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Life, the Multiverse, and Fine-Tuning

Fact, Fiction, and Misconceptions

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Abstract

Few topics in cosmology are as hotly debated as the Multiverse: for some it is untestable and hence unscientific; for others it is unavoidable and a natural extension of previous science. A third position is that it is seen to follow from other theories, but those other theories might themselves be seen as too speculative. The idea of fine-tuning has a similar status. Some of this disagreement might be due to misunderstanding, in particular the degree to which probability distributions are necessary to interpret conclusions based on the Multiverse, especially with regard to the Anthropic Principle. I present undisputed facts, discuss some common misunderstandings, and investigate the role played by probability. The Multiverse is perhaps an important component necessary for interpreting cosmological and other physical parameters.

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Notes

  1. According to [1], the second sense is the usual one: ‘The usual meaning of “fine-tuning” is that small changes in the value of a parameter can lead to significant changes in the system as a whole.’ He also discusses ‘[a] second type of fine-tuning ...when a parameter has a vastly different value from that expected’ and in the context of such hierarchical fine-tuning discusses the near equality of two large numbers necessary for them to almost cancel and the concept of naturalness, all also mentioned in this section.

  2. Of course, the reciprocal of a small number is a large number. I will always assume that the smaller number is the numerator when discussing ratios. One should also concentrate on ratios and not differences. One reason is that differences depend on the dimensions used, which are arbitrary; ratios are automatically dimensionless. Another is that, even when the difference between a and b is important, one should always consider the dimensionless quantity \((|(a-b)|)/(|a|+|b|)\) (if a and b have the same sign, that is equivalent to \(|(a-b)/(a+b)|\)) since the important quantity is the size of the difference compared to the size of the numbers involved.

  3. Note that Dicke’s argument is an example of the use of the Anthropic Principle which does not involve the Multiverse. There is also the subtle issue as to the difference between invoking the Multiverse as an explanation for fine-tuning and seeing fine-tuning as evidence for the Multiverse (e.g. [6]).

  4. Of course, specific outcomes are highly contingent and random (e.g. [8]), but the basic concept, e.g. predators have a fine-tuned digestive system so that they can subsist on whatever prey is abundant, is not.

  5. “Universe” refers to our Universe, while “universe” refers to a model universe in the sense of a cosmological model or to a different physical universe in the Multiverse.

  6. I would be willing to bet a rather large sum that the next toss is also heads against someone who takes the view that such a sequence is just as probable as any other and, thus, we shouldn’t be surprised to have seen one-hundred heads in a row, but also that the chances of the 101st head is 50%.

  7. That should be extended to obvious derivatives, such as two-number sequences with digits other than 0 and 1, compressed sequences in which the number of successive heads or tails codes for the corresponding number, and so on.

  8. \(\lambda _0\) and \(\varOmega _0\) are the current values of \(\lambda\) and \(\varOmega ,\) the normalized cosmological constant and density parameter, defined as \(\Lambda /(3H^{2})\) and \((8\pi G\rho )/(3H^{2})\), respectively, where \(\Lambda\) is the cosmological constant (here in units of time\(^{-2}\)), G the gravitational constant, H the Hubble constant, and \(\rho\) the density. See [10,11,12,13] and references therein for further details on the notation and discussion of the flatness problem in general, including discussions of fine-tuning related to the flatness problem, which I don’t address here since it is not an example of problematic fine-tuning: although the Universe is fine-tuned in the second sense mentioned above, most literature on the flatness problem is concerned with the alleged improbability, but that is due to a misunderstanding. Interestingly, it seems that it was not really perceived to be much of a problem before [14] claimed it to be a problem [15].

  9. See the Appendix for more details.

  10. The extreme view that the Universe could not be other than it is with respect to the laws of nature is known as scientific essentialism (e.g. [33]) (I thank one of the referees for raising this point.), though it is usually seen as the idea that the laws of nature are intrinsic to the contents of the Universe, rather than being imposed from without, in contrast to the idea that constants of nature couldn’t be other than what they are, though arguably the former claim implies the latter.

  11. See [34, Sect. 4.2] for a similar list.

  12. One could claim that the Universe does not have to be fine-tuned for life because some sort of life would arise whatever the conditions. However, since most of the parameter space is “boring” (e.g. [31]), that seems unlikely.

