How Far Could Light Travel by the Time of Decoupling in an Expanding Universe?

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SUMMARY

The discussion centers on calculating the distance light could travel by the time of decoupling in an expanding universe, specifically when the universe was 1/1000 of its current size. Participants highlight the importance of the scale factor in a radiation-dominated universe, emphasizing that light travels a distance of cdt modified by the scale factor, expressed as dr = cdt/a(t). The confusion arises from reconciling this with the simpler equation provided in the textbook, which states that the distance light has traveled equals c x t.

PREREQUISITES
  • Understanding of cosmological principles, specifically the concept of decoupling.
  • Familiarity with the scale factor in cosmology, particularly in a radiation-dominated universe.
  • Knowledge of the speed of light and its implications in a Newtonian framework.
  • Basic grasp of differential equations as they apply to cosmological models.
NEXT STEPS
  • Study the implications of the scale factor in cosmological models, focusing on radiation-dominated universes.
  • Explore the derivation of the light travel distance in expanding universes using general relativity.
  • Investigate the differences between Newtonian and relativistic treatments of light propagation in cosmology.
  • Review the concept of decoupling and its significance in the evolution of the universe.
USEFUL FOR

Astronomy students, cosmologists, and physicists interested in the dynamics of the early universe and the behavior of light in expanding space.

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Homework Statement



At the time of decoupling the universe was 1/1000 of its present size. How for could light have traveled in the time up to decoupling? (assume that the universe was dominated by radiation until then)


Homework Equations





The Attempt at a Solution


I'm a little confused about how to include the fact that the universe was expanding while the light was traveling up to the time of decoupling.

I have the age of the universe at decoupling(calculated earlier) and I have calculated the scale factor as a function of time for a radiation dominated universe. I assume that the scale factor means that light travels less distance with time as distance is expanding but I'm not sure about this...and how would I calculate this distance?
 
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Here's a hint: light travels a distance of cdt in a Newtonian world, but there's a scale factor, so dr=cdt/a(t).
 
the equation given above is right but according to the book's answer the distance light has traveled is equal to simple [c x t]
 

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