B Particle Horizon & Coformal Time Near c - Observer Effects

Chris Miller
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The effect of relativity on particle horizon, coformal time and Hubble expansion.
How would an observer's particle horizon and coformal time be affected by her traveling at very near c (relative to the CMB), both in and opposite the direction of travel (ahead and behind)? Also, how would Hubble expansion be impacted in her frame of reference? (I apologize in advance for misconceptions and inaccuracies in my question.)
 
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Is there any particular reason you put this as a B level question?
 
I don't consider my understanding of relativity or cosmology to be beyond that.
 
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