# Cosmology and Matter-Induced Branes

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## Abstract

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## 1. Introduction

## 2. The Extra Dimensions

#### 2.1. From D Dimensions to 4 Dimensions: General Remark

#### 2.2. The Planck Mass and the Extra Space Structure

#### 2.2.1. Kaluza–Klein Model

#### 2.2.2. Hyperbolic Extra Dimensions

#### 2.2.3. f(R) Theories

#### 2.2.4. Brane Models

#### 2.3. Brane as a Clump of Matter?

## 3. Matter-Induced Branes

#### 3.1. Matter Distribution within Extra Space

#### 3.2. Matter-Induced Branes and Variation of 4-Dimensional Physical Parameters

## 4. Fine-Tuning of the Lambda Term and Matter-Induced Branes

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Dependence of the 2-dimensional extra space radii $r(\theta )$ on the azimuthal angle $\theta $: The parameter values are $a=-100;b=1;c=-2.1\xb7{10}^{-3};m=0.01;and{m}_{D}=1$. Additional conditions: ${R}_{\pi}=0.00458$, and ${\varphi}_{\pi}$ varies continuously within the interval $(0\xf72.28)$. Several points of this interval are taken: ${\varphi}_{\pi}=0.57nandn=0,1,2,3,4$. The more matter is placed in the extra space, the more metric deviates from the sphere $r(\theta )=const$.

**Figure 2.**Dependence of the $\Lambda $-term (arbitrary units): see (47) on the discrete set of the additional conditions ${\varphi}_{i}(\theta =\pi ),\phantom{\rule{1.em}{0ex}}i=1,\dots ,5$. Each point relates to the specific curve in Figure 1. The cosmological constant varies from negative to positive values. At the same time, their set has the cardinality of the continuum. Therefore, we sure can find such additional conditions for which the $\Lambda $-term is arbitrary close to zero.

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Rubin, S.G.
Cosmology and Matter-Induced Branes. *Symmetry* **2020**, *12*, 45.
https://doi.org/10.3390/sym12010045

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Rubin SG.
Cosmology and Matter-Induced Branes. *Symmetry*. 2020; 12(1):45.
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Rubin, Sergey G.
2020. "Cosmology and Matter-Induced Branes" *Symmetry* 12, no. 1: 45.
https://doi.org/10.3390/sym12010045