Details of the Ekpyrotic Universe theory
A new theory of the very early universe that resolves the famous puzzles of the hot Big Bang picture -- the horizon, flatness and monopole problems -- and that generates fluctuations in energy that seed galaxy formation and produce temperature variations in the cosmic microwave background. The model is based on the idea that our hot Big Bang universe was created from the collision of two three-dimensional worlds moving along a hidden, extra dimension.
The inflationary model of the universe, developed in the 1980's by Alan Guth (MIT), Andre Linde (Stanford), Andreas Albrecht (UC Davis) and Steinhardt, was designed to resolve these very same problems, relying on a period of exponential hyper-expansion, or inflation.
Conceptually, the ekpyrotic model is very different. There is no inflation or rapid change happening at all. The approach to collision takes places very slowly over an exceedingly long period of time. It is quite fascinating that rapid change and very slow change can produce nearly the same effects. The difference results in one distinctive observational prediction, though: Inflationary cosmology predicts a spectrum of gravitational waves that may be detectable in the cosmic microwave background. The ekpyrotic model predicts no gravitational wave effects should be observable in the cosmic microwave background.
In the ekpyrotic model, when the two three-dimensional worlds collide and "stick," the kinetic energy in the collision is converted to the quarks, electrons, photons, etc. that are confined to move along three dimensions. The resulting temperature is finite, so the hot Big Bang phase begins without a singularity. The universe is homogeneous because the collision and initiation of the Big Bang phase occurs nearly simultaneously everywhere.
The energetically preferred geometry for the two worlds is flat, so their collision produces a flat Big Bang universe. According to Einstein's equations, this means that the total energy density of the universe is equal to the critical density. Massive magnetic monopoles, which are over-abundantly produced in the standard Big Bang theory, are not produced at all in this scenario because the temperature after collision is far too small to produce any of these massive particles.
Quantum effects cause the incoming three-dimensional world to ripple along the extra-dimension prior to collision so that the collision occurs in some places at slightly different times than others. By the time the collision is complete, the rippling leads to small variations in temperature, which seed temperature fluctuations in the microwave background and the formation of galaxies. We have shown that the spectrum of energy density fluctuations is scale-invariant (the same amplitude on all scales). The production of a scale-invariant spectrum from hyper-expansion was one of the great triumphs of inflationary theory, and here we have repeated the feat using completely different physics.
The building blocks of the Ekpyrotic theory are derived from Superstring theory. Superstring theory requires extra dimensions for mathematical consistency. In most formulations, 10 dimensions are required. In the mid 1990s, Petr Horava (Rutgers) and Ed Witten (IAS, Princeton) argued that, under certain conditions, an additional dimension opens up over a finite interval. Six dimensions are presumed to be curled up in a microscopic ball, called a Calabi-Yau manifold.
The ball is too small to be noticed in everyday experience, and so our universe appears to be a four-dimensional (three space dimensions and one time dimension) surface embedded in a five-dimensional space-time. This five-dimensional theory, called heterotic M-theory, was formulated by Andre Lukas (Sussex). Ovrut and Dan Waldram (Queen Mary and Westfield College, London). According to Horava-Witten and heterotic M-theory, particles are constrained to move on one of the three-dimensional boundaries on either side of the extra dimensional interval.
Our visible universe would be one of these boundaries; the other boundary and the intervening space would be hidden because particles and light cannot travel across the intervening space. Only gravity is able to couple matter on one boundary to the other sides. In addition, there can exist other three-dimensional hyper-surfaces in the interval, which lie parallel to the outer boundaries and which can carry energy.
These intervening planes are called "branes," short for membranes. The collision that ignites the hot Big Bang phase of the ekpyrotic model occurs when a three-dimensional brane is attracted to and collides into the boundary corresponding to our visible universe.
The term ekpyrosis means "conflagration" in Greek, and refers to an ancient Stoic cosmological model. According to the model, the universe is created in a sudden burst of fire, not unlike the collision between three-dimensional worlds in our model. The current universe evolves from the initial fire. However, in the Stoic notion, the process may repeat itself in the future. This, too, is possible in our scenario in principle if there is more than one brane and, consequently, more than one collision. We plan to discuss this possibility in future work, along with further speculations about what preceded the collision that made our present universe.
As a final remark, we feel that it is important to realize that Inflationary theory is based on Quantum Field theory, a well-established theoretical framework, and the model has been carefully studied and vetted for 20 years. Our proposal is based on unproven ideas in String theory and is brand new. While we appreciate the enthusiasm and interest with which the paper has been received, we would suggest some patience before promulgating these ideas in order to leave time for us to produce some follow-up papers that introduce additional elements and to allow fellow theorists time for criticism and sober judgmen
Contact
Justin Khoury, Princeton; Burt Ovrut, UPenn; Paul Steinhardt, Princeton and Neil Turok, Cambridge):
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