are in order for us to exist in the first place.

Richard Swinburne (2004, 156–57) gives a helpful example against this argument. A madman operates a machine that shuffles ten packs of cards simultaneously. He tells his kidnapped victim that, unless the machine produces, and continues to produce for every draw, ten aces of hearts, the machine will explode so that the victim will be killed and no longer able to observe any draws. But when the victim does observe successive draws, his conclusion is surely that the machine is rigged rather than that there is nothing to explain, because he would not be around if anything else but ten aces of hearts were drawn.

John Leslie (1989, 13–14) has a similar example that also brings out the fallacy of thinking that because we can only observe “our” set of parameters, the need for explanation is thereby removed. A firing squad of fifty sharpshooters is lined up against me. If they all miss, it is not adequate to shrug my shoulders and reply, “If they hadn’t all missed, then I shouldn’t be considering the affair.” My still being alive requires explanation—either the sharpshooters all deliberately missed or perhaps “immensely many firing squads are at work and I’m among the very rare survivors.” I consider the latter possibility, which corresponds to the many-universes hypothesis, here.

Given that I am here to tell the tale, the (posterior) probability that the sharpshooters all missed is of course 1 (they certainly had to), but the prior probability that they would all miss, on the basis of random chance, is very low indeed. The fact that they did so has a better explanation than chance, namely, they all deliberately missed. I actually doubt whether invoking a huge ensemble of firing squads around the universe makes any difference to my survival, and this may indicate a problem for the multiverse explanation—a point I shall return to later.

Nobel Prize-winning physicist Richard Feynman (1995, xix) once gave a public lecture in which a different issue was raised. He described how, on his way into the lecture, he observed a car in the parking lot with Tennessee number plate ARW 357: “Can you imagine? Of all the millions of license plates in the state, what was the chance I would see that particular one tonight? Amazing!” Of course, the a priori probability is very small, but this causes Feynman no problem, because any other car would be just as unlikely and just as insignificant. It just so happens that the car with number plate ARW 357 was the one that showed up. Similarly, according to some physicists, we do indeed live in a universe in which the laws of physics are ordered in a particular way, but if they were different in any number of equally improbable ways, we would not be here. Some cosmologists and philosophers believe that life is insignificant, a bit of froth on the surface of a meaningless universe, in which case alternative universes are just like alternative cars showing up in the car park. An example of an author who takes a view akin to this is M. C. Bradley (2002), who does not see life as significant in the sense of having objective value and therefore supports the car park analogy.

This argument is vulnerable at two points (Holder 2004, 43–47; 2013, 100–4). First, surely most of us would regard life, and in particular our own existence, not as mere froth but, contra Bradley and others, of real significance and value. For this reason, the universe that actually exists is in a different category than the vast majority of universes that do not possess this value. Second, we can provide an explanation, namely the theistic hypothesis, for why, of the vastly many universes that could exist, one of meaning and value actually does.

I had a schoolmaster, Mr. A. R. Williams, who collected classic cars. He was born on May 3, 1907. One day, a 1920 Wolseley Fifteen Tourer with the number plate ARW 357 turned up in the school car park. The car and number plate are highly significant, and there is a perfectly rational and superior alternative explanation to pure chance for this particular car to turn up.

As another example, suppose I shuffle a pack of cards and deal them out on the table. Suppose they come out in the order: ace, king, queen, all the way down to the two of clubs, then the same for diamonds, hearts, clubs, and spades. This hand is in fact just as improbable as any other. Indeed, it has about a 1 in 10⁶⁸ chance of of occurring. It seems to me, however, that there is a better explanation in this case than just sheer luck. If I were a card sharp, it would not be in the least surprising that I could produce such a hand, and it would be more rational to suppose that I am a card sharp than to believe the outcome to be entirely due to chance.

The difference between the hand dealt and the vast majority of other hands is that this one is meaningful—indeed, it displays a perfect pattern. Hence, it makes sense to look for an explanation beyond mere randomness. Added to which, there is a straightforward explanation available.

