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

In summary, the question asks how far light could have traveled during the time of decoupling when the universe was dominated by radiation and was 1/1000 of its present size. The answer involves calculating the distance light travels based on the age of the universe at decoupling and the scale factor for a radiation dominated universe. The equation for this distance is dr=cdt/a(t). However, according to the book's answer, the distance traveled by light is simply [c x t], where t is the age of the universe at decoupling.
  • #1
Cheetox
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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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  • #2
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).
 
  • #3
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]
 

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

What is the concept of "Cosmology Time of Decoupling"?

The "Cosmology Time of Decoupling" refers to a period in the history of the universe when photons and matter became decoupled, meaning they were no longer tightly bound together. This occurred approximately 380,000 years after the Big Bang and marks the transition from the opaque, hot plasma state of the early universe to the transparent, cooler state it is in now.

What caused the "Cosmology Time of Decoupling"?

The main cause of the "Cosmology Time of Decoupling" is the expansion of the universe. As the universe expanded and cooled, the photons and matter that were tightly bound together were able to separate and move more freely, resulting in the decoupling.

Why is the "Cosmology Time of Decoupling" important?

The "Cosmology Time of Decoupling" is important because it marks a significant event in the history of the universe. It allowed light to travel freely without being absorbed by matter, resulting in the universe becoming transparent. This also allowed the first atoms to form, leading to the creation of structure and eventually the formation of stars and galaxies.

How is the "Cosmology Time of Decoupling" related to the Cosmic Microwave Background (CMB) radiation?

The "Cosmology Time of Decoupling" is closely related to the Cosmic Microwave Background (CMB) radiation. The CMB is the leftover thermal radiation from the early universe, which was emitted at the "Cosmology Time of Decoupling" when photons and matter decoupled. This radiation is an important source of information about the early stages of the universe.

How do scientists study the "Cosmology Time of Decoupling"?

Scientists study the "Cosmology Time of Decoupling" through various methods such as analyzing the CMB, studying the light from distant galaxies, and using computer simulations. By studying the properties of the CMB and the large-scale structure of the universe, scientists can determine the timing and events that occurred during the "Cosmology Time of Decoupling" and gain a better understanding of the early universe.

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