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Buzz Bloom
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I have been puzzled about the possible interaction mechanisms among the various particles during inflation that would have performed the mixing of mass-energy (ME) required for the uniformity of the CBR. Here is my understanding about what must happen to acheve the necessary mixing of ME during inflation.
At the time when inflation starts, say ts, let Ds be the length of the diameter then of the space that now is our observable universe. Let A and B the pair of points at opposite ends of an arbitrary diameter. The distance between A and B is Ds. Assume two regions of space of the same size, one surrounding A and one surrounding B, say RA and RB respectively, have MEs respectively EA and EB. Assume EA has significantly greater ME than significantly greater than EB.
To solve the horizon problem, during inflation, (1/2) (EA - EB) of ME must move from RA to RB.
It seems to me unreasonable to assume that the ME movement from the RA to RB happens by means of particles moving directly from RA to RB without interacting with any particles along the way. The question then arises: what is the expected mean free path (MFP) of these particles. As the universe expands, the MFP will of course also increase. So, the path of ME from RA to RB will require a number of particle interations along the way, say on the average Navg. (An estimate of Navg would have to be calculated taking the expansion of the universe into account.)
It seems reasonable that the path ME travels would be a random walk. In a non-expanding space, the effective speed of a random walk would proportional to the square-root of the number of steps: √Navg. Therefore, if particles move at speed c (with an adjustment for the expansion) , the effective speed of ME moving from A to B would be c/√Navg, (similarly adjusted).
Can anyone point out a flaw in this random walk concept regarding inflation?
Can anyone suggest a source about inflation that discusses this issue about a random walk?
At the time when inflation starts, say ts, let Ds be the length of the diameter then of the space that now is our observable universe. Let A and B the pair of points at opposite ends of an arbitrary diameter. The distance between A and B is Ds. Assume two regions of space of the same size, one surrounding A and one surrounding B, say RA and RB respectively, have MEs respectively EA and EB. Assume EA has significantly greater ME than significantly greater than EB.
To solve the horizon problem, during inflation, (1/2) (EA - EB) of ME must move from RA to RB.
It seems to me unreasonable to assume that the ME movement from the RA to RB happens by means of particles moving directly from RA to RB without interacting with any particles along the way. The question then arises: what is the expected mean free path (MFP) of these particles. As the universe expands, the MFP will of course also increase. So, the path of ME from RA to RB will require a number of particle interations along the way, say on the average Navg. (An estimate of Navg would have to be calculated taking the expansion of the universe into account.)
It seems reasonable that the path ME travels would be a random walk. In a non-expanding space, the effective speed of a random walk would proportional to the square-root of the number of steps: √Navg. Therefore, if particles move at speed c (with an adjustment for the expansion) , the effective speed of ME moving from A to B would be c/√Navg, (similarly adjusted).
Can anyone point out a flaw in this random walk concept regarding inflation?
Can anyone suggest a source about inflation that discusses this issue about a random walk?