It is similar with the universe. I would argue, despite philosophical controversy surrounding the objectivity of value, that this universe possesses precisely that, namely, objective value. It is not just “any old universe.” The vast majority of universe configurations obtained by changing the parameters by the smallest amount are completely dead and boring. They are almost entirely devoid of meaning and value. This universe is shot through with meaning and value because, at least in one small part of it, it has produced creatures with rational powers to understand it and appreciate its beauty and the capacity to exercise moral responsibility. The universe has in a sense “become aware of itself.” Moreover, many scientists see objective value exhibited in the universe (why else study it?). Paul Davies (1992, 214) says this: “My own inclination is to suppose that qualities such as ingenuity, economy, beauty, and so on have a genuine transcendent reality—they are not merely the product of human experience—and that these qualities are reflected in the structure of the natural world.”

Explaining the Fine-Tuning

If the parameters of physics and cosmology were not fine-tuned, the universe would be lifeless. This fact demands an explanation. The theist has a ready-made one: God designed the universe this way, intending that life would arise. More than this, God intended the existence of rational creatures possessing free will who would be able to explore his handiwork and relate to him.

Of course, this explanation is not universally popular. The idea of divine design is anathema to scientists and philosophers of an atheist persuasion. Thus, it is important to consider possible alternatives.

Two main options for avoiding the design inference have been suggested:

1. Perhaps there is a better, more fundamental theory from which the constants can be derived. This may be what has been dubbed a “theory of everything,” an ultimate theory that unites general relativity and quantum theory. Einstein (1949, 63) himself, having argued that one could express the basic equations of physics using only “dimension-less constants,” went on to remark:

   Concerning such I would like to state a theorem which at present can not be based upon anything more than upon a faith in the simplicity, i.e., intelligibility, of nature: there are no arbitrary constants of this kind; that is to say, nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants occur (not constants, therefore, whose numerical value could be changed without destroying the theory).

   A similar argument pertains to the initial conditions: perhaps they too can be predicted from a more fundamental theory (see later discussion of inflation).

2. In total contrast is the suggestion that not only can the constants and initial conditions take different values from those we observe, but they actually do take different values in other existing universes. This is the multiverse hypothesis. The implication is that in a sufficiently comprehensive multiverse, while the vast majority of universes will be life-averse, a set of parameters within the bio-friendly region of parameter space is nevertheless bound to be instantiated. This is supposed to remove the surprise we find when we consider fine-tuning.

Option 1 can be interpreted in two ways. The first is to say that, given our laws of nature, the constants that go into them can be calculated from a more fundamental theory and hence must take the values they do. From the point of view of fine-tuning, this simply transfers our astonishment at the constants taking just the right values for life to the new fundamental theory itself. Why is that particular theory instantiated in the universe?

The second, more radical interpretation of option 1 goes further to say that there is only one set of self-consistent laws, and the physical constants are also determined to be what they are. There is then no alternative configuration for the universe and, provided it exists, it must necessarily exist as it does.

If this is the case, we are presented with a huge puzzle, namely, why is the only possible universe bio-friendly? In our imaginations, we can think of vastly simpler universes, perhaps comprising just a few isolated particles. How is it that the only self-consistent possibility is the universe we inhabit?

The puzzle may be helpfully elucidated by an analogy. Philosopher Peter van Inwagen (1993, 137–38) postulates dividing a square into a million smaller squares by dividing each side into a thousand equal lengths. He then supposes that we assign the first million digits of the decimal part of π to the million small squares, going left to right and line by line from top to bottom. Finally, we assign a color to each of the numbers zero through nine and paint each of the small squares with the color corresponding to the number assigned to it.

Suppose the result of this procedure were a stunningly beautiful painting. Surely this would be totally amazing and unexpected. Yet, it would be such by necessity, given that the digits of π are necessarily what they are. Somewhere in the infinite, unrepeating decimal part of π there will be a picture-generating million-digit sequence, but it would be truly astonishing if that were the case for the first million. I would not want to place a bet on it turning out so. It is similar for a universe, which is necessarily the only possibility, to be life-generating. To quote van Inwagen (1993, 137): “To me, in my ignorance, it seems as unlikely that a ‘cosmos design’ that was the only possible cosmos design should turn out to be life-permitting as that π should turn out to be picture-generating.”

