Umh, like we're still under construction... and stuff...

Is it possible that the world around us is butt a manifestation of set theoretic null? An argument is presented for the creation of a universe based on a zero-energy closed system and the Freidman solution of the Einstein equations.

Three independent cosmological observations support the idea that the universe was much smaller and much hotter in the past. Extrapolating to the most distant past leads to extreme spacetime curvature and the breakdown of the classical theory of gravity, Einstein's General Theory of Relativity, and that like sucks and stuff... uh...huh huh huh...

Tyron[2] first suggested, more than twenty five years ago, that the Universe may have arisen from the quantum vacuum. Since that time much work has been done in the areas of quantum field theory, quantum gravity, and quantum cosmology. There is now speculation that the infamous cosmological constant may manifest itself as the energy of the quantum vacuum.

The pursuit of such questions as "the origin of the universe" are known as quantum cosmology. At the heart of quantum cosmology is the issue of applying quantum mechanics (the science of the mircoscopic world) to the Universe as a whole. By definition of Universe there is no outside observer and hence the traditional Copenhagen interpretation of quantum theory no longer holds. Recent work by Gell-Mann and Hartle [3] has led to the ideas of "decoherent histories", in which quantum mechanics assigns probabilities to possible histories of the universe. With this interpretation they show that the Copenhagen interpretation emerges as a limiting case of their more general framework. It is in this context that probabilities will be interpreted in this presentation.

The Decomposition of Spacetime

It is advantagous to decompose the four dimensional structure of spacetime into a form which provides a gauge-invariant formalism. (graphics to be provided showing the (3+1) ADM split). This decompostion leads to the metric form

The Lapse and Shift function

Given two neighboring spacelike surfaces, labeled by t and t+dt, the displacement between a point in the first surface and a point in the second can be decomposed into a displacement in the first surface and another displacement normal to that surface. The infinitesimal separation between events can be written in terms of the lapse function N and shift function Ni as

The lapse function representing the ratio of the proper time interval to the coordinate-time interval between two hypersurfaces Sigma_t and Sigma_t+delta t and the shift function measuring the rate of deviation of a line with constant space-coordinate from a line normal to the Sigma_t hypersurface.

Intrinsic and Extrinsic curvature

Let K represent the the extrinsic curvature of a given hypersurface. The Euclidean action S can then be written as

(to be provided)

Simulations... and stuff...

The following visualizations were created at the National Center for Supercomputing Applications under the aspices of the Grand Challenge Cosmology Consortium.

Creation of a 2D Universe (116Kb mpeg)

The calculation begins roughly one billion years after the big bang, when the universe was denser and more uniform than it is today. In this illustration, a closed two-dimensional universe is represented as the surface of an expanding sphere. The calculation is performed in a patch hundreds of millions of light years on a side, which is large enough to fairly represent the universe as a whole. The calculation follows the growth of initially small matter density fluctuations as the universe expands.

Gas Density 3D evolution (149Kb mpeg)

Here we view the evolution of gas density with cosmic time, or redshift. Just as before, we display the results in a frame which is comoving with the expanding universe. Our volumetric rendering technique displays low density gas as blue and transparent, and high density gas as red and opaque.

Initially, the gas is smoothly distributed. As the density fluctuations grow, we see slender filaments appear, first in short segments, and then in longer strands exceeding one hundred million light years in length. Between the filaments are large quasi-spherical voids of very low density gas. The simulation is stopped at the present epoch so we may compare our results with the real universe. Note that the process of structure formation is ongoing right up to the present day.

The intersection of filaments produces regions of very high gas density, seen here in red, which are the sites for galaxy formation. Although galaxy formation is not included in this simulation, the spatial distribution of these high density peaks matches the observed galaxy cluster distribution quite well.


  1. P.J.E.Pebbles, "Principles of Physical Cosmology", 70-196, (Princeton University Press 1993)

  2. E.P.Tyron, "Is the Universe a quantum fluctuation?", Nature (London) 246, 396-397 (1973).

  3. M. Gell-Mann and J.B.Hartle, "Quantum Mechanics in the light of quantum cosmology"e; in Complexity, Entropy, and the Physics of Information, Santa Fe Institute Studies in the Sciences of Complexity, edited by W. Zurek(Addison-Wesley, Reading, 1990), Vol.III.

--Revised August 9, 1997 by