  13. Note that while the term “Multiverse” is often used for all, the four Levels according to Tegmark are quite distinct. Thus, arguments for or against one type have little or no bearing on other types. [48, Sects. 10.1 and 10.3], for example, rejects Tegmark’s Levels III and IV but not I and II. His Level I certainly exists, but would not be called a Multiverse by many. Level III is tied to the many-worlds interpretation of quantum mechanics. Level IV, an extreme form of Platonism, is probably supported by few other than Tegmark himself. Level II is often discussed within the context of eternal inflation, which is somewhat speculative (some would even say that inflation itself is speculative!), but is logically independent of it-the Level II Multiverse, in the sense of several (perhaps an infinite number of) instances of FRW universes, could, as far as we know, exist even without eternal inflation, just as one could conceive of other planets before it was known how solar systems are formed.

  14. While both Ellis and Silk are very well known and influential cosmologists, note that Martin Rees, probably the most famous living astronomer, is a supporter of the Multiverse (e.g. [52,53,54,55]). Also note that while Ellis is sceptical, he by no means dismisses the concept entirely. An overview is provided by [56], arguments against some aspects of the Multiverse by [57], and a rebuttal by [58]. An excellent impartial discussion is given by [48].

  15. I thank one of the referees for raising this point.

  16. Named in honour of [60], though he credited his assistant Schütz, Boltzmann brains are the idea that most of spacetime consists of a high-entropy equilibrium state, with observers existing only within low-entropy fluctuations. As first pointed out by [61], that means that most observers (i.e., a “brain” of some sort with a given mental state) will have fake memories of a previous lower-entropy state, rather than real memories of a state with higher entropy, because the former are overwhelmingly more probable.

  17. The same idea is sometimes expressed by stating that it explains anything, or that it explains everything. While explaining nothing is clearly not satisfactory, perhaps one shouldn’t be so sceptical of something which explains everything, for some definition of “explain”.

  18. Indeed, Tegmark’s Level I Multiverse is what many call a universe, e.g. in FRW model that which is described by that model, which for example in a spatially closed case can have a definite mass, even though part of it might lie beyond our particle horizon, and might even always lie beyond our particle horizon.

  19. [80] counted 30 different versions of the Anthropic Principle. Also note that sometimes various authors use the same name for different versions and/or call the same version by different names. The concept has evolved over time; a nice introduction is given by [50]. Also important is the fact that the Anthropic Principle is not in conflict with the Copernican Principle, i.e. while the latter claims that we are not in a privileged position in time or space, that does not imply that our position is not special in any way; it is perhaps best described as unrepresentative or biased (e.g. [81, 82]). See [83] for a historical overview of the Anthropic Principle.

  20. ‘Does the idea that “all that can exist, exists” in the ensemble context provide an explanation for the anthropic puzzles? Yes it does do so. The issue of fine-tuning is the statement that the biophilic set of universes is a very small subset of the set of possible universes; but if all that can exist exists then there are universe models occupying this biophilic subspace.’ That is one of the conclusions of [84], who provide an interesting survey of the topic of Multiverses in physical cosmology. To be sure, Ellis has also been critical of the Multiverse (e.g. [57]), but usually with respect to the question as to whether it is a testable hypothesis, rather than a good explanation for observations.

  21. The explanation is an interesting one: Weinberg assumed that the naïve particle-physics prediction of an extremely large cosmological constant is correct, and that there is in addition a “bare” cosmological constant with a negative value which almost but not quite cancels the particle-physics vacuum-energy contribution, the value of the resulting effective cosmological constant being selected according to the Anthropic Principle.

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Acknowledgements

An earlier version of this work was presented at the conference Cosmology 2018 in Dubrovnik (https://indico.cern.ch/event/736594/). This research has made use of NASA’s Astrophysics Data System Bibliographic Services.