Option 2, the multiverse hypothesis, proposes that the constants and laws of physics can indeed be different from those pertaining to our universe. Not only that, they are different in different existing universes, and this fact is supposed to render it more probable that one or more bio-friendly universes exists. One possible interpretation of this, analogous to the second interpretation of option 1 mentioned earlier, would be to say that there is a unique self-consistent set of laws that governs the multiverse and that the laws and constants for the individual universes, including our own, are what they are out of necessity. I would argue that the astonishment I expressed earlier for the unique single universe described would transfer in this case to the multiverse itself.

In practice, it would appear there are different ways of getting a multiverse, and this creates a puzzle. What determines which of the possible multiverses exists? Stephen Hawking (1988, 174) famously asked, “What is it that breathes fire into the equations and makes a universe for them to describe?” We now need to know which sets of equations have fire breathed into them, how many universes are generated, and how these choices are determined.

Cosmologist Max Tegmark (2003, 40–51) answers this conundrum with the bold proposal that all mathematical structures exist physically (his Level IV multiverse). Our universe with its particular mathematical structure is of course then bound to exist. This is, however, pure metaphysical speculation. It is not an answer that can be derived from science, which is how I understand a multiverse to be intended by atheists who invoke one to explain fine-tuning. Of course, theism is also a metaphysical explanation, though I argue that it is a better one. Moreover, the Level IV multiverse presents its own difficulties. Simply to formulate “all mathematical structures” is problematic. Furthermore, we can see that not everything that is possible can be physically instantiated, e.g., I am currently writing about cosmic fine-tuning, though it would be perfectly possible for me to be watching TV instead. There could be copies of me in other universes who have made different choices, but I have made this particular choice.

A Brief History of Modern Cosmology

The Big Bang theory is well established but presents a number of problems in its simplest form, not least the fine-tuning. In 1979, cosmologist Alun Guth (1997) proposed a theory called “inflation” as a solution. According to inflation, the universe expanded exponentially rapidly for a tiny fraction of a second after the origin—more specifically, by a factor of something like 10²⁶ between roughly 10^–35 and 10^–32 seconds from the beginning. One effect of this is that the density is driven ultra-close to the critical value, thus solving the flatness problem. Inflation also implies that all parts of our visible universe have been in causal contact, thus explaining the temperature uniformity of the microwave background across the universe—this is to solve the so-called “smoothness problem.”

This would seem to be positive. However, it turns out that the fine-tuning is not eliminated, just put up a level into inflation itself. If inflation has to be fine-tuned, it can hardly be regarded as a solution to the fine-tuning issue.

The consequence of this is a profusion of inflation models—Paul Shellard (2003, 764) counted 111 back in 2003, wryly noting that “[t]he most difficult model to rule out may well be supernatural inflation.” Of particular interest is the shift from option 1 to option 2 represented by Andrei Linde’s chaotic and eternal inflationary scenarios proposed in the 1980s. In chaotic inflation, different regions of the universe experience different amounts of inflation, with some regions growing large enough to produce galaxies, stars, and observers. This goes a step further in eternal inflation, with subregions of inflating domains themselves inflating so that we get regions giving rise to subregions giving rise to sub-subregions ad infinitum. These regions and subregions, etc., in which density and temperature and even the forces and constants of nature will vary, can be regarded as the different universes comprising a multiverse (Barrow 2005, 193–98).

Inflation is not yet the much sought-after theory of everything. That is what is required to describe the first 10^–43 seconds of cosmic history. To do so, the theory must unite the fundamental forces of nature, i.e., it must combine Einstein’s theory of gravity, the general theory of relativity, with quantum mechanics, which via the standard model describes the other three forces.

That theory is as yet unknown. A leading candidate has been string theory, which posits that the fundamental constituents of matter are no longer point-like particles but ultra-small objects that behave like vibrating strings. The particles we observe in nature are the product of different vibrational states of the strings. Unfortunately, the theory is only mathematically consistent in more than the usual four space-time dimensions. Since we do not observe these extra dimensions, they rather mysteriously have to be “compactified” or curled up so small as to be beyond detection in our most powerful particle accelerators.

