The Start and Finish of the Universe
The present standard model of cosmology tells us that the universe started with an initial singularity that produced the Big Bang, then expanded and cooled off enough to permit the formation of particles, atoms, molecules, stars, planets, and galaxies, and that it will expand at an accelerating rate until matter becomes so diffuse that all such structure will come to an end, leaving the universe a dark, empty, boring place forever that will ultimately contain only a thin veneer of photons and leptons. However, this is not the only story that fits the observable facts, and two recent works in the field of cosmology have explored some interesting alternative scenarios of the past and future of the universe.
Alexander Vilenkin’s group at Tufts University has considered three alternatives to the standard model for how the universe began, all hypothesizing that the universe has been in existence forever. These are: (1) a universe undergoing eternal expansion, (2) a universe undergoing infinite repeating cycles, and (3) an “emergent” universe that had existed for an infinite time in the past as a small static clump before expanding into the present universe. Let’s take these one at a time.
The standard model describes the present universe as a number of isolated regions, each in thermal equilibrium, all embedded in a continually expanding background of underlying space-time. The boundaries of the isolated regions (one of which we call our universe) expand into the background at nearly the speed of light, but the space-time expansion itself is even faster, so that the regions never touch, collide, or merge. It is not possible to send a signal from one of the regions to another, once they are isolated by the expansion. This picture appears to apply today, and (barring a Big Rip, see below) into the infinite future. This raises the question of whether the eternal expansion can be extended backwards, into the infinite past.
Vilenkin’s group has examined this question and has made a few mild and very plausible assumptions about it. From these they have proved mathematically that extension to negative infinity is “incomplete” and that somewhere in the past there must be a singularity that starts the expansion. Thus, even in this seemingly eternal scenario, the universe must have had a beginning.
One version of the cyclic scenario, the “clapping branes” model of Steinhardt and Turok, was the subject of my column in the November 2002 issue of Analog. Basically, the idea is that two parallel extra-dimensional “branes” from superstring theory, one of which is our universe, periodically separate and then collide, with each “clap” creating conditions that closely resemble the immediate aftermath of the Big Bang. The resulting universe would be consistent with all of our observational details about the cosmos, from primordial nucleosynthesis, the cosmic microwave background, galaxy formation, etc, with one important exception. The large amount of energy that the standard model predicts should present in the form of primordial gravitational waves from the Big Bang would be absent in the Steinhardt/Turok brane-clapping universe, and the details of the polarization of the cosmic microwave background would also be slightly different. However, since we have not yet been able to observe either the fine structure of the CMB polarization or any gravitational waves, the Steinhardt/Turok model cannot (yet) be ruled out.
Vilenkin’s group has studied the class of recycling universe scenarios, of which the Steinhardt/Turok model is a leading example. They conclude that such models also cannot be extrapolated into the infinite past. Again, somewhere in the past there must be a singularity that starts the clapping brane process, and that represents a beginning point in time.
The third scenario, the emergent universe or “cosmic egg” model, depicts the universe as existing in a small dormant state back into the infinite past, until some random fluctuation “hatches” the cosmic egg and the Big Bang commences. Vilenkin’s group has shown the same mathematical logic applies to this model, and that it cannot be extrapolated backwards into the infinite past. The “egg” would have to begin with some singularity that brought it into existence.
The bottom line from these considerations is that, even in scenarios that seem to extend into the infinite past, there must be some starting point. The two-way time-symmetry of a creation scenario that extends into both the infinite past and the infinite future has been ruled out. The universe must have a starting point. If that is the case, the standard model’s singularity that started the Big Bang would seem to me to be as good a choice for a starting point as any other.
So if the universe is required to have a start, what about its finish? Can it go on for an infinite time, as the current standard model of cosmology seems to imply? A recent paper by Li, Wang, Huang, Zhang, and Li (here abbreviated LWHZL) working at five academic institutions in China examined this question by considering the action of dark energy. Recent observations of Type 1a supernovas and of the detailed structure of the cosmic microwave background radiation are now conventionally interpreted as showing that about 74% of the mass-energy in our universe is in the form of dark energy. Dark energy is related to Einstein’s cosmological constant as a form of energy intrinsic to space itself, which increases when a volume of space increases due to cosmological expansion. The dominance of dark energy in the universe produces a repulsive pressure that drives the observed accelerating expansion of the universe.
