By Paul Preuss, paul_preuss@lbl.gov
and Jon Bashor, jbashor@lbl.gov

The power of supercomputers at the National Energy Research Scientific Computing Center (NERSC) has enabled Julian Borrill of the Department of Energy’s Lawrence Berkeley National Laboratory to model, in striking detail, a possible state of the universe only a hundred billionth of a trillionth of a trillionth of a second (10^-35 second) after the Big Bang.

In 3-D computer movies created by Borrill and his colleague Kevin Campbell, objects called "semilocal strings" condense out of interacting quantum fields to form writhing tubes of energy. Some link with other tubes in space-spanning filaments. Some, like the Worm Ourobouros, join head to tail and devour themselves, ultimately popping out of existence. These images, redolent of alchemy but firmly grounded in theoretical physics, may provide insight into the past and present structure of our universe.

Borrill, a postdoctoral fellow at NERSC, is working with researchers at the Center for Particle Astrophysics at the University of California, Berkeley, to answer fundamental cosmological questions. Among them: if the universe began in equilibrium, why is there now far more matter than antimatter? Why, given its exceedingly smooth beginnings, is the universe so clumpy, on all scales from galaxies to galactic superclusters?

"Given enough time, gravity can do the job of building stars and galaxies and larger structures," says Borrill, "so long as the right sort of initial perturbations occurred in the density of the very early universe. One candidate for causing those perturbations is the semilocal string."

Borrill stresses that semilocal strings are not to be confused with the fundamental entities of string theory, which may give rise to the particles of the subatomic world. Rather they are related to other putative inhabitants of the very early universe, cosmic strings. While cosmic strings are purely a product of the topology of the vacuum, however, semilocal strings involve a complex interplay of quantum matter and force fields.

"Semilocal strings are more complicated," says Borrill. "They are like magnetic tubes with north and south poles. They originate in a four-dimensional vacuum; it takes eight quantum fields to construct them—four matter fields and four force fields."

What traditional cosmic strings and semilocal strings have in common is a link to phase transitions in the early universe. In a way analogous to expanding water vapor, which condenses to liquid water and then freezes to ice, all the disparate forces seen today—electromagnetism, the weak force, the strong force, and gravity—"condensed" from the single, unified force that existed at the moment of the Big Bang. During these phase changes strings could have been generated, and with them the primordial density fluctuations that were the seeds of large-scale structure.

Semilocal strings have theoretical advantages over cosmic strings, however. For one thing, says Borrill, "they could answer the question of why there is more matter than antimatter in the universe. One place to look for the generation of this asymmetry—so-called baryogenesis—is in interactions on the surfaces of these magnetic tubes."

Until Borrill’s recent work on the Cray T3E, however, the strings were too complex to model, much less understand. Previous calculations on workstation computers could handle only a million initial quantum field values, simulating a tiny volume of the universe—far too small to investigate the strings' properties.

"Some people claimed semilocal strings couldn’t form, or if they did, it wouldn’t make a difference," Borrill says. "If only a few formed—if their density was too low—they might just close up on themselves, shrink, and quickly disappear."

The NERSC supercomputer allowed Borrill to specify well over 3 billion initial quantum field values. Once the initial conditions had been set, the Cray was set loose to calculate the evolution of the system.

To interpret the results of the simulations, Borril worked with Kevin Campbell of Berkeley Lab’s Visualization Group, generating 3-D images and movies that enabled them to get a qualitative understanding of the strings' behavior; many of these images and movies are available on the web at http://www.nersc.gov/~borrill/defects/semilocal.html.

"We couldn’t have known what we were going to see," Borrill says. "In fact we proved that semilocal strings can exist—enough strings formed that they tended to join onto their neighbors rather than themselves, so that many of them rapidly grew, and the network of strings as a whole persisted. But I was surprised that there was no intercommuting—where two strings cross each other and swap partners—which is considered a crucial process in the case of cosmic strings."

Having done the initial calculations as a proof of principle, Borrill says, "we can now address more complicated questions," including further studies of baryon formation and of the implications for patterns of fluctuations in the cosmic microwave background radiation—the earliest moment in the history of the universe which can be directly observed.

"It’s a challenge to try to test theories of the early universe when the only observations we can make are billions of years after the fact," says Borrill. "Computers are essential to model the initial conditions and see how they evolve, so we can compare the results with what we can observe. That’s why we need machines like the 512-processor Cray T3E at NERSC." Borrill jokes that the computer-generated strings in his movies are "bigger than the Titanic and a fraction of the cost."

Borril and his colleagues published earlier results on semilocal string formation in Physical Review D, Volume 57, Number 6, 15 March 1998. Recent results have been submitted to Physical Review Letters.

Berkeley Lab is a U.S. Department of Energy national laboratory located in Berkeley, Calif. It conducts unclassified research and is managed by the University of California.