We look up to an expanse of sky that is billions of light-years in size, but the universe may be far larger than what we are able to see. Subtle clues are beginning to reveal some of the properties of the regions of space hidden beyond our cosmic horizon. Our world appears to be only a small part of a “multiverse,” an expanse vastly larger than the visible universe, and for the most part completely different from it.

To account for what we do see, cosmologists invented a theory many years ago called “inflation,” in which a brief, ultra-accelerated expansion of the early universe stretched space to a size far greater than what we observe. Inflation explains why, despite the violence of the big bang, the universe appears to us uniform and smooth, and the theory has made predictions confirmed by measurements of subtle variations in the radiation left over from the big bang. But inflation does not really make the universe more uniform — just huge. If inflation is correct, then the billions of light-years that our telescopes probe are a mere dot on a far vaster canvas.

The multiverse comprises a large number of distinct patches, each far bigger than our night sky. What observers see, therefore, also depends on where they find themselves. Most of the regions in the multiverse are inhospitable to life, and their properties will not be observed.

Because extra dimensions need not be tied up the same way everywhere, physical laws may vary from place to place. Inflation makes each “legal district” much larger than the visible universe, giving us the illusion that particles and forces are the same everywhere. But beyond our cosmic horizon, inflation allows the universe to grow so enormous that it contains every set of possible laws that can be constructed from string theory. Eight years ago, Joe Polchinski and I estimated that the number of possibilities is truly enormous: a one with roughly 500 zeros behind it (10^500).

We compute trivariate probability distributions in the landscape, scanning simultaneously over the cosmological constant, the primordial density contrast, and spatial curvature. We consider two different measures for regulating the divergences of eternal in ation, and three different models for observers. In one model, observers are assumed to arise in proportion to the entropy produced by stars; in the others, they arise at a xed time (5 or 10 billion years) after star formation. The star formation rate, which underlies all our observer models, depends sensitively on the three scanning parameters. We employ a recently developed model of star formation in the multiverse, a considerable re nement over previous treatments of the astrophysical and cosmological properties of di erent pocket universes. For each combination of observer model and measure, we display all single and bivariate probability distributions, both with the remaining parameter(s) held xed, and marginalized. Our results depend only weakly on the observer model but more strongly on the measure. Using the causal diamond measure, the observed parameter values (or bounds) lie within the central 2 of nearly all probability distributions we compute, and always within 3 . This success is encouraging and rather nontrivial, considering the large size and dimension of the parameter space. The causal patch measure gives similar results as long as curvature is negligible. If curvature dominates, the causal patch leads to a novel runaway: it prefers a negative value of the cosmological constant, with the smallest magnitude available in the landscape.

There is a deep cosmological mystery: although dependent on very different underlying physics, the time scales of structure formation, of galaxy cooling (both radiatively and against the CMB), and of vacuum domination do not differ by many orders of magnitude, but are all comparable to the present age of the universe. By scanning four landscape parameters simultaneously, we show that this quadruple coincidence is resolved. We assume only that the statistical distribution of parameter values in the multiverse grows towards certain catastrophic boundaries we identify, across which there are drastic regime changes. We find order-of-magnitude predictions for the cosmological constant, the primordial density contrast, the temperature at matter-radiation equality, the typical galaxy mass, and the age of the universe, in terms of the fine structure constant and the electron, proton and Planck masses. Our approach permits a systematic evaluation of measure proposals; with the causal patch measure, we find no runaway of the primordial density contrast and the cosmological constant to large values.

FURTHER READING

130 papers on Arxiv related to Multiverse

Drake equation for the multiverse (6 page pdf)

How many universes are in the multiverse (Stanford, 12 page pdf)

We argue that the total number of distinguishable locally Friedmann universes generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by e^{e^{3 N}}, where N is the number of e-folds of slow-roll post-eternal inflation. For simplest models of chaotic inflation, N is approximately equal to de Sitter entropy at the end of eternal inflation; it can be exponentially large. However, not all of these universes can be observed by a local observer. In the presence of a cosmological constant Lambda the number of distinguishable universes is bounded by e^{|Lambda|^{-3/4}}. In the context of the string theory landscape, the overall number of different universes is expected to be exponentially greater than the total number of vacua in the landscape. We discuss the possibility that the strongest constraint on the number of distinguishable universes may be related not to the properties of the multiverse but to the properties of observers.

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