# Newtonian Cosmology and Evolution of κ-Deformed Universe

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Kappa Deformed Space-Time

#### 2.1. $\phi $-realization

#### 2.2. $\alpha $, $\beta $, and $\gamma $-realization

## 3. Modified Friedmann Equations from Newtonian Dynamics

#### 3.1. $\phi $-realization

#### 3.2. $\alpha $, $\beta $ and $\gamma $-realization

## 4. Non-Commutative Corrections to Scale Factor

#### 4.1. For $\phi $-realization

#### 4.1.1. Radiation $(\gamma =\frac{4}{3})$

#### 4.1.2. Dust $(\gamma =1)$

#### 4.1.3. Vacuum $(\gamma =0)$

#### 4.2. For $\alpha $, $\beta $ and $\gamma $-realization

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | Using $\phi ={e}^{-A}={e}^{a{p}_{0}}$, from Equation (2), we find $\widehat{R}=\sqrt{{\widehat{x}}_{i}{\widehat{x}}^{i}}=\sqrt{{x}_{i}{x}^{i}(1+2a{p}_{0})}=R(1+a{p}_{0})$ and, hence, $-\frac{GMm}{\widehat{R}}=-\frac{GMm}{R}(1-a{p}_{0})+O\left({a}^{2}\right)$. |

2 | Note that in Section 2 and Section 3, we have used $\gamma $ for representations of one particular realization of non-commutative functions (See Equations (9)–()). However, using $\gamma =1+\alpha $, we have replaced $\gamma $ in favor of $\alpha $. Thus, from now on, we use $\gamma $ representing a constant in Equation (33). |

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Harikumar, E.; Sreekumar, H.; Panja, S.K.
Newtonian Cosmology and Evolution of *κ*-Deformed Universe. *Universe* **2023**, *9*, 343.
https://doi.org/10.3390/universe9070343

**AMA Style**

Harikumar E, Sreekumar H, Panja SK.
Newtonian Cosmology and Evolution of *κ*-Deformed Universe. *Universe*. 2023; 9(7):343.
https://doi.org/10.3390/universe9070343

**Chicago/Turabian Style**

Harikumar, E., Harsha Sreekumar, and Suman Kumar Panja.
2023. "Newtonian Cosmology and Evolution of *κ*-Deformed Universe" *Universe* 9, no. 7: 343.
https://doi.org/10.3390/universe9070343