As described in my column “The Big Rip at the End of Time” in the March 2005 issue of Analog, despite settling on a standard model, there is not universal consensus among the theorists working in general relativity and cosmology about just what the equation of state of the universe is and how the density of dark energy is related to the size and accelerated expansion of the universe. In particular, the equation of state parameter w, a dimensionless number representing the pressure produced by dark energy divided by its density, assumed by Einstein to have a constant value of –1, could be time-dependent and/or could have other values that might lead to disastrous and spectacular consequences for the fate of the universe. In particular, for values of w more negative than –1, the repulsion of dark energy will grow as the universe expands until its force is large enough to rip apart the galaxy, unbind the Solar System, detach the Moon, explode the Sun and the Earth, dissociate atoms, and rip apart nuclei.
For estimating w there is relevant information from astrophysical observations: Type 1a supernovas, the cosmic microwave background, the Sloan Digital Sky Survey data, and the Hubble Space Telescope estimates of the value of the Hubble constant. These can lead to estimates of the value of w in the present era and in eras in the past. However, the information content of such data is capable of determining no more than two independent parameters, so various two-parameter models have been proposed by cosmologists. The technique for using such models is to separate the available observational data into “bins,” i.e., groups characteristic of a particular range of values for the red-shift factor z, and attempt to determine if w is constant with z or is changing in a particular way. LWHZL criticizes several other two-parameter models for characterizing w as containing unacceptable divergences, and they focus on the divergence-free model given by the equation: w(z) = w0 + wa[ln(2+z)/(1+z) – ln(2)], where ln is a natural logarithm and w0 and wa are the two parameters to be determined from the data. LWHZL then fits the available data with this model, and they extract the parameter values: w0 = –1.0862+0.4689–0.2993 and wa = – 0.0567+ 13.8399–2.2345. Here the plus and minus errors represent possible excursions in the reported value that fall within one standard deviation of the central value.
The quintessence model of Steinhardt is disfavored by this analysis. It indicates that while the parameter values consistent with Einstein’s cosmological constant model (w0 = –1, wa = 0) fall just within the 68.3% confidence limits of the analysis, the best fit to the data is obtained around w0 = –1.09 and wa = –0.06, i.e., w is slightly more negative than –1 and its negativity is increasing as the universe expands. These parameter values, if taken seriously, would imply that our universe is doomed, and that in particular it is in for a Big Rip in times to come.
LWHZL then calculates just when the arrival of the Big Rip of doomsday is likely to occur. Fore Einstein’s values, the universe would last forever, but for their best-fit values, the Big Rip would come about 103.5 billion years in the future. The soonest it might come, using the values at the “fast” edge of the 95.4% confidence limit, would be about 16.7 billion years.
Writers of SF may be interested in just what occurs when this doomsday comes, as our world and our universe are ripped apart by the repulsive effects of the growing dark energy. About 33 million years before the end in the final stages of the Big Rip, our Milky Way galaxy comes apart. About two months before the end, the Solar system becomes unbound and the planets detach from the Sun and go their separate ways. About five days before the end, the Moon leaves its orbit around the Earth. About 28 minutes before the end the Sun becomes gravitationally unbound and explodes. At 16 minutes before the end the Earth also explodes. At 3 x 10?-17 seconds before the end, all the electrons come loose from their atoms and chemistry ends. Just a bit later nuclei come apart into clouds of neutrons and protons, and a bit later still the neutrons and protons come apart into quarks.
You wouldn’t want to stay around for that.
So there you have it. Recent work in cosmology indicates that our universe must have had a definite starting point, and may have a well-defined ending point. Nothing is forever, not even universes.
Copyright © 2012 John G. Cramer
AV Columns Online: Electronic reprints of over 160 “The Alternate View” columns by John G. Cramer, previously published in Analog, are available online at: http://www.npl. washington.edu/av.
The Start of the Universe:
“Did the universe have a beginning?” Audrey Mithani and Alexander Vilenkin, 20 April, 2012, arXiv 1204.4658v1 [hep-th].
The Finish of the Universe:
“Dark Energy and the Fate of the Universe,” X-D Li, S. Wang, Q-G Huang, X. Zhang, and M. Li, 24 April, 2012, arXiv 1202.4060v2 [astro-ph.CO].