Thursday, June 03, 2010

Larger than our Hubble volume...

Last Lights On - Mandelbrot fractal zoom to 6.066 e228 (2^760) from teamfresh on Vimeo.

However, the CMB is a fairly uniform temperature, and space is quite flat... If one adds a scalar field to GR in such a way that the potential energy is much larger than the kinetic energy, then spacetime responds by growing exponentially. This inflation provides a nice explanation for the uniform temperature of the CMB and the flatness (among other things). The scalar field can then decay at a point and bring inflation to an end, as it did in our region of the multiverse after expanding the scale of the metric by about a factor of e^60. However, generally speaking there will be regions where the scalar field has not yet decayed and inflation is continuing. After each e-fold expansion, the spacetime volume will have grown by a factor of e^3 ~ 20, thus if the probability that the scalar field does not decay is greater than 1/20, then inflation will continue forever - this is eternal inflation. If the e-folding time is the Planck time, which is ~ 5*10^-44 seconds, and there have elapsed ~ 1.37*10^10 * 365 * 24 * 3600 seconds so far in our Hubble volume, then there has been expansion in scale over the multiverse of about e^(8*10^(61)) since the big bang... In fairness however, the video didn't exhaust the Mandelbrot set...

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