Light Cones in Flat and Finite Universes

[muccasen]

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

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 into eventually intersect the BB origin.

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.

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.

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.

 

[AndyW]

Thank you for sharing your thoughts on past and future light cones in flat and finite universes. I find your ideas intriguing and would like to offer some insights on this topic.

Firstly, I would like to clarify that the concept of past and future light cones is a fundamental aspect of Einstein's theory of relativity. These cones represent the boundaries of events that can be causally connected to a given point in spacetime. In flat infinite space, the sides of the cones are indeed straight at 45 degrees and their boundary surface is flat. This is because the geometry of flat space is well-defined and does not change over time.

However, in a finite universe with slight positive curvature, the geometry of space is no longer flat and can change over time. This means that the sides of the past and future light cones will not remain straight at 45 degrees throughout the history of the universe. As you correctly pointed out, as we go back in time towards the Big Bang, the sides of the cones will eventually intersect at the origin. This is because the curvature of space will cause the cones to converge towards a single point.

When it comes to the shape of the future light cones, I would like to offer a different perspective. The curvature of space will indeed cause the top surface of the cone to be slightly curved, but this curvature will not necessarily lead to a trumpet shape when all the cones are amalgamated. This is because the curvature of space is not constant and can vary over time. So, while the top surface of individual light cones may be curved, the overall shape of the composite boundary will depend on the specific curvature of space at that point in time.

In terms of the expansion rate of the universe, it is true that the rate of expansion can affect the shape of the future light cones. A faster expansion rate would lead to a more inward tendency of the cone sides, while a slower expansion rate would result in a more trumpet-like shape. However, this does not necessarily mean that the idea of an accelerating universe is wrong. In fact, observations have shown that the expansion of the universe is indeed accelerating due to the presence of dark energy.

In summary, the shape of the past and future light cones in a finite universe with slight positive curvature will not remain constant and will be affected by the changing geometry of space and the expansion rate of the universe. These are complex concepts that require further study and observation to fully understand. Thank