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The Ekpyrotic model is based on the idea that our hot big bang universe was created from the collision of two three-dimensional worlds (branes) moving along a hidden, extra dimension. The two branes then move apart, but after trillions of years will come together again, causing another "Big Bang". It is a neverending cycle. This theory is only 13 years old and was created as an alternative to the standard "inflation" model.
It does not contradict the Big Bang theory, but it does replace the beginnig of it which states there was an infinite temperature and density. Instead, the Ekpyrotic model shows that the universe began in a very cold, static, and nearly vacuous.
The reason why they needed to replace the current inflation theory to the Big Bang was that it did not provide a way for stars, galaxies, and larger structures to arise.
A parallel universe moving along a hidden dimension smaked into ours. The two branes "stick", and the kinetic energy heated our universe, creating a sea of quarks, electrons, protons, photons, and other subatomic particles. The resulting temperature is finite, so the hot big bang phase begins without a singularity.
This collision also imparted microscopic ripples, similar to ocean waves crashing on a shore. These ripples generated tiny fluctuations in temperature and density, the seeds for which all cosmic architecture--from stars to large clusters of galaxies to galactic super clusters--arose.
The Ekpyrotic model allows for a twist on the string theory: the idea of surfaces (or branes) rather than strings.
In this model, our cosmos could have plenty of company. Other would-be universes (also represented as branes) could be floating around in 5th-dimensional space. However, they would remain invisible to us because light particles can't travel through the 5th dimension.