# Entropy of the Universe and Hierarchical Dark Matter

## Abstract

**:**

## 1. Introduction

## 2. Entropy

- SMBHs ∼${10}^{103}$;
- Photons ∼${10}^{88}$;
- Neutrinos ∼${10}^{88}$;
- Baryons ∼${10}^{80}$.

**first clue**. From the point of view of entropy, the Universe would be only infinitesimally changed if everything except the SMBHs were removed. This suggests more generally that black holes totally dominate the entropy, as we shall find in the following.

**second clue**about dark matter. It suggests that the plasma of electrons and protons prior to recombination is in excellent thermal equilibrium, and hence the matter sector was in thermal equilibrium for the first 300,000 years. This, combined with the thermal isolation mentioned already, underwrites the use of entropy and the second law during this period.

**third clue**, the final one about dark matter, lies in the holographic principle [7], which provides, as an upper limit on the entropy of the visible universe, the area of its surface in units of the Planck length. Given its present co-moving radius of 44 Gly, this requires $S/k\le {10}^{123}$. The entropy of the contents which is so bounded might nevertheless tend to approach [8] a limit that is many orders of magnitude higher than the total entropy in the limited inventory listed above.

## 3. Second Law

## 4. Primordial Black Holes

## 5. Microlensing

## 6. Cosmic Infrared Background

## 7. Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

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Frampton, P.H.
Entropy of the Universe and Hierarchical Dark Matter. *Entropy* **2022**, *24*, 1171.
https://doi.org/10.3390/e24081171

**AMA Style**

Frampton PH.
Entropy of the Universe and Hierarchical Dark Matter. *Entropy*. 2022; 24(8):1171.
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**Chicago/Turabian Style**

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2022. "Entropy of the Universe and Hierarchical Dark Matter" *Entropy* 24, no. 8: 1171.
https://doi.org/10.3390/e24081171