# CPT Symmetry in Two-Fold de Sitter Universe

^{1}

^{2}

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^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Archaic Universe as a Non-local Hypersphere

_{0}~ 10

^{−23}s plays the role of the fundamental time interval (chronon), so ${T}_{c}$ is equal to approximately ${10}^{13}$ °K.

_{0}≤ cθ

_{0}, which is valid in the “pre-big bang” era, if one puts cθ

_{0}= 2πR one has p

^{0}x

_{0}≤ 2πp

^{0}R, i.e., Σ ≤ 2πFR/c. Thus, one obtains:

_{0}such that for x

_{0}/c>θ

_{0}the free energy of the pre-vacuum can be converted into real interactions between real elementary particles. The interval θ

_{0}can be identified with the time required for light to travel the classic radius of the electron (≈10

^{−23}s); it identifies the particle scale, that is, the scale on which matter appears granular because it is made up of micro-events of interaction between “elementary particles”.

## 3. Hemispheres in the Pre-Big Bang Epoch

`and`$\left[\mathit{C}\mathit{P}\mathit{T}\right]{\mathit{b}}_{0}\left(\mathit{k},\mathit{h}\right){\left[\mathit{C}\mathit{P}\mathit{T}\right]}^{-1}=-{\mathit{a}}_{0}\left(\mathit{k},-\mathit{h}\right)$. This implies that the corresponding vacuum defined by ${\mathit{a}}_{0}|{0}_{0}\rangle ={\mathit{b}}_{0}|{0}_{0}\rangle $ is CPT invariant: $\mathit{C}\mathit{P}\mathit{T}|{0}_{0}\rangle =|{0}_{0}\rangle $. In the Boyle, Finn and Turok model, among the continuous family of invariant vacua defined by a real SO(2) rotation of $\left({\mathit{a}}_{\mathit{\eta}}\left(\mathit{k},\mathit{h}\right),{\mathit{b}}_{\mathit{\eta}}^{+}\left(-\mathit{k},\mathit{h}\right)\right)$ through an angle $\mathit{\eta}$ satisfying $\mathit{\eta}\left(\mathit{k}\right)=-\mathit{\eta}\left(-\mathit{k}\right)$, the vacuum $|{0}_{0}\rangle $, which minimizes the Hamiltonian in the asymptotic +/− regions regarding the solutions in the far future and in the far past respectively, is preferred.

## 4. CPT Symmetry and Majorana Neutrinos

## 5. Perspectives: Micro and Macro CPT

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Fiscaletti, D.; Licata, I.; Tamburini, F.
CPT Symmetry in Two-Fold de Sitter Universe. *Symmetry* **2021**, *13*, 375.
https://doi.org/10.3390/sym13030375

**AMA Style**

Fiscaletti D, Licata I, Tamburini F.
CPT Symmetry in Two-Fold de Sitter Universe. *Symmetry*. 2021; 13(3):375.
https://doi.org/10.3390/sym13030375

**Chicago/Turabian Style**

Fiscaletti, Davide, Ignazio Licata, and Fabrizio Tamburini.
2021. "CPT Symmetry in Two-Fold de Sitter Universe" *Symmetry* 13, no. 3: 375.
https://doi.org/10.3390/sym13030375