Originally, string theory could be regarded as a form of option 1, since the aim was to calculate the properties, such as mass and charge, of all the fundamental particles. A serious problem has been the complete lack of observational or experimental evidence for the theory, whence the motivation has shifted to its mathematical elegance. Some physicists still pursue the theory with its original aim, though an interesting development has been the discovery of a small positive value of the cosmological constant, which I discuss later, and which seems to require option 2. Since nothing has been calculated in practice, some string theorists, notably Leonard Susskind (2006), have in any case switched to option 2. Interestingly, Susskind (2006, 12–13, 126–30, 288–89, 377, 379) denies string theory’s elegance and likens it to a “Rube Goldberg machine,” i.e., a “Heath Robinson contraption” in English English.

Susskind and his colleagues talk about the “landscape of string theory.” They find that there is not just one but many solutions of the theory, anywhere between 10¹⁰⁰ and 10¹⁰⁰⁰, with 10⁵⁰⁰ as the best estimate (Woit, 2006, 242; Susskind 2006, 21). These solutions represent possible universes, so questions arise as to how they are instantiated, how the “landscape” is populated, and how the possibilities become realized. The neat answer is that they are generated as the bubble universes of eternal inflation (Davies 2006, 192–94). It should be acknowledged that if there is a theory that in some sense naturally gives rise to many universes, then the plausibility of a multiverse is enhanced. However, this whole idea remains at the level of speculation and is controversial among physicists and philosophers. While the theistic hypothesis is no doubt regarded as speculative and controversial by many, I shall go on to explain why I see it as explanatorily superior to an atheistic multiverse.

There are a number of other ways of conceiving a multiverse than by inflation and string theory. Given the speculative nature of these proposals and inability to adjudicate them by means of observational evidence, a remark attributed to Russian physicist Lev Landau would seem apposite: “[C]osmologists are often in error, but never in doubt.” The next section expands on some of the difficulties that arise from the multiverse proposal.

Problems with the Multiverse Hypothesis

Of course God could create as many universes as he likes, and there are Christian philosophers and scientists who are happy to affirm that he did create a multiverse. However, it seems to me that there are many problems with the idea, and I now enumerate what I regard as the most significant of them (Holder 2004, 113–29; 2013, 130–54). Philosopher of science Simon Friederich (2021) has given a detailed, balanced account of some these, not least the issue of empirical testability, in a recent book.

1. I have stated that the multiverse proposal is speculative. It is notable that there is division even among string theorists over the existence of the landscape. Nobel Prizewinner David Gross (2005), a string theorist himself, is a skeptic regarding the multiverse, as are Gordon Kane et al. (2000), who go back to option 1, which they believe evades anthropic arguments. Tom Banks (2004; 2012) too is skeptical about the landscape, arguing that it is illusory to regard the different universe solutions as arising from the same theory.

   It is important to recognize that we cannot, even in principle, observe the other universes proposed by multiverse models since they are not in causal contact. The lack of empirical testing leads some to doubt that the multiverse idea is science at all. Thus, George Ellis and Joe Silk (2014) believe that the very integrity of physics is at stake where string theory and the multiverse are concerned.

   Cosmologist Martin Rees (2000, 138) numbers himself among “cautious empiricists” who feel “more at home” contemplating an era of the universe’s history beginning at about 10^–3 seconds from the beginning when we have known physics and empirical support (it is when the light elements are manufactured). Elsewhere, however, Rees ([2001] 2002, 164) opts for a multiverse in preference to providential design while admitting that his choice is “a highly speculative one” and “can be no more than a hunch.” The physics of multiverses takes us back, not to 10^–3 seconds from the beginning, but to 10^–35 seconds (inflation) or even 10^–43 seconds (string theory). Rees’s normal scientific preference for empirical evidence appears to be trumped by his ideological preference as an atheist. Although Rees ([2001] 2002, xi) recognizes that the ultimate question of why there is anything at all lies beyond science and leaves that to philosophers and theologians, he nevertheless favors a multiverse so as to avoid divine design. String theory pioneer Leonard Susskind is similar. The question of why there is something rather than nothing is untouched by the theory, but the landscape does explain the fine-tuning without the need to invoke a creator (Susskind 2006, 380).

