## 1. Introduction: Some (Observational) Facts about Dark Matter

## 2. Mass and Symmetries

- negative curvature $-{\varkappa}_{\mathrm{dS}}=-H/c=-\sqrt{{\mathrm{\Lambda}}_{\mathrm{dS}}/3}$
- positive curvature ${\varkappa}_{\mathrm{AdS}}=\sqrt{|{\mathrm{\Lambda}}_{\mathrm{AdS}}|/3}$

## 3. Minkowskian Content of dS and AdS Elementary Systems: The Garidi Mass

## 4. Dark Matter as a Relic AdS Curvature Energy?

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

## 5. Discussion

...it is amusing to notice that, in the Newton Universe ${N}_{-}$, resulting from $c\to \infty $ contraction of AdS, the kinetic energy of the elementary system on the quantum level, that is,

is quantized, which is not surprising in view of the “compactness” of the corresponding universe. The oscillator levels have a separation $\delta {E}_{\mathrm{kin}}^{{N}_{-}}\approx \hslash {\tau}^{-1}$ in agreement with the uncertainty principle, since τ may be thought of as the “lifetime” of this oscillating universe.

## Funding

## Conflicts of Interest

## References

- Planck Collaboration. Planck 2018 results XIII. Cosmological parameters. arXiv
**2018**, arXiv:1807.06209v1. [Google Scholar] - Baudis, L. The Search for Dark Matter. Eur. Rev.
**2017**, 26, 70–81. [Google Scholar] [CrossRef] - Behroozi, P.S.; Wechsler, R.H.; Conroy, C. The average star formation histories in dark matter halos from z = 0– 8. Astrophys. J.
**2013**, 770, 57. [Google Scholar] [CrossRef] - Van Dokkum, P.; Danieli, S.; Cohen, Y.; Merritt, A.; Romanowsky, A.J.; Abraham, R.; Brodie, J.; Conroy, C.; Lokhorst, D.; Mowla, L.; et al. A galaxy lacking dark matter. Nat. Lett.
**2018**, 555, 629–632. [Google Scholar] [CrossRef] - van Dokkum, P.; Danieli, S.; Cohen, Y.; Romanowsky, A.J.; Conroy, C. The Distance of the Dark Matter Deficient Galaxy NGC 1052DF2. Astrophys. J. Lett.
**2018**, 864, L18. [Google Scholar] [CrossRef] - van Dokkum, P.; Danieli, S.; Abraham, R.; Conroy, C.; Romanowsky, A.J. A Second Galaxy Missing Dark Matter in the NGC 1052 Group. Astrophys. J. Lett.
**2019**, 874, L5. [Google Scholar] - Pasechnik, R.; Šumbera, M. Phenomenological Review on Quark-Gluon Plasma: Concepts vs. Observations. Universe
**2017**, 3, 7. [Google Scholar] [CrossRef] - Newton, T.D.; Wigner, E.P. Localized States for Elementary Systems. Rev. Mod. Phys.
**1949**, 21, 400–406. [Google Scholar] [CrossRef] - Wigner, E.P. On Unitary Representations of the Inhomogeneous Lorentz Group. Ann. Math.
**1939**, 40, 149–204. [Google Scholar] [CrossRef] - Bacry, H.; Lévy-Leblond, J.-M. Possible Kinematics. J. Math. Phys.
**1968**, 9, 1605. [Google Scholar] [CrossRef] - Gürsey, F. Introduction to the de Sitter group. In Group Theoretical Concepts and Methods in Elementary Particle Physics; Gordon and Breach Science Publishers, Inc.: New York, NY, USA, 1964. [Google Scholar]
- Fronsdal, C. Elementary particles in a curved space. Rev. Mod. Phys.
**1965**, 37, 221–224. [Google Scholar] [CrossRef] - Carroll, S.M.; Press, W.H.; Turner, E.L. The Cosmological Constant. Ann. Rev. Astron. Astrophys.
**1992**, 30, 499–542. [Google Scholar] [CrossRef] - Dixmier, J. Représentations intégrables du groupe de De Sitter. Bull. Soc. Math. Fr.
**1961**, 89, 9–41. [Google Scholar] [CrossRef] - Takahashi, R. Sur les représentations unitaires des groupes de Lorentz généralisés. Bull. Soc. Math. Fr.
**1963**, 91, 289–433. [Google Scholar] [CrossRef] - Evans, N.T. Discrete series for the universal covering group of the 3 + 2 de Sitter group. J. Math. Phys.
**1967**, 8, 170–184. [Google Scholar] [CrossRef] - Barut, A.O.; Böhm, A. Reduction of a class of O(4,2) representations with respect to SO(4,1) and SO(3,2). J. Math. Phys.
**1970**, 11, 2938–2945. [Google Scholar] [CrossRef] - Fronsdal, C. Elementary particles in a curved space. II. Phys. Rev. D
**1974**, 10, 589–598. [Google Scholar] [CrossRef] - Mizony, M. 3 semigroupes de causalité et formalisme hilbertien de la mécanique quantique. Publ. Dep. Math. Lyon
**1984**, 3B, 47–64. [Google Scholar] - Mickelsson, J.; Niederle, J. Contractions of representations of de Sitter groups. Commun. Math. Phys.
**1972**, 27, 167–180. [Google Scholar] [CrossRef] - Garidi, T.; Huguet, E.; Renaud, J. de Sitter waves and the zero curvature limit. Phys. Rev. D
**2003**, 67, 124028. [Google Scholar] - Bros, J.; Gazeau, J.-P.; Moschella, U. Quantum Field Theory in the de Sitter Universe. Phys. Rev. Lett.
**1994**, 73, 1746. [Google Scholar] [CrossRef] - Garidi, T. What Is Mass in de Sitterian Physics? arXiv
**2003**, arXiv:hep-th/0309104. [Google Scholar] - Dooley, A.H.; Rice, J.W. On contractions of semisimple Lie groups. Trans. Am. Math. Soc.
**1985**, 289, 185–202. [Google Scholar] [CrossRef] - Gazeau, J.-P.; Novello, M. The question of mass in (anti-) de Sitter spacetimes. J. Phys. A Math. Theor.
**2008**, 41, 304008. [Google Scholar] [CrossRef] - Gazeau, J.-P.; Novello, M. The Nature of Λ and the Mass of the Graviton: A Critical View. Int. J. Mod. Phys. A
**2011**, 26, 3697–3720. [Google Scholar] [CrossRef] - Gazeau, J.-P.; Renaud, J. Relativistic harmonic oscillator and space curvature. Phys. Lett. A
**1993**, 179, 67. [Google Scholar] [CrossRef] - Andronic, A.; Braun-Munzinger, P.; Redlich, K.; Stachel, J. Decoding the phase structure of QCD via particle production at high energy. Nature
**2018**. [Google Scholar] [CrossRef]

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