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    Phillip Helbig

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Appendix: Several Types of Confusion

Appendix: Several Types of Confusion

The blog post by [16] is a real-world example (from social media, but that is where some influential discussion takes place, some of which shows up in the refereed literature) and also illustrates many of the types of confusion which I address in this paper, but is confusing for other reasons as well. (One which I don’t hold against her is that by \(\varOmega\) she means, in my notation above, \(\varOmega +\lambda\). Both conventions are common.) Her ‘curvature density parameter’ is apparently \(\varOmega -1\) (‘its value today is smaller than 0.1 or so’; actually, current observations suggest that it is smaller than 0.01 in absolute value, but with unknown sign) but by ‘curvature density’ many will assume that she means \(\varOmega\) (‘at early times should have been close to 1’), but the only consistent reading is that she means that \(|\varOmega -1|\) should be close to 1 in the early Universe. She claims to have ‘no idea’ why ‘cosmologists ...think a likely value for the curvature parameter at early times should have been close to 1’. I have no idea where she got the idea that cosmologists believe that. If we are concerned with the classical flatness problem, then assuming FRW model, we can calculate what \(\varOmega\) was in the early Universe, and indeed it was very close to 1, hence \(|\varOmega -1|\) was close to zero. The debate about the flatness problem hinges around whether such a small value of \(|\varOmega -1|\) in the early Universe is somehow unexpected. However, the typical formulation is not that \(|\varOmega -1|\) should be \(\approx 0\), but rather that it could be anything. (She rightly complains that, with respect to the flatness problem, ‘so many of them tell a story that is nonsense’ and ‘keep teaching it to students, print it in textbooks, and repeat it in popular science books’, but does so herself, just with a different wrong story.) It then becomes clear that she thinks that the assumption (which it is not) that \(\varOmega\) was very close to 1 in the early Universe is something akin to particle-physics naturalness: ‘Numbers close to 1 are good. Small or large numbers are bad’. That is a classic example of confusing two different types of fine-tuning. She even makes the confusion explicit: ‘Therefore, cosmologists and high-energy physicists believe that numbers close to 1 are more likely initial conditions. It’s like a bizarre cult that you’re not allowed to question.’ That is certainly not the case in cosmology, even among those who get the flatness problem wrong. To be sure, the flatness problem is the idea that \(\varOmega -1=0\) to very high accuracy in the early Universe is unlikely, but not because of the perceived likelihood that \(|\varOmega -1|\approx 1\) in the early Universe. While the classical flatness problem is bogus (e.g. [10,11,12,13] and references therein), and hence inflation is not needed to solve the flatness problem as the latter is usually understood (which does not mean that inflation cannot have happened), it is still legitimate to question, as she does, whether the cure of inflation is worse than the disease in that, in order to work, it requires more improbable initial conditions than the improbable conditions it is trying to explain (e.g. [105]). However, for some reason Hossenfelder thinks that Penrose’s initial condition is \(|\varOmega -1|\approx 1\). Furthermore, she presents a completely wrong-headed characterization of inflation, namely that it is just ‘pulling exponential factors out of thin air’ while it would make more sense to ‘put them into the probability distribution instead’. The whole point of inflation in connection with the flatness problem is that it makes the Universe flat today regardless of the initial conditions. She seems to think that the assumption that \(|\varOmega -1|\approx 1\) is necessary because inflation reduces it by ‘I dunno, 100 or so orders of magnitude’ and hence would not work if the initial value of \(|\varOmega -1|\) were ‘some very large value, say \(10^{60}\)’. Actually, however, no-one claims to know the number of e-foldings produced by inflation, and that is essentially a free parameter of the theory. Whether that is good or bad is beside the point, but the assumption that \(|\varOmega -1|\approx 1\) in the early Universe is needed in order for inflation to work is wrong. Indeed, most who believe that inflation solves the flatness problem probably do think that the initial value was \(10^{60}\) or something. Ironically, later in the post she actually mentions the correct explanation: ‘you should look for a mechanism that explains the initial probability distribution and not a dynamical mechanism to change the uniform distribution later’, which is an important part of the solution of the flatness problem-or, rather, the realization that it does not exist (e.g. [10,11,12,13] and references therein), and, of course, completely different from her ‘initial value that’s constrained by observation and that’s really all there is to say about it’, i.e. things are as the are because they were as they were, which explains nothing. For values which are not special, that is usually sufficient, but not for special values. She makes a similar mistake [106] by claiming that matter–antimatter asymmetry needs no explanation since allegedly the problem exists only because ‘physicists think that ...the number 1.0000000000 is prettier than 1.0000000001’.

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Helbig, P. Life, the Multiverse, and Fine-Tuning. Found Phys 53, 93 (2023). https://doi.org/10.1007/s10701-023-00732-8

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