2. There is a question mark over whether actual infinities can exist in nature. Cantorian set theory was developed to handle different degrees of infinity consistently in the abstract realm of mathematics. However, when we consider the possibility of infinite numbers of physical entities existing in the real world, we come up against some well-known paradoxes. For example, Hilbert’s Hotel has an infinite number of rooms and all of them are full. Nevertheless, infinitely many new guests can easily be accommodated! Simply move the guest in room 1 to room 2, the guest in room 2 to room 4, etc., and in general the guest in room n to room 2n for every value of n. There is now room for another infinity of guests since, while all the even-numbered rooms are full, all the odd-numbered rooms are vacant. It was the existence of paradoxes, famously Bertrand Russell’s paradox concerning the set of all sets that are not members of themselves, that led mathematician David Hilbert ([1926] 2012, 191) himself to state that “the infinite is nowhere to be found in reality, no matter what experiences, observations and knowledge are appealed to.”

   Suppose now that the parameters of physics vary across an infinite number of regions. Identical and near-identical copies of me will then arise, and arise an infinite number of times. Some of them will be writing about multiverses, others will be watching TV instead. It is quite bizarre even to begin to think about this. Among the issues raised is that of free will. Some cosmologists and philosophers rule out a multiverse with infinitely many member universes in light of the paradoxes (e.g., Ellis, Kirchner, and Stoeger 2004; Stoeger, Ellis, and Kirchner 2018; Copan and Craig 2004, 200–11; though the main interest of the latter is the impossibility of an infinite temporal regress).

3. When comparing competing hypotheses that are all compatible with the data, scientists would normally adopt that which is simplest. As William of Ockham put it in the fourteenth century, “[e]ntities should not be multiplied beyond necessity.” This is the principle known as Ockham’s razor, and it would seem to be violated by the multiverse idea. As noted, we also need to ask, “Why this and not another possible multiverse?”—unless of course we adopt the empirically unverifiable Tegmark Level IV multiverse, or, even more radically, David Lewis’s modal realism, whereby all possible universes (not just those realizing mathematical structures) exist. I note the problem concerning a possible alternative universe containing me making the free choices I did not make in this universe. Phenomenologically, it would seem simplest to suppose that I am where I am doing what I am doing rather than question notions such as personal identity and free will that would arise with the alternative. Philosopher and theologian Keith Ward (2008, 67–82) notes further consequences of the “maximal multiverse” proposal, in which “anything that can happen does happen.” Thus, on the one hand, there will be universes in which a virgin birth occurs, and on the other hand, universes where there is vastly more and greater evil than in our own.

4. The turn from option 1 to option 2 implies a departure from scientific method in another way. Scientists use their theories to make predictions. Suppose some unexplained phenomenon occurs in the laboratory or elsewhere in the cosmos. Rather than attempting to explain it rationally using science, we may now be tempted to say, “We just happen to live in a universe that produces that phenomenon.” Theories of this kind cannot be falsified (though see point 6).

   Related to this is the problem of induction, a point drawn out by Tim Mawson (2011). We rely on the future resembling the past, but it is not a necessary truth that it do so. We think all emeralds are green, but perhaps they are “grue,” green up until now but turning blue at midnight tonight, as in Nelson Goodman’s (1946) “new riddle of induction.” For every universe similar to ours up to time t, there will be an infinity of possible universes in which normal inductive procedures as we know them break down at that point in their history.

5. I referred earlier to the cosmological constant, which represents a repulsive force in opposition to gravity. Denoted by the Greek letter Λ (lambda), Einstein added this to his equations in 1917 so they would yield a static universe. He later called this his “biggest blunder,” since, without Λ, the equations would have predicted either an expanding or contracting cosmos. Einstein accepted that Λ was zero once we had the evidence of the expansion, and this was the position until a few years ago. Then, in 1998, a small positive value of Λ was observed, indicating an accelerating expansion (Riess et al. 1998; Schmidt et al. 1998; Perlmutter et al. 1999).

   Physicists think they know where Λ comes from. In quantum theory, the vacuum is not empty but a hive of constantly fluctuating activity, and possesses energy. Λ is believed to be the energy of the vacuum. Unfortunately, when Λ is calculated, it gives a value 10¹²⁰ times that which is compatible with observations. If Λ really took the calculated value, any material object would be pulled apart in an instant, with parts flying away to the ends of the universe.

