The solution of Olbers' Paradox is:

- The universe is opaque at large scales
- The universe expands
- There is simply not enough starlight in the universe
- Matter is clustered in such a way that the integral brightness converges

The expanding universe is one way to explain Olbers' paradox. The most distance regions are highly red-shifted and do not deliver enough energy to make the night sky infinitely bright, when integrating to infinite distance.

There isn't enough starlight in the universe, as strange as that sounds. But redshift does dim stars that are moving away from us at near-c speeds.

Olbers' Paradox is an interesting problem in cosmology that tries to address the question of why the night sky is dark when there are seemingly an infinite number of stars in the universe. There are several proposed solutions to this paradox, and I'll explain each one.

1. The universe is opaque at large scales: This solution suggests that the universe is not transparent on large scales, meaning that light from distant stars and galaxies gets absorbed or scattered by intervening matter before reaching our telescopes. This would prevent the accumulation of starlight from filling the entire sky and keep it dark.

2. The universe expands: An expanding universe can provide a solution to Olbers' Paradox. As the universe expands, the wavelengths of light from distant stars and galaxies also stretch, causing them to shift towards the red end of the spectrum. This leads to a phenomenon called cosmological redshift, where the energy of the light decreases as it travels through expanding space. Therefore, the light from extremely distant objects becomes so redshifted that it falls below the detectable threshold, making those regions effectively dark.

3. There is simply not enough starlight in the universe: This solution suggests that the total amount of starlight emitted in the universe might be limited. Even though there are an enormous number of stars, they are spread out over vast distances, creating relatively low levels of overall brightness. This explanation suggests that the combined light from all the stars is not enough to fill the entire sky with a uniform level of illumination.

4. Matter is clustered in such a way that the integral brightness converges: This solution builds on the idea that matter in the universe is not uniformly distributed but instead forms clusters, such as galaxies and galaxy clusters. In this scenario, the gravitational forces between the matter cause it to clump together rather than spreading out evenly. As a result, the combined light from distant objects is blocked or masked by the surrounding matter, preventing the sky from being uniformly bright.

These proposed solutions to Olbers' Paradox provide different perspectives on why the night sky is dark. They demonstrate the complexity of the universe and the need to consider various factors when trying to understand observable phenomena.