There are untested but suggestive speculations in the string theory (which in itself is not what one would call a sound physical model), and most models of the universe being significantly larger than some 10^15 light years in whichever direction are also speculative. Certainly there are no indication of a size large enough to duplicate our corner of it in any kind of detail.
Space is big. It is very, very big. On the currently most favored cosmological theories, we are living in an infinite world, a world that contains an infinite number of planets, stars, galaxies, and black holes. This is an implication of most “multiverse theories”, according to which our universe is just one in a vast ensemble of physically real universes. But it is also a consequence of the standard Big Bang cosmology, if combined with the assumption that our universe is open or flat, as recent evidence suggests it is. An open or flat universe – assuming the simplest topology[1] – is spatially infinite at any time and contains infinitely many planets etc.[2] [...]
[1] I.e. that space is simply connected. There is a recent burst of interest in the possibility that our universe might be multiply connected, in which case it could be both finite and hyperbolic. A multiply connected space could lead to a telltale pattern consisting of a superposition of multiple images of the night sky seen at varying distances from Earth (roughly, one image for each lap around the universe that the light has traveled). Such a pattern has not been found, although the search continues. For an introduction to multiply connected topologies in cosmology, see M. Lachièze-Rey and J.-P. Luminet, J.-P., “Cosmic Topology,” Physics Reports, 254(3) (1995): 135-214.
[2] A widespread misconception is that the open universe in the standard Big Bang model becomes spatially infinite only in the temporal limit. The observable universe is finite, but only a small part of the whole is observable (by us). One fallacious intuition that might be responsible for this misconception is that the universe came into existence at some spatial point in the Big Bang. A better way of picturing things is to imagine space as an infinite rubber sheet, and gravitationally bound groupings (such as stars and galaxies) as buttons glued on to it. As we move forward in time, the sheet is stretched in all directions so that the separation between the buttons increases. Going backwards in time, we imagine the buttons coming closer together until, at “time zero”, the density of the (still spatially infinite) universe becomes infinite everywhere. See e.g. J. L. Martin, General Relativity (London: Prentice Hall, 1995).
How large is space? Observationally, the lower bound
has grown dramatically (Figure 2) with no indication of
an upper bound. We all accept the existence of things
that we cannot see but could see if we moved or waited,
like ships beyond the horizon. Objects beyond cosmic
horizon have similar status, since the observable universe
grows by a light-year every year as light from further
away has time to reach us. Since we are all taught about
simple Euclidean space in school, it can therefore be difficult to imagine how space could not be infinite—for
what would lie beyond the sign saying “SPACE ENDS
HERE—MIND THE GAP”? Yet Einstein’s theory of
gravity allows space to be finite by being differently connected
than Euclidean space, say with the topology of
a four-dimensional sphere or a doughnut so that traveling
far in one direction could bring you back from the
opposite direction. The cosmic microwave background
allows sensitive tests of such finite models, but has so
far produced no support for them -
flat infinite models fit the data fine and strong limits have been placed on
both spatial curvature and multiply connected topologies.
In addition, a spatially infinite universe is a generic
prediction of the cosmological theory of inflation (Garriga
& Vilenkin 2001b). The striking successes of inflation
listed below therefore lend further support to the
idea that space is after all simple and infinite just as we
learned in school.
How uniform is the matter distribution on large scales?
In an “island universe” model where space is infinite but
all the matter is confined to a finite region, almost all
members of the Level I multiverse would be dead, consisting
of nothing but empty space. Such models have
been popular historically, originally with the island being
Earth and the celestial objects visible to the naked
eye, and in the early 20th century with the island being
the known part of the Milky Way Galaxy. Another nonuniform
alternative is a fractal universe, where the matter
distribution is self-similar and all coherent structures
in the cosmic galaxy distribution are merely a small part
of even larger coherent structures. The island and fractal
universe models have both been demolished by recent observations
as reviewed in Tegmark (2002). Maps of the
three-dimensional galaxy distribution have shown that
the spectacular large-scale structure observed (galaxy
groups, clusters, superclusters, etc.) gives way to dull
uniformity on large scales, with no coherent structures
larger than about 10^24m. More quantitatively, imagine
placing a sphere of radius R at various random locations,
measuring how much mass M is enclosed each time, and
computing the variation between the measurements as
quantied by their standard deviation M. The relative
fluctuations M/M have been measured to be of order
unity on the scale R ~ 3 X 10^23m, and dropping on larger
scales. The Sloan Digital Sky Survey has found M/M
as small as 1% on the scale R ~ 10^25m and cosmic microwave
background measurements have established that
the trend towards uniformity continues all the way out to
the edge of our observable universe (R ~ 10^27m), where
M/M ~ 10^(-5). Barring conspiracy theories where the
universe is designed to fool us, the observations thus
speak loud and clear: space as we know it continues far
beyond the edge of our observable universe, teeming with
galaxies, stars and planets.
Though those papers are from 2002 and 2003 - have the theories in question been disproven since then? If so, I’d be curious to read about it.
It is accepted that the Universe is likely much bigger than what is visible. There are no indications that it is infinite or even large enough to ensure the Big Worlds-type recurrence. My point is that your decision of whether to sign up for cryonics now should not depend on whether the universe is 10^10 (not big enough for recurrence) or 10^10^10 times larger than what we can presently see.
Big World theories are derived from existing theories of mainstream physics, which are not generally considered untestable.
You are using the world “derived” rather loosely.
There are untested but suggestive speculations in the string theory (which in itself is not what one would call a sound physical model), and most models of the universe being significantly larger than some 10^15 light years in whichever direction are also speculative. Certainly there are no indication of a size large enough to duplicate our corner of it in any kind of detail.
Hmm. I was under the impression that Big World theories would be relatively accepted. At least Bostrom and Tegmark seem to argue as if they were:
Self-Locating Belief in Big Worlds: Cosmology’s Missing Link to Observation (Bostrom 2002):
Parallel Universes (Tegmark 2003):
Though those papers are from 2002 and 2003 - have the theories in question been disproven since then? If so, I’d be curious to read about it.
It is accepted that the Universe is likely much bigger than what is visible. There are no indications that it is infinite or even large enough to ensure the Big Worlds-type recurrence. My point is that your decision of whether to sign up for cryonics now should not depend on whether the universe is 10^10 (not big enough for recurrence) or 10^10^10 times larger than what we can presently see.