   If one accepts the landscape proposal of string theory (but see earlier for reservations), there may be a multiverse solution to this problem. This is because the different universes within the landscape correspond to varying values of Λ. Moreover, as noted, the landscape is populated via eternal inflation, the bubble universes that are the different universes of the landscape. Universes with small values of Λ like ours will inevitably be instantiated.

   Given the proviso that the landscape exists, this would appear to explain the fine-tuning. However, there are further questions to ask. In order for this to work, there need to be enough solutions to make it probable that at least one fine-tuned universe exists. A mere 10¹⁰⁰ solutions would not be enough to make it probable that Λ alone would be in the anthropic range. 10⁵⁰⁰ or 10¹⁰⁰⁰ solutions would do that, but careful analysis would be needed for this to make it probable that the whole set of free parameters is fine-tuned. If this succeeded, one would still have to ask, “Why are there enough solutions to do the trick?” Our surprise would transfer to the landscape itself.

   A further question arises because, as Dennis Sciama (1989, 111) pointed out some years ago, and others have done since, we ought to regard our universe as typical of those conducive to producing observers. Is that the case, or is the universe more special than required?

   It turns out that the average bio-friendly Λ value exceeds the value compatible with observation by a significant margin. Steven Weinberg’s (1987) initial calculations demonstrated that vacuum energy density could be a factor of 100 greater than mass density and be compatible with life. This ratio has come down with subsequent calculations by Weinberg (2007, 32), but the observed vacuum energy level still looks a bit low, as Weinberg himself acknowledges. Paul Davies (2007, 492) notes that Λ could be an order of magnitude greater and not threaten the existence of galaxies or stars, and hence life. For Davies (2007, 491), this means our universe is not “minimally biophilic” but may be “optimally biophilic,” i.e., characterized by parameters close to the center of biologically compatible parameter space rather than taking typical life-conducive values.

   Of course, there could be many other parameters of our universe besides Λ that are more finely tuned than is strictly required for our own existence. It would appear there are. The charge on the electron is fixed to eleven significant figures, but it could fluctuate by 1 part in 10⁶ without affecting biochemistry (Davies 2007, 492–93). The lifetime of the proton is at least 2 x 10³² years, i.e., at least 10²² times the age of the universe, vastly longer than needed for life (Wilczek 2007, 52). These numbers make our universe look distinctly atypical of those comprising the tiny subset of life-bearing universes in a multiverse. I return to a highly significant further example in point 7.

6. A multiverse is usually taken to mean an overarching infinite space-time in which there are many distinct regions, which are denoted “universes” since there is no causal connection between them. If the total mean density of the universe is greater than the critical value, however, the universe will not be infinite but finite. Given the huge range of possible values of density that may well be probable, and a finite, not infinite universe most likely.

   This raises the possibility that observations of our universe could falsify multiverse models such as the string landscape. Indeed, there is tentative evidence that we already have such observations. It has been understood by cosmologists that data on the cosmic background radiation from the Planck satellite confirms inflation. The mean density is very close to the critical value, which has been taken to imply that the universe is spatially flat or very close to being spatially flat (Planck Collaboration 2020, reporting on Planck 2018 results). However, in a significant paper, Eleonora Di Valentino, Alessandro Melchiorri, and Joseph Silk (2019) calculate that the best fit to the data for the density parameter corresponds to a closed universe. The parameter Ω, which measures the ratio of actual density to the critical value, lies between 1.007 and 1.095 to 99% confidence level. That is to say, space-time has positive curvature, and the universe is closed and finite. The authors acknowledge that this result is in tension with data on other cosmological parameters, which to them indicates a possible crisis in cosmology.

   If a finite universe were sufficiently small, that is to say, of dimension less than fifty billion light years or so, it might be possible to “see all round the universe,” in the sense that we might see the same object in the sky at two different locations. Models of this kind have been suggested in the past (see Luminet et al. 2003a, 2003b; Luminet 2005). Such models would have the advantage of being empirically testable and avoid the paradoxes of infinity. If the finite universe were too large, we would not be able to confirm it in this way, and it might just be that we are in an over-dense region of an infinite universe. On the other hand, if density measurements indicated Ω to be slightly below unity, it would not necessarily follow that our universe was open and infinite. As pointed out by Barrow (2005, 144), it might just be that we inhabit an under-dense region of a finite universe.

