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Light Cones

  1. Jan 2, 2008 #1
    Past and future light cones in flat infinite space have straight sides at 45 degrees and their boundary surface is flat i.e. if you cut the side of the cone (one straight cut) you could spread it on a flat suface. We can tilt the cone by injecting spatial speed. I have no issue with this :cool:

    However, with a finite universe with slight positive curvature the situation is different. The past light cone has the 45 degrees sides except where the BB is approached. As we draw the cone back into the inflationary period the cone sides are pulled in to eventually intersect the BB origin.:wink:

    Ok now this is the bit that may be controversial. If the ball surface has curvature {the 2d surface of the sphere analogy for our possible universe} then the ultimate forward drawn cone has to be slightly curved on it's top surface. Further if we draw future light cones in a series, say every million years, then the curvature will produce a trumpet shape when all the cones are amalgamated and the composite boundary will no longer be flat (when cut it will not lay flat). Each 45 degree angle from the surface will gradually rotate for each subsequent cone as the top surface increases in size.:uhh:

    However, the universe itself is expanding. Possibly the expansion rate will match the cone such that the trumpet shape cannot develop as the proportion of the universe 2d surface, as a percentage of the whole, neither increases nor decreases. In this case the flat sides remain. A fast expansion would mean an inward tendency to future light cone sides. A slowing expansion would take us back to the trumpet shape.:frown:

    Ok maybe I have got something silly wrong in this but if not then,
    Flat space would indicate a constant expansion rate and the idea that things are speeding up would be wrong. Lol I suspect a few leapes too far.:blushing:
  2. jcsd
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