# Exploring Olbers' Paradox in Matt Roots' Introduction to Cosmology

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• alejandromeira
In summary, the conversation discusses Olbers' Paradox and how the total luminosity of stars in a static universe of infinite extent would result in an infinite amount of energy. To calculate this, the author uses the equation B=L/A, where A is the surface area of an average star. However, there is confusion about the use of the variable r, which is used for both the radius of the shell and the radius of the star. It is clarified that A should be the area of a sphere with a radius equal to the distance to the star.

#### alejandromeira

I'm beginning to study the Matt Roots book Introduction to Cosmology and in the section 1.3 Olbers' Paradox he writes:
"If the surface area of an average star is A, then its brightness is B=L/A. The sun may be taken to be such an average star, mainly because we know it so well.
The number of stars in a spherical shell of radius r and thickness dr is then ##4\pi r²ndr##. Their total radiation as observed at the origin of a static universe of infinite extent is then found by integrating the spherical shells from 0 to ##\infty##:"
$$\int_{0}^\infty 4\pi r^2nBdr = \int_{0}^\infty nLdr = \infty$$
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I suppose that he use ##B=\frac{L}{4\pi r^2} ## for obtain the second integral, but r is the radius of the shell not the average radius of the stars. I'm a little bit confused whit that.

Of course if the Universe is infinite and the integration runs from 0 to infinity the total luminosity must be infinity.

My doubt is about the use of r above, in the radius of shell and also the same letter for the radius of a star... and then vanishing...   I'm a little bit confused.

##A## should be the area of a sphere with radius equal to the distance to the star. This is because the energy flux from the star is assumed to be evenly spread over that sphere.

Ok. it is understood. Also just after your answer I was thinking that the energy that we receive from a star a distance r, must be spreaded in a sphere of radius r.
Ok thanks a lot!  Thread solved.

## 1. What is Olbers' Paradox and why is it significant in cosmology?

Olbers' Paradox is a paradox that states that if the universe is infinite, static, and uniformly filled with stars, then the entire night sky should be as bright as the surface of the sun. This paradox is significant in cosmology because it raises questions about the true nature of the universe and the distribution of matter within it.

## 2. How does Matt Roots' Introduction to Cosmology explain Olbers' Paradox?

Matt Roots' Introduction to Cosmology explains Olbers' Paradox by proposing that the universe is not infinite, but rather has a finite size. This means that there is a limit to the number of stars and galaxies that can be observed, and therefore, the night sky is not infinitely bright.

## 3. Can Olbers' Paradox be solved by the expansion of the universe?

Yes, the expansion of the universe can help to explain Olbers' Paradox. As the universe expands, the light from distant stars and galaxies becomes redshifted, making it more difficult to detect. This means that not all of the light from distant objects reaches us, contributing to the darkness of the night sky.

## 4. Are there any other proposed solutions to Olbers' Paradox?

Yes, there are other proposed solutions to Olbers' Paradox. Some scientists suggest that the universe is not uniformly filled with stars and galaxies, and there are voids or gaps in between them. This would explain why the night sky is not as bright as it should be. Others propose that there may be some unknown mechanism that prevents the light from distant objects from reaching us.

## 5. How does Olbers' Paradox relate to the Big Bang Theory?

Olbers' Paradox is closely related to the Big Bang Theory, as it provides evidence for the expansion of the universe. The fact that the night sky is not infinitely bright suggests that the universe is not infinite and has a beginning. This aligns with the idea that the universe began with a big bang and has been expanding ever since.