7. Perhaps the most serious challenge to a multiverse explanation of fine-tuning comes from Roger Penrose. Penrose has calculated the entropy of the universe, which measures the amount of disorder in it and which increases over time. He calculates that, at the beginning, “the Creator” had to choose one from a set of ${10}^{{10}^{123}}$ possible universe configurations to give our universe, with all the order and structure it possesses (Penrose 1989, 342–44). That is fine-tuning in the extreme, although a multiverse with ${10}^{{10}^{123}}$ members or more would give a good chance of its existence.

   Penrose, however, goes further. A bio-friendly universe needs to be very highly ordered, but much less so than to 1 part in ${10}^{{10}^{123}}$ (Penrose 1989, 354). A universe with 10²² stars with their planets is not required; rather, a single solar system would suffice. Penrose notes that the entire solar system with all its inhabitants could be created by random collisions of particles with an “improbability” of one part in much less than ${10}^{{10}^{60}}$ .

   ${10}^{{10}^{123}}$ utterly swamps ${10}^{{10}^{60}}$ . Hence, we may infer that, given a multiverse, the probability of our being in a universe as ordered and structured as ours is one in ${10}^{{10}^{123}}$ . The multiverse is no advance on the single universe! We are very far from being in a typical universe within the subset of bio-friendly universes, which, as we have seen, is how we ought to regard ourselves. Typical life-conducive universes would be much more like the single solar system surrounded by chaos than like our universe. Even more common than these would be universes in which the “life” produced comprises something like Boltzmann brains (isolated, disembodied, but self-aware entities) rather than embodied conscious agents (Collins 2012, 174–80). Our atypicality to the highest degree as observers places a large question mark over the multiverse solution to fine-tuning. In particular, the ultra-fine-tuning of entropy does that much more strongly than the earlier instances of extra-special fine-tuning noted earlier.

Comparing the Explanatory Hypotheses

I will now compare the two main hypotheses advanced to explain fine-tuning, namely, a multiverse and divine design. In common with Richard Swinburne and others, I argue that invoking God as designer gives a simple explanation. At least part of why this is so is that the God of theism exists necessarily and is necessarily omnipotent and omniscient. In contrast, I note (point 3) that the multiverse explanation is not simple. Not only is it complex because it multiplies entities (universes) beyond necessity but also because each of those entities in turn is a complex physical universe. On the design hypothesis, God deliberately created our universe, intending that it produce intelligent creatures able to exercise reason and free will and relate to him. Moreover, God is likely to have created the highly ordered universe we observe rather than the single solar system or Boltzmann-brain universe discussed in point 7.

This assessment takes us back to my earlier point about objective value. I argue that embodied conscious agents are of far greater value than mere Boltzmann brains. I noted earlier Robin Collins’s point about extra fine-tuning enabling scientific discovery and technology. This includes discovering the rich cosmos well beyond our solar system. We gaze in wonder at the night sky and at images of distant spiral and elliptical galaxies millions of light years distant. This universe seems to possess a more complete objective value than a single solar system embedded in chaos. If God wanted to create rational creatures like ourselves, he could of course have simply created the latter. But it seems to me that the God of classical theism would indeed be much more likely to create greater order, not just for our own but for his contemplation, perhaps as on a smaller scale he brings rain “on a land where no one lives” (Job 38:26). God may even intend that other rational creatures evolve elsewhere in the universe, though that is not a topic that can be delved into here. The point is that surely any reasonable probability for the existence of the ultra-fine-tuned universe we observe, given that there is a God, will totally outweigh the almost infinitesimal probability of one in ${10}^{{10}^{123}}$ .

We can express the fine-tuning argument formally utilizing Bayesian confirmation theory, widely employed in the philosophy of religion (Holder 2021, 60–62). I ignore for the moment the hypothesis that there is just one universe, since that leaves the fine-tuning unexplained, and focus simply on the multiverse hypothesis (with no God) as an alternative to God.

Let FT = the fine-tuning evidence, G = the hypothesis that there is a God, and M = the multiverse and no-God hypothesis. Bayes’s theorem for the two hypotheses states:

$P\left[G|\mathit{\text{FT}}\right]=\frac{P\left[\mathit{\text{FT}}|G\right].P[G]}{P[\mathit{\text{FT}}]}$ (1)

and

$P\left[M|\mathit{\text{FT}}\right]=\frac{P\left[\mathit{\text{FT}}|M\right].P[M]}{P[\mathit{\text{FT}}]}$ (2)

A simple and useful consequence of Bayes’s theorem is obtained by dividing the left-hand sides and right-hand sides of these equations:

$\frac{P[G|\mathit{\text{FT}}]}{P[M|\mathit{\text{FT}}]}=\frac{P[\mathit{\text{FT}}|G]}{P[\mathit{\text{FT}}|M]}.\frac{P[G]}{P[M]}$ (3)

Of course, I recognize that it is not possible to assign precise values to the terms in this equation. However, as noted, the lesson from our utter atypicality as observers within a multiverse is that P[FT|M] is extremely low. Indeed, Penrose’s calculations would indicate that the probability of finding ourselves in a universe, necessarily a member of the bio-friendly subset of universes but with the ultra-high degree of order and structure that ours has, is of order $1/{10}^{{10}^{123}}$ .

Any reasonable values for the other probabilities in equation (3) will be completely swamped by this ultra-low value of P[FT|M]. The probability that God would create a totally ordered universe, P[FT|G], is hugely greater since God would have good reason to do so, as discussed. Suppose, for the sake of argument, that P[FT|G] = 1/10. The first factor on the right-hand side of equation (3) would then be ${10}^{{10}^{123}}$ .

Assigning probabilities to the numerator and denominator of the second factor in the third equation, i.e., the prior probabilities that God and the multiverse exist, is more controversial. Swinburne (2004, 96–109, 165, 185–88) argues that P[G] >> P[M] on the grounds of divine simplicity versus universe, and, a fortiori, multiverse complexity. Davies (2006, 249) in contrast regards G and M as of equal probability. Yet, even if we thought P[G] < P[M], there would be no reason to assign an absurdly low value to P[G] when compared with P[M]. Given the dominance of the first factor, any reasonable estimate of the second will yield

$\frac{P[G|\mathit{\text{FT}}]}{P[M|\mathit{\text{FT}}]}={10}^{{10}^{123}}$ (4)

The implication is that God as designer provides a far more highly probable explanation for fine-tuning than a multiverse. The enormous number ${10}^{{10}^{123}}$ washes out any moderate probabilities that may be inserted in the third equation.

Expanding the denominator of the first equation, we obtain

$P\left[G|\mathit{\text{FT}}\right]=\frac{P\left[\mathit{\text{FT}}|G\right].P[G]}{P\left[\mathit{\text{FT}}|G\right].P\left[G\right]+P\left[\mathit{\text{FT}}|~G\right].P[~G]}$ (5)

To obtain an absolute value for P[G|FT] from the fifth equation would entail estimating not P[FT|M] but the more comprehensive P[FT|~G], where ~G embraces all non-theistic explanations for the fine-tuning, not just M. The main alternative to M is the single universe U without God. However, I have focused on M precisely because P[FT|U] is small, indeed ultra-small and of order $1/{10}^{{10}^{123}}$ . What is seen, perhaps surprisingly, is that M is no advance on U in light of the typicality requirement.

There are also alternative theistic hypotheses to that which have been considered. Chief of these would be a plurality of gods rather than the one God of the monotheistic Abrahamic faiths. Swinburne argues, again on grounds of simplicity, that the existence of many gods is far less probable than the existence of one (Swinburne 2004, 145–47). It certainly violates Ockham’s razor. Moreover, the universal validity of the laws of physics across space and time is much better explained by a single divine designer than by many. It is hard to see why, with any reasonable values assigned to the probabilities P[FT|G] and P[G], P[FT|G].P[G] should not be much greater than P[FT|~G] and hence than P[FT|~G].P[~G], from which it would follow from the fifth equation that P[G|FT] would lie very little short of unity.

In response to this argument, it seems to me that the atheist is almost forced to assert that the prior probability of God’s existence before consideration of the evidence is ultra-small, i.e., that P[G] < $1/{10}^{{10}^{123}}$ . The only plausible way to justify that is to argue that the very idea of God is incoherent, so that in fact P[G] = 0. That is a challenge to which, in my view, the most implacable atheist would be hard pressed to rise.